In this paper, we introduce the integer programming in neutrosophic environment, by considering coffecients of problem as a triangulare neutrosophic numbers. The degrees of acceptance, indeterminacy and rejection of objectives are simultaneously considered. The Neutrosophic Integer Programming Problem (NIP) is transformed into a crisp programming model, using truth membership (T), indeterminacy membership (I), and falsity membership (F) functions as well as single valued triangular neutrosophic numbers. To measure the efficiency of the (...) model, we solved several numerical examples. (shrink)

The science of operations research is one of the modern sciences that have made a great revolution in all areas of life through the methods provided by it, suitable and appropriate to solve most of the problems that were facing researchers, scholars and those interested in the development of societies, and the most beneficiaries of this science were companies and institutions that are looking for scientific methods that help them manage their work so that they achieve the greatest profit and (...) the lowest cost, and one of the important methods that have been used in the management of companies we offer in this research two methods, Dynamic programming method. This method has been used in many practical matters and helped decision-makers in companies to achieve a maximum profit and less cost by formulating the reality of the state of the company and the data provided by decision-makers with a dynamic mathematical model that is solved using methods of solving dynamic models and we will provide in this research an example of this through the issue of choosing the optimal investment for the budget of a company so that it achieves a maximum profit, and the method of programming with integers: the method that provided these companies with solutions with integer values suitable for the nature of its work, through the use of the binary integer in the formulation of the appropriate mathematical model on the one hand, and on the other hand, the use of the binary integer variable helped to convert some nonlinear models that lead to some practical problems into linear models, and it should be noted here that in the previous two methods there is something indeterminable because we must make a decision in choosing or not choosing something, but the optimal solution that we will get remains A specific value because we are building the mathematical model for any realistic issue through the data provided by those responsible for the work and these data are calculated quantities and therefore they are uncertain values because their validity depends on the circumstances surrounding the work environment, they may be exposed to increase or decrease, and therefore the optimal solution on which the company will base its decision is suitable for specific values and any change in them can cause the company an uncalculated loss, so in this research we will use the concepts of neutrosophic science, the branch of science founded by the American scientist Florentin Smarandache in 1995 based on his belief that there is no absolute truth, a science that is interested in the study of ideas and concepts that are neither true nor false, but just in between, and we will take the data (calculated quantities) neutrosophic values that are specified or unspecified values are any set close to the calculated quantities, then the resulting mathematical model is a neutrosophic model and the optimal solution has neutrosophic values and thanks to the indefinite uncertainty that these values have, companies from the development of appropriate plans for all circumstances and thus achieve the greatest profit and the lowest cost, and we will clarify the above through two issues, the issue of optimal designation of a warehouse site, which we will formulate the mathematical model of using the neutrosophic integer programming method - and the issue of capital budget, which we will present in two different forms, we use in the first form the neutrosophic integer programming method and in the second the neutrosophic dynamic programming method. (shrink)

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to (...) find the optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming. (shrink)

In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method for solving (...) neutrosophic multi-objective programming problem at end of this paper. (shrink)

Operations research science is defined as the science that is concerned with applying scientific methods to complex problems in managing and directing large systems of people, including resources and tools in various fields, private and governmental work, peace and war, politics, administration, economics, planning and implementation in various domains. It uses scientific methods that take the language of mathematics as a basis for it and uses computer, without which it would not have been possible to achieve numerical solutions to the (...) raised problems, those that need correct solutions, when the solutions abound and the options are multiple, so we need a decision based on correct scientific foundations and takes into account all the circumstances and changes that you can encounter the decision-maker during the course of work, and nothing is left to chance or luck, but rather everything that enters into the account and plays its role in decision-making, and we get that when we use the concepts of neutrosophic science to reformulate what the science of operations research presented in terms of methods and methods to solve many practical problems, so we will present in this research a study aimed at shedding light on the most important methods used to solve nonlinear models, which is the Lagrangian multiplier method for nonlinear models constrained by equality and then reformulated using the concepts of neutrosophic science. (shrink)

An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the issue under (...) study is classical data. In this research, we will present a study through, which we present the graphical method for solving Neutrosophical nonlinear models in the following case: A nonlinear programming issue, the objective function is a nonlinear function, and the constraints are linear functions. Note that we can use the same method if (i) the objective function follower is a linear follower and the constraints are nonlinear; (ii) the objective function is a non-linear follower and the constraints are non-linear. In the three cases, the nonlinear models are neutrosophic, and as we know, the mathematical model is a nonlinear model if any of the components of the objective function or the constraints are nonlinear expressions, and the nonlinear expressions may be in both. At the left end of the constraints are neutrosophic values, at least one or all of them. Then, the possible solutions to the neutrosophic nonlinear programming problem are the set of rays that fulfills all the constraints. As for the region of possible solutions, it is the region that contains all the rays that fulfill the constraints. The optimal solution is the beam that fulfills all constraints and at which the function reaches a maximum or minimum value, depending on the nature of the issue under study (noting that it is not necessary to be alone). (shrink)

In this book the notion of semigroups under + is constructed using: the MOD natural neutrosophic integers, or MOD natural neutrosophic-neutrosophic numbers, or MOD natural neutrosophic finite complex modulo integer, or MOD natural neutrosophic dual number integers, or MOD natural neutrosophic special dual like number, or MOD natural neutrosophic special quasi dual numbers.

In this paper, we have developed an Excel package to be utilized for calculating neutrosophic data and analyze them. The use of object oriented programming techniques and concepts as they may apply to the design and development a new framework to implement neutrosophic data operations, the c# programming language, NET Framework and Microsoft Visual Studio are used to implement the neutrosophic classes. We have used Excel as it is a powerful tool that is widely accepted (...) and used for statistical analysis. Figure 1 shows Class Diagram of the implemented package. Figure 2 presents a working example of the package interface calculating the complement. Our implemented Neutrosophic package can calculate Intersection, Union, and Complement of the neutrosophic set. Figure 3 presents our neutrosophic package capability to draw figures of presented neutrosophic set. Figure 4 presents charting of Union operation calculation, and figure 5 Intersection Operation. neutrosophic set are characterized by its efficiency as it takes into consideration the three data items: True, Intermediate, and False. -/- . (shrink)

India dropped its target of 500 GW of renewable energy capacity fossil fuel sources by 2030. Its responsibilities the United Nations Framework Convention Climate Change [UNFCCC],and reducing radiations by one billion tonnes by the end of the decade at the COP26 conference, held in Glasgow in November 2022. Researchers are continually searching for inexhaustible and reasonable energy sources. Solar energy is one of the greenest sources of energy and is also one of the cleanest. The most important factor in using (...) solar energy is the location of the solar power plant. The main objective of this study is to find the best location for a new solar power plant in a specific region called Bundelkhand region of Uttar Pradesh in India. Here we offer an extension of ELECTRE III method as two-phase Pythagorean neutrosophic elimination and choice translating reality PN-ELECTRE-III) method to adapt with fuzzy, ambiguous, unsure, and indeterminate criteria. The Pythagorean neutrosophic numbers [PNNs] used by the group decision support system of PN-ELECTRE III to measure performance of the alternatives. The options are entirely outclassed in the subsequent stage in view of the past stage's evaluations of them. By defining PNN we describe the technique of indifference threshold functions, preference treshold and veto threshold functions, which provide a more stable basis to drop outranking relations. By calculating the concordance credibility, discordance credibility and net credibility degrees of each alternative, the ranking module of the PN-ELECTRE III approach is made simpler. In order to confirm the applicability of the strategy suggested in this paper, the location selection problem for solar plants is finaly solved. (shrink)

One purpose of cognitive diagnostic model is designed to make inferences about unobserved latent classes based on observed item responses. A heuristic for test construction based on the CDM information index proposed by Henson and Douglas has a far-reaching impact, but there are still many shortcomings. He and other researchers had also proposed new methods to improve or overcome the inherent shortcomings of the CDI test assembly method. In this study, one test assembly method of maximizing the minimum inter-class distance (...) is proposed by using mixed-integer linear programming, which aims to overcome the shortcomings that the CDI method is limited to summarize the discriminating power of each item into a single CDI index while neglecting the discriminating power for each pair of latent classes. The simulation results show that compared with the CDI test assembly and random test assembly, the new test assembly method performs well and has the highest accuracy rate in terms of pattern and attributes correct classification rates. Although the accuracy rate of the new method is not very high under item constraints, it is still higher than the CDI test assembly with the same constraints. (shrink)

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the (...) practical and scientific issues that we face in our daily lives, and we need careful study to enable us to avoid losses. For this, the linear programming method was used, which is one of the research methods. Processes, where the problem data is converted into a linear mathematical model for which the optimal solution achieves the desired goal. Since these models are linear models, we can solve them using the direct simplex method and its modifications, but the specificity that these models enjoy has enabled scholars and researchers to find special methods that help us in obtaining the optimal solution. Whatever the method used, the goal is to determine the number of units transferred from any material from production centers to consumption centers, or to allocate a machine or person to do a job so that the cost or time is as short as possible. These issues were addressed according to classical logic, but the ideal solution was a specific value appropriate to the conditions in which the data was collected and does not take into account the changes that may occur in the work environment. In order to obtain results that are more accurate and enjoy a margin of freedom, we present in this book a study of transport issues and neutrosophic allocation issues and some methods for solving them. By neutrosophic issues we mean These are the problems in which the data are neutrosophic values, i.e. the required quantities and the available quantities. (shrink)

In this paper, we propose a new technique for the enhancing images. It will work on removing the noise contained in the image as well as improving its contrast based on three different enhancing transforms, we commence by embedding the image into a neutrosophic domain; where the image will be mapped in three different levels, a level of trueness, a level of falseness and a level of indeterminacy. Hence, we act separately on each level using the enhancement transforms. Finally, (...) we introduce a new analysis in the field of analysis and processing of images using the neutrosophic crisp set theory via Mat lab program where has been obtained three images, which helps in a new analysis to improve and retrieve images. (shrink)

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available (...) resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort. (shrink)

Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph Theory and (...) Algorithms is a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory. (shrink)

In this book, we present a study of linear models and algorithms to find the optimal solution for them using the concepts of neuroscientific science. We know that the linear programming method is one of the important methods of operations research, the science that was the product of the great scientific development that our contemporary world is witnessing. The name operations research is given to the group of scientific methods used. In analyzing problems and searching for optimal solutions, it (...) is a science whose applications have achieved widespread success in various fields of life. What is meant by neutrosophic models are models in which the data are neutrosophic values, that is, variables such as in the objective function, which expresses profit if the model is a maximization model, and expresses a cost if the model is a minimization model, which in turn is affected by environmental conditions. (shrink)

The linear programming method is one of the important methods of operations research that has been used to address many practical issues and provided optimal solutions for many institutions and companies, which helped decision makers make ideal decisions through which companies and institutions achieved maximum profit, but these solutions remain ideal and appropriate in If the conditions surrounding the work environment are stable, because any change in the data provided will affect the optimal solution and to avoid losses and (...) achieve maximum profit, we have, in previous research, reformulated the linear models using the concepts of neutrosophic science, the science that takes into account the instability of conditions and fluctuations in the work environment and leaves nothing to chance. While taking data, neutrosophic values carry some indeterminacy, giving a margin of freedom to decision makers. In another research, we reformulated one of the most important methods used to solve linear models, which is the simplex method, using the concepts of this science, and as a continuation of what we did in the previous two researches, we will reformulate in this research. The graphical method for solving linear models using the concepts of neutrosophics. We will also shed light on a case that is rarely mentioned in most operations research references, which is that when the difference between the number of unknowns and the number of constraints is equal to one, two, or three, we can also find the optimal solution graphically for some linear models. This is done by taking advantage of the conditions of non-negativity that linear models have, and we will explain this through an example in which the difference is equal to two. Also, through examples, we will explain the difference between using classical values and neutrosophic values and the extent of this’s impact on the optimal solution. (shrink)

This book introduces readers to the concept of the neutrosophic set which can deal with dynamic and complex decision-making problems. With the complexity of the socio-economic environment, today's decision-making is one of the most notable ventures, whose mission is to decide the best alternative under numerous known or unknown criteria. This book provides a large amount of theoretical and practical information about the latest research in the field, allowing readers to gain an extensive understanding of both the fundamentals and (...) applications of neutrosophic sets to solve different kinds of decision-making problems and mathematical programming such as medical diagnosis, pattern recognition, construction problems, technology selection etc. (shrink)

Order picking, which is collecting a set of products from different locations in a warehouse, has repeatedly been described as one of the most laborious and time-consuming internal logistic processes. Each order is issued to pick some products located at given locations in the warehouse. In this paper, we consider an order picking problem, in which a number of orders with different delivery due dates are going to be retrieved by a limited number of order pickers in multiperiods such that (...) the total tardiness is minimized. The aim is to determine a retrieval plan in terms of order batching and order picker multitrip routing as decision variables. Besides, products are arrived and replenished at the predetermined locations at different periods. Therefore, products sitting in those locations should be delivered soon to provide empty rooms for replenishment. A mixed integer linear programming formulation is proposed for this new problem. The model is optimally solved for small-size problems. For larger instances, grouping metaheuristic algorithms are proposed based on particle swarm optimization and the league championship algorithm that use group-based operators to generate reasonable batches of orders. Improvement heuristics are designed as well. The performance of the MILP formulation and metaheuristic algorithms is analyzed for different problem instances whose designs are based on real data gathered from an auto parts warehouse. Results indicate that our algorithms can stably solve large instances of the problem in a reasonable time. (shrink)

This book is the fifth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. This volume specifically delves into the concept of Various SuperHyperConcepts, building on the foundational advancements introduced in previous volumes. The series aims to explore the ongoing evolution of uncertain combinatorics through innovative methodologies such as graphization, hyperization, and uncertainization. These approaches integrate and extend core concepts from fuzzy, neutrosophic, soft, and rough (...) set theories, providing robust frameworks to model and analyze the inherent complexity of real-world uncertainties. At the heart of this series lies combinatorics and set theory—cornerstones of mathematics that address the study of counting, arrangements, and the relationships between collections under defined rules. Traditionally, combinatorics has excelled in solving problems involving uncertainty, while advancements in set theory have expanded its scope to include powerful constructs like fuzzy and neutrosophic sets. These advanced sets bring new dimensions to uncertainty modeling by capturing not just binary truth but also indeterminacy and falsity. In this fifth volume, the exploration of Various SuperHyperConcepts provides an innovative lens to address uncertainty, complexity, and hierarchical relationships. It synthesizes key methodologies introduced in earlier volumes, such as hyperization and neutrosophic extensions, while advancing new theories and applications. From pioneering hyperstructures to applications in advanced decision-making, language modeling, and neural networks, this book represents a significant leap forward in uncertain combinatorics and its practical implications across disciplines. -/- The book is structured into 17 chapters, each contributing unique perspectives and advancements in the realm of Various SuperHyperConcepts and their related frameworks: Chapter 1 introduces the concept of Body-Mind-Soul-Spirit Fluidity within psychology and phenomenology, while examining established social science frameworks like PDCA and DMAIC. It extends these frameworks using Neutrosophic Sets, a flexible extension of Fuzzy Sets, to improve their adaptability for mathematical and programming applications. The chapter emphasizes the potential of Neutrosophic theory to address multi-dimensional challenges in social sciences. Chapter 2 delves into the theoretical foundation of Hyperfunctions and their generalizations, such as Hyperrandomness and Hyperdecision-Making. It explores higher-order frameworks like Weak Hyperstructures, Hypergraphs, and Cognitive Hypermaps, aiming to establish their versatility in addressing multi-layered problems and setting a foundation for further studies. Chapter 3 extends traditional decision-making methodologies into HyperDecision-Making and n-SuperHyperDecision-Making. By building on approaches like MCDM and TOPSIS, this chapter develops frameworks capable of addressing complex decision-making scenarios, emphasizing their applicability in dynamic, multi-objective contexts. Chapter 4 explores integrating uncertainty frameworks, including Fuzzy, Neutrosophic, and Plithogenic Sets, into Large Language Models (LLMs). It proposes innovative models like Large Uncertain Language Models and Natural Uncertain Language Processing, integrating hierarchical and generalized structures to advance the handling of uncertainty in linguistic representation and processing. Chapter 5 introduces the Natural n-Superhyper Plithogenic Language by synthesizing natural language, plithogenic frameworks, and superhyperstructures. This innovative construct seeks to address challenges in advanced linguistic and structural modeling, blending attributes of uncertainty, complexity, and hierarchical abstraction. Chapter 6 defines mathematical extensions such as NeutroHyperstructures and AntiHyperstructures using the Neutrosophic Triplet framework. It formalizes structures like neutro-superhyperstructures, advancing classical frameworks into higher-dimensional realms. Chapter 7 explores the extension of Binary Code, Gray Code, and Floorplans through hyperstructures and superhyperstructures. It highlights their iterative and hierarchical applications, demonstrating their adaptability for complex data encoding and geometric arrangement challenges. Chapter 8 investigates the Neutrosophic TwoFold SuperhyperAlgebra, combining classical algebraic operations with neutrosophic components. This chapter expands upon existing algebraic structures like Hyperalgebra and AntiAlgebra, exploring hybrid frameworks for advanced mathematical modeling. Chapter 9 introduces Hyper Z-Numbers and SuperHyper Z-Numbers by extending the traditional Z-Number framework with hyperstructures. These extensions aim to represent uncertain information in more complex and multidimensional contexts. Chapter 10 revisits category theory through the lens of hypercategories and superhypercategories. By incorporating hierarchical and iterative abstractions, this chapter extends the foundational principles of category theory to more complex and layered structures. Chapter 11 formalizes the concept of n-SuperHyperBranch-width and its theoretical properties. By extending hypergraphs into superhypergraphs, the chapter explores recursive structures and their potential for representing intricate hierarchical relationships. Chapter 12 examines superhyperstructures of partitions, integrals, and spaces, proposing a framework for advancing mathematical abstraction. It highlights the potential applications of these generalizations in addressing hierarchical and multi-layered problems. Chapter 13 revisits Rough, HyperRough, and SuperHyperRough Sets, introducing new concepts like Tree-HyperRough Sets. The chapter connects these frameworks to advanced approaches for modeling uncertainty and complex relationships. Chapter 14 explores Plithogenic SuperHyperStructures and their applications in decision-making, control, and neuro systems. By integrating these advanced frameworks, the chapter proposes innovative directions for extending existing systems to handle multi-attribute and contradictory properties. Chapter 15 focuses on superhypergraphs, expanding hypergraph concepts to model complex structural types like arboreal and molecular superhypergraphs. It introduces Generalized n-th Powersets as a unifying framework for broader mathematical applications, while also touching on hyperlanguage processing. Chapter 16 defines NeutroHypergeometry and AntiHypergeometry as extensions of classical geometric structures. Using the Geometric Neutrosophic Triplet, the chapter demonstrates the flexibility of these frameworks in representing multi-dimensional and uncertain relationships. Chapter 17 establishes the theoretical groundwork for SuperHyperGraph Neural Networks and Plithogenic Graph Neural Networks. By integrating advanced graph structures, this chapter opens pathways for applying neural networks to more intricate and uncertain data representations. (shrink)

As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formulaHaving graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules. It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations. In the course of time, slide rules were (...) replaced by pocket calculators and personal computers, but I stuck to my original decision.My computer phobia did not prevent me from taking an interest in the theoretical question: what is a computation? This question goes back to Hilbert's 10th problem, which asks for an algorithm, or computational procedure, to decide whether any given polynomial equation is solvable in integers. It quickly leads to the related question: which numerical functionsf: ℕn→ ℕ are computable?While Hilbert's 10th problem was only resolved in 1970, this related question had some earlier answers, of which I shall single out the following three:f is recursive,f is computable on an abstract machine,f is definable in the untyped λ-calculus.These tentative answers were shown to be equivalent by Church [1936] and Turing [1936–7].I shall discuss here some of the more recent developments of these notions of computability and their relevance to linguistics and logic. I hope to be forgiven for dwelling on some of the work I have been involved with personally, with greater emphasis than is justified by its historical significance. (shrink)

We study a hierarchy of Kalmàr elementary functions on integers based on a classification of LOOP programs of limited complexity, namely those in which the depth of nestings of LOOP commands does not exceed two. It is proved that -place functions in can be enumerated by a single function in , and that the resulting hierarchy of elementary predicates (i.e., functions with 0,1-values) is proper in that there are predicates that are not in . Along the way the rudimentary predicates (...) of Smullyan are classified as. (shrink)

It was Kronecker who sought to avoid the use in mathematics of all numbers other than the positive integers, and he outlined the means for carrying through this program. In the introductory sections of his memoir he briefly indicates the personal philosophy which made such a project appear desirable.

The recent rapid development of information technology, such as sensing technology, communications technology, and database, allows us to use simulation experiments for analyzing serious accidents caused by hazardous chemicals. Due to the toxicity and diffusion of hazardous chemicals, these accidents often lead to not only severe consequences and economic losses, but also traffic jams at the same time. Emergency evacuation after hazardous chemical accidents is an effective means to reduce the loss of life and property and to smoothly resume the (...) transport network as soon as possible. This paper considers the dynamic changes of the hazardous chemicals’ concentration after their leakage and simulates the diffusion process. Based on the characteristics of emergency evacuation of hazardous chemical accidents, we build a mixed-integer programming model and design a heuristic algorithm using network optimization and diffusion simulation. We then verify the validity and feasibility of the algorithm using Jinan, China, as a computational example. In the end, we compare the results from different scenarios to explore the key factors affecting the effectiveness of the evacuation process. (shrink)

A vehicle-commodity matching problem is presented for service providers to reduce the cost of the logistics system. The vehicle classification model is built as a Gaussian mixture model, and the expectation-maximization algorithm is designed to solve the parameter estimation of GMM. A nonlinear mixed-integer programming model is constructed to minimize the total cost of VCMP. The matching process between vehicle and commodity is realized by GMM-EM, as a preprocessing of the solution. The design of the vehicle-commodity matching platform (...) for VCMP is designed to reduce and eliminate the information asymmetry between supply and demand so that the order allocation can work at the right time and the right place and use the optimal solution of vehicle-commodity matching. Furthermore, the numerical experiment of an e-commerce supply chain proves that a hybrid evolutionary algorithm is superior to the traditional method, which provides a decision-making reference for e-commerce VCMP. (shrink)

Disturbance-generated biomass results from endogenous and exogenous natural and cultural disturbances that affect the health and productivity of forest ecosystems. These disturbances can create large quantities of plant biomass on predictable cycles. A systems analysis model has been developed to quantify aspects of system capacities (harvest, transportation, and processing), spatial aspects of the biomass generation process, and deterioration impacts on biomass quality in the various inventory states (field stands, field-harvested inventories, transportation prepared inventories, and production facility inventories). Optimal decision alternatives (...) can be used to guide responses to reclamation, utilization, mitigation, and control. This is particularly advantageous in insect and disease outbreaks, in which the process may last several years, with varying levels of intensity. The prescriptive system description, assuming capacities are fixed, results in a linear programming model. The time-dependent capacity decision model results in a mixed-integer programming model. The analytical model is developed in detail in this analysis. (shrink)

Virtual reality provides an immersive 360-degree viewing experience and has been widely used in many areas. However, the transmission of panoramic video usually places a large demand on bandwidth; thus, it is difficult to ensure a reliable quality of experience under a limited bandwidth. In this paper, we propose a field-of-view prediction methodology based on limited FoV feedback that can fuse the heat map and FoV information to generate a user view. The former is obtained through saliency detection, while the (...) latter is extracted from some user perspectives randomly, and it contains the FoV information of all users. Then, we design a QoE-driven panoramic video streaming system with a client/server architecture, in which the server performs rate adaptation based on the bandwidth and the predicted FoV. We then formulate it as a nonlinear integer programming problem and propose an optimal algorithm that combines the Karush–Kuhn–Tucker conditions with the branch-and-bound method to solve this problem. Finally, we evaluate our system in a simulation environment, and the results show that the system performs better than the baseline. (shrink)

Hybrid renewable energy system arises regularly in real life. By optimizing the capacity and running status of the microgrid, HRES can decrease the running cost and improve the efficiency. Such an optimization problem is generally a constrained mixed-integer programming problem, which is usually solved by linear programming method. However, as more and more devices are added into MG, the mathematical model of HRES refers to nonlinear, in which the traditional method is incapable to solve. To address this (...) issue, we first proposed the mathematical model of an HRES. Then, a coevolutionary multiobjective optimization algorithm, termed CMOEA-c, is proposed to handle the nonlinear part and the constraints. By considering the constraints and the objective values simultaneously, CMOEA-c can easily jump out of the local optimal solution and obtain satisfactory results. Experimental results show that, compared to other state-of-the-art methods, the proposed algorithm is competitive in solving HRES problems. (shrink)

Numbers. Natural numbers -- Integers -- Real numbers -- Irrational and transcendental numbers -- Funny numbers. Zero -- e : the unnatural natural number -- [Phi] : the golden ratio -- i : the imaginary number -- Writing numbers. Roman numerals -- Egyptian fractions -- Continued fractions -- Logic. Mr. Spock is not logical -- Proofs, truth, and trees : oh my! -- Programming with logic -- Temporal reasoning -- Sets. Cantor's diagonalization : infinity isn't just infinity -- Axiomatic (...) set theory : keep the good, dump the bad -- Models : using sets as the LEGOs of the math world -- Transfinite numbers : counting and ordering infinite sets -- Group theory : finding symmetries with sets -- Mechanical math. Finite state machines : simplicity goes far -- The turing machine -- Pathology and the heart of computing -- Calculus : no, not that calculus- [lambda] calculus -- Numbers, booleans, and recursion -- Types, types, types : modeling [lambda] calculus -- The halting problem. (shrink)

Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic of henceforth, next, and until, and to the propositional dynamic logic of regular programs.

Information has usually been defined as one of the properties of substance and a reflection of the substance world. A new perspective is introduced in this paper concerning the nature of information and its role in the cosmos. The five characteristics of information are discussed in the first part of this paper. While the passivity allows information to be transferred, copied, recorded, and displayed, the other four characteristics of information (i.e. initiative, independent, expressive, and holographic) make it the fundamental element (...) of the cosmos, which generates the cosmos, life, consciousness and human culture. Based on the findings of physics and astrophysics, this view is explored more by defining information as a pattern of orders throughout the cosmos, with series of parameters, functions and programs. It is argued that, the cosmos is the existence of process instead of things; the information is reality itself instead of a property of substance; and the substance is one of the forms in which information expresses itself during its evolution. An original framework named “Information Order N” (N is any integer between 0 and 7) is described in the second part of this paper. This scale of information evolution starts from initial information, which is an intrinsic pattern that inhered from maternal universes. The seven orders after that are dimension and superstring, substance and energy, life, consciousness, system of the earth (with a combination of eco-system and human culture), system of the Milky Way Galaxy, system of the cosmos. This “Information Order N” scale unifies substance,life, consciousness, human culture, and everything in the cosmos into one system of information evolution. In another word, the cosmos is information itself. (shrink)

This paper uses neo-Fregean-style abstraction principles to develop the integers from the natural numbers (assuming Hume’s principle), the rational numbers from the integers, and the real numbers from the rationals. The first two are first-order abstractions that treat pairs of numbers: (DIF) INT(a,b)=INT(c,d) ≡ (a+d)=(b+c). (QUOT) Q(m,n)=Q(p,q) ≡ (n=0 & q=0) ∨ (n≠0 & q≠0 & m⋅q=n⋅p). The development of the real numbers is an adaption of the Dedekind program involving “cuts” of rational numbers. Let P be a property (of (...) rational numbers) and r a rational number. Say that r is an upper bound of P, written P≤r, if for any rational number s, if Ps then either s<r or s=r. In other words, P≤r if r is greater than or equal to any rational number that P applies to. Consider the Cut Abstraction Principle: (CP) ∀P∀Q(C(P)=C(Q) ≡ ∀r(P≤r ≡ Q≤r)). In other words, the cut of P is identical to the cut of Q if and only if P and Q share all of their upper bounds. The axioms of second-order real analysis can be derived from (CP), just as the axioms of second-order Peano arithmetic can be derived from Hume’s principle. The paper raises some of the philosophical issues connected with the neo-Fregean program, using the above abstraction principles as case studies. (shrink)

A desirable quality of a coreference resolution system is the ability to handle transitivity constraints, such that even if it places high likelihood on a particular mention being coreferent with each of two other mentions, it will also consider the likelihood of those two mentions being coreferent when making a final assignment. This is exactly the kind of constraint that integer linear programming (ILP) is ideal for, but, surprisingly, previous work applying ILP to coreference resolution has not encoded (...) this type of constraint. We train a coreference classifier over pairs of mentions, and show how to encode this type of constraint on top of the probabilities output from our pairwise classifier to extract the most probable legal entity assignments. We present results on two commonly used datasets which show that enforcement of transitive closure consistently improves performance, including improvements of up to 3.6% using the b3 scorer, and up to 16.5% using cluster f-measure. (shrink)

This paper is about a support information management system for a wind power producer having an energy storage system and participating in a day-ahead electricity market. Energy storage can play not only a leading role in mitigation of the effect of uncertainty faced by a WP producer, but also allow for conversion of wind energy into electric energy to be stored and then released at favourable hours. This storage provides capability for arbitrage, allowing an increase on profit of a WP (...) producer, but must be supported by a convenient problem formulation. The formulation proposed for the support information management system is based on an approach of stochasticity written as a mixed integer linear programming problem. WP and market prices are considered as stochastic processes represented by a set of scenarios. The charging/discharging of the ESS are considered dependent on scenarios of market prices and on scenarios of WP. The effectiveness of the proposed formulation is tested by comparison of case studies using data from the Iberian Electricity Market. The comparison is in favour of the proposed consideration of stochasticity. (shrink)

This paper describes an AFOSR-supported basic research program that focuses on developing a new framework for combining hard with soft data in order to improve space situational awareness. The goal is to provide, in an automatic and near real-time fashion, a ranking of possible threats to blue assets (assets trying to be protected) from red assets (assets with hostile intentions). The approach is based on Conceptual Spaces models, which combine features from traditional associative and symbolic cognitive models. While Conceptual Spaces (...) are revolutionary, they lack an underlying mathematical framework. Several such frameworks have attempted to represent Conceptual Spaces, but by far the most robust is the model developed by Holender. His model utilizes integer linear programming in order to obtain an overall similarity value between observations and concepts that support the formation of hypotheses. This paper will describe a method for building Conceptual Spaces models for threats that utilizes ontologies as a means to provide a clear semantic foundation for this inferencing process; in particular threat ontologies and space domain ontologies are developed and employed in this approach. A space situational awareness use-case is presented involving a kinetic kill scenario and results are shown to assess the performance of this fusion-based inferencing framework. (shrink)

The overall goal of the approach developed in this paper is to estimate the likelihood of a given kinetic kill scenario between hostile spacebased adversaries using the mathematical framework of Complex Conceptual Spaces Single Observation. Conceptual spaces are a cognitive model that provide a method for systematically and automatically mimicking human decision making. For accurate decisions to be made, the fusion of both hard and soft data into a single decision framework is required. This presents several challenges to this data (...) fusion framework. The first is the challenge involved in handling multiple complex terminologies, which is addressed by drawing on a set of Space Domain Ontologies. Another challenge is the complex combinatorics involved when considering all possible feature combinations. This can be mitigated by using integer linear programming optimization that is outlined by the Complex Conceptual Spaces Single Observation mathematical model framework. A third challenge is the complicated physics that is involved in a spacecraft collision that must be addressed to obtain a better understanding of threat assessment. Overcoming these various challenges allows for a quantitative ranking for the potential of a kinetic kill collision across multiple spacecraft pairs. In addition to overcoming these challenges this paper will break down threat assessment into four domains and identify a ranking of threat both for each individual domain and for the four domains combined. Simulation results are shown to verify the developed concepts. (shrink)

We present the first effectively presentable fully abstract model for Starkʼs Reduced ML, a call-by-value higher-order programming language featuring integer-valued references. The model is constructed using techniques of nominal game semantics. Its distinctive feature is the presence of carefully restricted information about the store in plays, combined with conditions concerning the participantsʼ ability to distinguish reference names. We show how it leads to an explicit characterization of program equivalence.

The paper considers two-agent order acceptance scheduling problems with different scheduling criteria. Two agents have a set of jobs to be processed by a single machine. The processing time and due date of each job are known in advance. In the order accepting scheduling problem, jobs are allowed to be rejected. The objective of the problem is to maximize the net revenue while keeping the weighted number of tardy jobs for the second agent within a predetermined value. A mixed-integer (...) linear programming formulation is provided to obtain the optimal solution. The problem is considered as an NP-hard problem. Therefore, MILP can be used to solve small problem instances optimally. To solve the problem instances with realistic size, heuristic and metaheuristic algorithms have been proposed. A heuristic method is used to determine and secure a quick solution while the metaheuristic based on particle swarm optimization is designed to obtain the near-optimal solution. A numerical experiment is piloted and conducted on the benchmark instances that could be obtained from the literature. The performances of the proposed algorithms are tested through numerical experiments. The proposed PSO can obtain the solution within 0.1% of the optimal solution for problem instances up to 60 jobs. The performance of the proposed PSO is found to be significantly better than the performance of the heuristic. (shrink)

Clearing algorithms are at the core of modern payment systems, facilitating the settling of multilateral credit messages with (near) minimum transfers of currency. Traditional clearing procedures use batch processing based on MILP - mixed-integer linear programming algorithms. The MILP approach demands intensive computational resources; moreover, it is also vulnerable to operational risks generated by possible defaults during the inter-batch period. This paper presents TORC3 - the Token-Ring Clearing Algorithm for Currency Circulation. In contrast to the MILP approach, TORC3 (...) is a real time heuristic procedure, demanding modest computational resources, and able to completely shield the clearing operation against the participating agents’ risk of default. (shrink)

Previous work has shown that the Complex Conceptual Spaces − Single Observation Mathematical framework is a useful tool for event characterization. This mathematical framework is developed on the basis of Conceptual Spaces and uses integer linear programming to find the needed similarity values. The work of this paper is focused primarily on space event characterization. In particular, the focus is on the ranking of threats for malicious space events such as a kinetic kill. To make the Conceptual Spaces (...) framework work, the similarity values between the contents of observations on the one hand and the properties of the entities observed on the other needs to be found. This paper shows how to exploit Dempster-Shafer theory to implement a statistical approach for finding these similarities values. This approach will allow a user to identify the uncertainty involved in similarity value data, which can later be propagated through the developed mathematical model in order for the user to know the overall uncertainty in the observation-to-concept mappings needed for space event characterization. (shrink)

Let G V, E be a simple undirected complete graph with vertex and edge sets V and E, respectively. In this paper, we consider the degree-constrained k -minimum spanning tree problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d ≤ k − 2. In particular, in this paper, we consider degree values of d (...) ∈ 2,3. Notice that DC k MST generalizes both the classical degree-constrained and k -minimum spanning tree problems simultaneously. In particular, when d = 2, it reduces to a k -Hamiltonian path problem. Application domains where DC k MST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few. It is easy to see from the literature that the DC k MST problem has not been studied in depth so far. Thus, our main contributions in this paper can be highlighted as follows. We propose three mixed-integer linear programming models for the DC k MST problem and derive for each one an equivalent counterpart by using the handshaking lemma. Then, we further propose ant colony optimization and variable neighborhood search algorithms. Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy. We also propose a pure Q-learning algorithm that is competitive with the ACO ones. Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes. Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively. Moreover, we report better solutions than CPLEX for the large-size instances. Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Philosophic Foundations of Mimetic Theory and Cognitive Science(Including Artificial Intelligence)Jean-Pierre Dupuy (bio)In the mid 1970s I discovered at the same time cognitive science and mimetic theory. Being a philosopher with a scientific background, I immediately brought them together and tried to reconceptualize the latter in terms of the former. In a sense, I haven't stopped doing that in the last 45 years. That is why I feel fully (...) at home with the goals pursued by the organizers of this conference.I do not believe it is feasible or even desirable to operate the rapprochement between the two disciplines at a global level. The history of cognitive science is exceedingly involved, and the part played by artificial intelligence in it compared to the part played by the neurosciences has varied greatly over time.1 Only a piecemeal approach makes sense. I present here four short case studies that cover the whole period, from the beginnings in cybernetics to today's artificial intelligence (AI).In order to better situate these studies within a broader frame, I propose the diagram in Figure 1. To comment on it would require more time than available for my whole presentation. Let me just say the following. [End Page 1]It is essential to distinguish between two kinds of AI. The first to bear this name was launched by economist Herbert Simon and computer scientist Allan Newell at a Dartmouth conference in 1956. It was based on the premise that thinking is computing, with this computation bearing on sentences of a "language of thought" implementable in a digital computer. It turns out that this AI(1) was progressively substituted from the 1980s onward by an AI(2), which, to some extent, was a return to a fundamental result obtained by cybernetics in 1943. Neurophysiologist Warren McCulloch and mathematician Walter Pitts had constructed a mathematical model of a network of elementary calculators called "neurons" and explored its properties. The capacity to "think" was one of these. It was not situated at the elementary level, as was the case in AI(1), but it emerged at the collective level from the interactions between the neurons.This model was heavily criticized by the supporters of AI(1),2 and its first implementations, in the notorious "Perceptron" in particular (1957), were pitiful failures. However, the emergence of "second-order cybernetics" under the guidance of cybernetician Heinz von Foerster and the theory of complex, self-organizing systems that it helped develop, in cooperation and rivalry with similar efforts in the physical sciences, enabled the neural network model to come to a second life under different names: formal neurons, deep learning, big data, and the like. Together, they constitute AI(2).The following network of influences wouldn't have been possible without its stem, that is, the boxes containing the names of Kurt Gödel and Alan Turing. The former revolutionized logic by showing that reasoning about arithmetic and arithmetic are one and the same, insofar as it is possible to code in a 1-to-1 fashion propositions about integers (for instance, "7 is a prime number") by means of integers. The latter demonstrated that some mechanisms can self-transcend inasmuch as they generate an ensemble of outputs that cannot be defined mechanistically. Later, John von Neumann, who is credited along with Alan Turing with having invented the digital computer, would use this logical possibility to define complexity: A mechanism is complex if it is capable of generating one more complex than itself. The gate was open for the theories of complex, self-organizing systems to thrive and, by way of consequence, for AI(2) to emerge.fascination with modelsHerbert Simon (1916–2001), winner of the Nobel Prize in economics for his work on what he called "bounded rationality," is generally considered to be one [End Page 2] Click for larger view View full resolutionFigure 1.of the founders of artificial intelligence. Some cognitive scientists still rely on the computer program that he devised with Alan Newell to simulate the creative processes of human thought—a program aptly named "General Problem Solver." The title of one of his principal works, The Sciences of the... (shrink)

Compared to a charging scheduling and management problem characterized by predetermined trip assignment, this study takes bus and driver scheduling into account, and mealtime windows must be guaranteed as one of the major labor regulations. A discretized mixed-integer linear programming model is developed based on a single electric bus route. We aim to obtain fast and high-quality global solutions for this problem, and the model can be easily executed by bus operators by directly invoking an available optimization solver (...) such as IBM ILOG CPLEX. We test our model on a real round-trip bus route. Numerical experiments show that CPLEX takes approximately 6 sec to obtain an optimal solution. The model can not only reasonably arrange daily trips for each electric bus and driver but also effectively determine the optimal charging schedule and management for an electric bus line. Besides, we analyze the sensitivity of the key parameters in the model. With the increase in the drivers’ maximum workload, the drivers’ average idle time decreases by approximately 11.25%. The objective value decreases by approximately 38.71% and 40.04% with increases in the battery capacity and fleet size, respectively, and the objective value increases by approximately 30.06% with the decrease in the initial battery driving range. In addition, we compare the effectiveness of our time discretization modeling method in solving the same case study to that from other similar studies, and the validity of our method can be verified by the calculation time. We also compare the computational efficiency of CPLEX in solving the same case study problem with and without implementing valid inequalities, and the computational efficiency of the valid inequality method is greatly improved. Finally, through the testing of a multiline network, the potential application of the model to a large-scale traffic network is verified. (shrink)

The phase φ of any wave is determined by the ratio x/λ consisting of the distance x propagated by the wave and its wavelength λ. Hence, the dependence of φ on λ constitutes an analogue system for the mathematical operation of division, that is to obtain the hyperbolic function f(ξ)≡1/ξ. We take advantage of this observation to decompose integers into primes and implement this approach towards factorization of numbers in a multi-path Michelson interferometer. This work is part of a larger (...) program geared towards unraveling the connections between quantum mechanics and number theory. We briefly summarize this aspect. (shrink)

In this article, a mixed integer linear program model is proposed for the production, lot sizing, and scheduling of automotive plastic components to minimize the setup, inventory, stockout, and backorder costs, by taking into account injection molds as the main index to schedule on parallel flexible injection machines. The proposed MILP considers the minimum and maximum inventory capacities and penalizes stockout. A relevant characteristic of the modeled problem is the dependence between mold setups to produce plastic components. The lot (...) sizing and scheduling problem solution results in the assignment of molds to machines during a specific time period and in the calculation of the number of components to be produced, which is often called lot size, following a sequence-dependent setup time. Depending on the machine on which the mold is setup, the number of units to be produced will be distinct because machines differ from one another. The stock coverage, defined in demand days, is also included in the MILP to avoid backorders, which is highly penalized in the automotive supply chain. Added to this, the proposed model is extended by considering setup common operators to respond to and fulfill the constraints that appear in automotive plastic enterprises. In this regard, the MILP presented solves a lot-sizing and scheduling problem, emerged in a second-tier supplier of a real automotive supply chain. Finally, this article validates the MILP by performing experiments with different sized instances, including small, medium, and large. The large-sized dataset is characterized by replicating the amount of data used in the real enterprise, which is the object of this study. The goodness of the model is evaluated with the computational time and the deviation of the obtained results as regards to the optimal solution. (shrink)

If a brain is duplicated so that there are two brains in identical states, are there then two numerically distinct phenomenal experiences or only one? There are two, I argue, and given computationalism, this has implications for what it is to implement a computation. I then consider what happens when a computation is implemented in a system that either uses unreliable components or possesses varying degrees of parallelism. I show that in some of these cases there can be, in a (...) deep and intriguing sense, a fractional (non-integer) number of qualitatively identical phenomenal experiences. This, in turn, has implications for what lessons one should draw from neural replacement scenarios such as Chalmers. (shrink)