Investigation on Multi Criteria Decision Making in Fuzzy Environment

Abstract

newline Abstract newlineThe main aim of this thesis is to investigate the multi-criteria decision-making newline(MCDM) problems based on a fuzzy and interval-valued fuzzy environment. The newlineMCDM problem emerges as a powerful framework to address complexities, providing newlinea systematic approach to finding an optimal solution in the presence of newlineuncertainty criteria. The decision-maker may be faced with ambiguity while deciding newlinehow to meet optimality due to the uncertain nature of criterion data. This newlineinspires us to pursue optimality research in a fuzzy environment with pertinent newlineapplications. This study looks into MCDM in a fuzzy environment and how it newlineapply to different applications such as software engineers, suppliers, and material newlineselection, etc. using different MCDM methods. The thesis is structured into newlineseven chapters, each addressing the different aspects of MCDM problems. newlineA brief outline of our contribution in this thesis as follows: newlineIn Chapter 1, we present the fundamental concepts of MCDM problems newlineusing various approaches and relevant research studies. Moreover, the study s newlineinterpretations and basic ideas of fuzzy sets are explained. newlineIn Chapter 2, we solve the MCDM problems using generalized fuzzy technique newlinefor order performance by similarity to ideal-solution (TOPSIS) technique newlineunder the presence of triangular fuzzy numbers (TFNs). This chapter demonstrates newlinethe usefulness of fuzzy TOPSIS using a numerical example and focuses newlineon applying it to decision-making problems. newlineIn Chapter 3, we present the min-max based fuzzy TOPSIS approach for newlinesolving fuzzy MCDM problems. The results of this method are analyzed through newlinea case study on optimal college location selection. Additionally, a comparative newlinestudy is conducted to highlight the differences between the proposed technique newlineand existing methods. newlineIn Chapter 4, we propose a TOPSIS-based method for MCDM problems newlinevi newlinewith unknown criteria weights and interval data. The right endpoint and length newlineare used in place of interval numbers to balance the entropy weight, and a weighting newlinefactor. After that, the TOPSIS approach is used to rank the possibilities. newlineThe feasibility of this method are analyzed through a numerical example. Additionally, newlineits stability and effectiveness are confirmed by a comparison with current newlineapproaches using actual data. newlineIn Chapter 5, we discuss the interval number matrices using two sort of newlineexact number i.e. average and right endpoint in group decision-making (GDM). newlineThe entropy weight approach is used to get the criteria weights for both matrices. newlineThe interval character of the criteria weights is then reflected by combining these newlineweighted values using a convex combination. Using TOPSIS, the alternatives newlineare ranked, and the final rankings are determined by calculating the combined newlinecloseness coefficient, which is an average. newlineIn Chapter 6, we describe interval-valued Pythagorean fuzzy soft sets (IVPFSSs) newlinein GDM to deal with ambiguity and uncertainty data. The two novel aggregation newlineoperators IVPFSS weighted average (IVPFSSWA) and IVPFSS weighted newlinegeometric (IVPFSSWG) are that are suggested to efficiently aggregate fuzzy newlinedata, along with new operational rules for IVPFSSs. For the purpose of choosing newlinematerials for product design and manufacture, these operators are used in a newlineMCDM methods. The method s applicability and dependability are illustrated newlinethrough a real-world case study. A comparison with current operators validates newlinethe suggested framework s efficacy, but it also identifies drawbacks including its newlinehigh sensitivity and computational complexity. newlineLastly, Chapter 7 addresses the concluding remarks of each chapter as well newlineas the future study directions based on the thesis results. newlineKeywords: Alternatives; Attributes; Aggregation operators; Benefits; Closevii newlineness coefficients; Criterion; Cost; DFPIS; DFNIS; DM; Entropy weight method; newlineFuzzy sets; Fuzzy TOPSIS; FMCDM; GDM; Interval number; Interval-valued newlinePythagorean fuzzy soft sets/numbers; IVPFSSWA/IVPFSSWG; Material selection; newlineMADM; MCDM; Min-max; Normalized; Parameter; TFN; TOPSIS. newlineviii