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 review of fuzzy AHP methods for decision-making with subjective judgements

Analytic Hierarchy Process (AHP) is a broadly applied multi-criteria decision-making method to determine the weights of criteria and priorities of alternatives in a structured manner based on pairwise comparison. As subjective judgments during comparison might be imprecise, fuzzy sets have been combined with AHP. This is referred to as fuzzy AHP or FAHP. An increasing amount of papers are published which describe different ways to derive the weights/priorities from a fuzzy comparison matrix, but seldomly set out the relative benefits of each approach so that the choice of the approach seems arbitrary. A review of various fuzzy AHP techniques is required to guide both academic and industrial experts to choose suitable techniques for a specific practical context. This paper reviews the literature published since 2008 where fuzzy AHP is applied to decision-making problems in industry, particularly the various selection problems. The techniques are categorised by the four aspects of developing a fuzzy AHP model: (i) representation of the relative importance for pairwise comparison, (ii) aggregation of fuzzy sets for group decisions and weights/priorities, (iii) defuzzification of a fuzzy set to a crisp value for final comparison, and (iv) consistency measurement of the judgements. These techniques are discussed in terms of their underlying principles, origins, strengths and weakness. Summary tables and specification charts are provided to guide the selection of suitable techniques. Tips for building a fuzzy AHP model are also included and six open questions are posed for future work

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

An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights

This article proposes an approach to multiattribute decision making with incomplete attribute weight information where individual assessments are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). By employing a series of optimization models, the proposed approach derives a linear program for determining attribute weights. The weights are subsequently used to synthesize individual IVIFN assessments into an aggregated IVIFN value for each alternative. In order to rank alternatives based on their aggregated IVIFN values, a novel method is developed for comparing two IVIFNs by introducing two new functions: the membership uncertainty index and the hesitation uncertainty index. An illustrative investment decision problem is employed to demonstrate how to apply the proposed procedure and comparative studies are conducted to show its overall consistency with existing approaches

COMPARISON OF THREE FUZZY MCDM METHODS FOR SOLVING THE SUPPLIER SELECTION PROBLEM

The evaluation and selection of an optimal, efficient and reliable supplier is becoming more and more important for companies in today’s logistics and supply chain management. Decision-making in the supplier selection domain, as an essential component of the supply chain management, is a complex process since a wide range of diverse criteria, stakeholders and possible solutions are embedded into this process. This paper shows a fuzzy approach in multi – criteria decision-making (MCDM) process. Criteria weights have been determined by fuzzy SWARA (Step-wise Weight Assessment Ratio Analysis) method. Chosen methods, fuzzy TOPSIS (Technique for the Order Preference by Similarity to Ideal Solution), fuzzy WASPAS (Weighted Aggregated Sum Product Assessment) and fuzzy ARAS (Additive Ratio Assessment) have been used for evaluation and selection of suppliers in the case of procurement of THK Linear motion guide components by the group of specialists in the “Lagerton” company in Serbia. Finally, results obtained using different MCDM approaches were compared in order to help managers to identify appropriate method for supplier selection problem solving

A NEW APPROACH ON SOLVING INTUITIONISTIC FUZZY LINEAR PROGRAMMING PROBLEM

ABSTRACT In this paper, we propose a new approach for solving Intuitionistic Fuzzy Linear Programming Problems (IFLPP) involving triangular intuitionistic fuzzy numbers (TIFN). We introduce a new algorithm for the solution of an Intuitionistic Fuzzy Linear Programming Problem without converting in to one or more classical Linear Programming Problems. Numerical examples are provided to show the efficiency of the proposed algorithm. Keywords: intuitionistic fuzzy set, fuzzy number, triangular intuitionistic fuzzy number, fuzzy linear programming problem. INTRODUCTION Modelling of real life problems involving optimization process. It is often difficult to get crisp and exact information for various parameters affecting the process and it involves high information cost. Furthermore the optimal solution of the problem depends on a limited number of constraints or conditions and thus some of the information collected is not useful. Under such situations it is highly impossible to formulate the mathematical model through the classical traditional methods. Hence in order to reduce information costs and also to construct a real model, the use of intuitionistic fuzzy number is more appropriate. Fuzzy sets are an efficient and reliable tool that allows us to handle such systems having imprecise parameters effectively. Atanossov [6] extended the fuzzy sets to the theory intuitionistic fuzzy sets. His studies emphasized that in view of handling imprecision, vagueness or uncertainty in information both the degree of belonging and degree of non-belonging should be considered as two independent properties as these are not complement of each other. Bellmann and Zade

Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem

During past few decades, fuzzy decision is an important attention in the areas of science, engineering, economic system, business, etc. To solve day-to-day problem, researchers use fuzzy data in transportation problem for presenting the uncontrollable factors; and most of multi-objective transportation problems are solved using goal programming. However, when the problem contains interval-valued data, then the obtained solution was provided by goal programming may not satisfy by all decision-makers. In such condition, we consider a fixed-charge solid transportation problem in multi-objective environment where all the data are intuitionistic fuzzy numbers with membership and non-membership function. The intuitionistic fuzzy transportation problem transforms into interval-valued problem using (α, β)-cut, and thereafter, it reduces into a deterministic problem using accuracy function. Also the optimum value of alternative corresponds to the optimum value of accuracy function. A numerical example is included to illustrate the usefulness of our proposed model. Finally, conclusions and future works with the study are described.Portuguese Foundation for Science and Technology ("FCT-Fundacao para a Ciencia e a Tecnologia"), through the CIDMA-Center for Research and Development in Mathematics and Applications UID/MAT/ 04106/2019Spanish Ministry of Economy and Competitiveness, FEDER funds from the European Union TIN2014-55024-P TIN2017-86647-

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