Intuitionistic Fuzzy Programming Technique to Solve Multi- Objective Transportation Problem

This paper presents an explanation of the multi-objective-transportation problem (MOTP) via Fuzzy programming algorithm and the goods is to be transported from origin to destination. The time and cost of transportation from origin i to destination j were recorded. Here we-have considered MOTP with-intuitionistic fuzzy numbers and completed the problem in both ways. Therefore, the optimal compromise solution will remain same both the exponential and linear membership function. For the solution the membership functions are used for such a problem. LINDO statistical-software was used in the present facts analysis and is completed in two stages

Soft Computing

Soft computing is used where a complex problem is not adequately specified for the use of conventional math and computer techniques. Soft computing has numerous real-world applications in domestic, commercial and industrial situations. This book elaborates on the most recent applications in various fields of engineering

Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

Soft Computing

Soft computing is used where a complex problem is not adequately specified for the use of conventional math and computer techniques. Soft computing has numerous real-world applications in domestic, commercial and industrial situations. This book elaborates on the most recent applications in various fields of engineering

A Multi Objective Programming Approach to Solve Integer Valued Neutrosophic Shortest Path Problems

Neutrosophic (NS) set hypothesis gives another way to deal with the vulnerabilities of the shortest path problems (SPP). Several researchers have worked on fuzzy shortest path problem (FSPP) in a fuzzy graph with vulnerability data and completely different applications in real world eventualities. However, the uncertainty related to the inconsistent information and indeterminate information isn't properly expressed by fuzzy set. The neutrosophic set deals these forms of uncertainty. This paper presents a model for shortest path problem with various arrangements of integer-valued trapezoidal neutrosophic (INVTpNS) and integer-valued triangular neutrosophic (INVTrNS). We characterized this issue as Neutrosophic Shortest way problem (NSSPP). The established linear programming (LP) model solves the classical SPP that consists of crisp parameters

Lexicographic Methods for Fuzzy Linear Programming

Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution methods are still being proposed. Among the existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables for handling inexactness and vagueness in data have experienced a remarkable development in recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is to present an updated review of advances in this particular area. Consequently, the paper briefly examines well-known models and methods for FLP, and expands on methods for fuzzy single- and multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical relevance. For this case, computer codes are provided that can be used to reproduce results presented in the paper and for practical applications. The paper demonstrates that FLP that is focused on lexicographic methods is an active area with promising research lines and practical implications.Spanish Ministry of Economy and CompetitivenessEuropean Union (EU) TIN2017-86647-

Gestão de Recursos Finitos em Empresas

The present work has as goal aiding decision makers, researchers, enterprises and practitioners by developing a proper literature review as a base for comparison among multiple-criteria decision making methods in finite resources management according to each of the most important areas of a business environment. Efficient resource management decision making in companies impacts its value creation capability and, therefore, its competitiveness and ultimate success. The methodology for paper research follows the PRISMA flow diagram, for correct paper filtrations according to the set of criteria stablished in alignment with the thesis goal. The papers included in the study are any that employ multiple-criteria decision making methods in their pure forms, in combination with each other forming hybrids, or in combination with other mathematical techniques for solving decision making problems across five major areas of a company’s body. The five major areas are: (1) Supply Chain Management and Logistics; (2) Environmental Management; (3) Business and Marketing Management; (4) Design, Engineering and Manufacturing Systems; and (5) Human Resources Management. The 204 final papers are presented separated by their corresponding application areas, ordered by number of citations, which is used as a measure of their scientific community relevance. They are also classified by, author, nationality, journal, year, type of research and methods used. All collected data is used for quantitative statistical analysis, with which is possible to collect more in-depth information on the literature research. Focused comments on the main methods are also present in this work, with observations made on the many applications and variations each of them had throughout the articles in the research. The AHP and TOPSIS approaches, either with their fuzzy set variations are by far the most popular methods in the referred applications. However, besides them other 51 MCDM or other mathematical techniques are employed in many different combinations and approaches, bringing a very interesting diversity to the study that is very useful for it to be used as a base for comparison among methods. A total number of 111 journals and authors and co-authors of 41 nationalities are involved in the publications between 2012 and 2018, with more than half of papers coming from either India, Turkey or Iran. Many other results are obtained, bringing the readers different perspectives on the subject. This paper contributes to the body of knowledge with a great and insightful overview on MCDM methods application in aiding in challenges part of a business environment, so that companies can better manage their resources and be more prosperous. It is a vast database that allows many comparisons and evaluations, offering more analysis than the standard literature review articles.O presente trabalho tem como objetivo auxiliar os tomadores de decisão, pesquisadores e profissionais, ao desenvolver uma revisão bibliográfica adequada como base para comparação entre os métodos de decisão multicritério na gestão de recursos finitos de acordo com cada uma das áreas mais importantes de um ambiente de negócios. A tomada eficiente de decisões de gestão de recursos nas empresas afeta sua capacidade de criação de valor e, portanto, sua competitividade e sucesso finais. A metodologia da investigação baseou-se na metodologia PRISMA, para a correta filtração das publicações de acordo com o conjunto de critérios estabelecidos, em alinhamento com o objetivo da tese. Os artigos incluídos no estudo são aqueles que apresentam métodos de decisão com critérios múltiplos em suas formas puras, em combinação uns com os outros ao formar híbridos, ou com outras técnicas matemáticas para resolver problemas em cinco áreas principais das empresas. As cinco áreas são: (1) Gestão da Cadeia de Suprimentos e Logística; (2) Gestão Ambiental; (3) Gestão de Negócios e Marketing; (4) Sistemas de Projeto, Engenharia e Manufatura; e (5) Gestão de Recursos Humanos. Os 204 artigos finais são apresentados de acordo com as áreas de aplicação correspondentes, ordenadas por número de citações, que são usadas como uma medida de sua relevância na comunidade científica. Eles são, ainda, classificados por autor, nacionalidade, revista, ano, tipo de pesquisa e métodos utilizados. Todos os dados coletados são utilizados para análise estatística quantitativa, com a qual é possível recolher informações mais aprofundadas sobre a pesquisa bibliográfica. São realizados comentários sobre os principais métodos e as maneiras que foram apresentados ao longo do estudo de todos os artigos durante a pesquisa. As abordagens AHP e TOPSIS, com suas variações em conjuntos difusos ou fuzzy, são de longe os métodos mais populares nas aplicações referidas. No entanto, além destes, outros 51 MCDM e outras técnicas são utilizadas em muitas combinações e abordagens, trazendo uma diversidade muito interessante para o estudo, servindo de base para comparação dos métodos. Um total de 111 revistas e autores e coautores de 41 nacionalidades estão envolvidos nas publicações entre 2012 e 2018, com mais de metade dos artigos provenientes da Índia, Turquia ou Irão. Estes e outros resultados levam aos leitores diferentes perspectivas sobre o assunto. Este documento contribui para o estado da arte, com um conhecimento geral excelente e perspicaz sobre a aplicação de métodos MCDM para ajudar nos desafios de um ambiente de negócios, para que as empresas possam melhor gerenciar seus recursos e serem mais prósperas. É um vasto banco de dados que permite muitas comparações e avaliações, oferecendo mais análises do que os artigos de revisão de literatura padrão

Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships