Intuitionistic Trapezoidal Fuzzy MAGDM Problems with Sumudu Transform in Numerical Methods

Intuitionistic Trapezoidal Fuzzy MAGDM Problems with Sumudu Transform in Numerical Methods

John Robinson P. (Bishop Heber College, Tamilnadu, India) and Jeeva S (Bishop Heber College, Tamilnadu, India)
Copyright: © 2019 |Pages: 46
DOI: 10.4018/IJFSA.2019070101

Abstract

Multiple attribute group decision making (MAGDM) is an important scientific, social, and economic endeavor. The ability to make consistent and correct choices is the essence of any decision process imbued with uncertainty. In situations where the information or data is in the form of an intuitionistic trapezoidal fuzzy numbers, or to construct the MAGDM problem, an intuitionistic trapezoidal fuzzy weighted averaging (ITzFWA) operator and an intuitionistic trapezoidal fuzzy hybrid aggregation (ITzFHA) operator are used. In this article, the decision maker provides the weights for aggregation in the form of an initial value problem of ordinary differential equations based on the study made on the data given by the decision maker. Decision maker weights are derived through sumudu transformation and various other numerical methods by obtaining the solution of differential equations. A numerical illustration is given to show the effectiveness and feasibility of the proposed approach.
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Introduction

Decision-making is a logical human judgment process for identifying and choosing alternatives based on the values and preferences of the decision that is mostly applied in the managerial level of concerned department of any organization. Multiple Attribute Group Decision Making (MAGDM) is the process in which multiple decision makers act collectively, analyze problems, evaluate alternative courses of actions and select a solution from the available alternatives. When a group makes a decision collectively, its judgment can be powerful than that of any of its members. Through discussing, questioning, and collaborative approach, group members can identify more complete and robust solutions and recommendations. The major challenge of decision making is uncertainty and the major goal of decision analysis is to reduce uncertainty. Robust decision efforts have formally integrated uncertainty and criterion subjectivity into the decision-making process. To deal with this kind of qualitative, imprecise and incomplete information in decision problems, Zadeh (1965) suggested employing the fuzzy set theory as a modeling tool for complex systems. Intuitionistic Fuzzy Sets (IFSs) proposed by Attanassov, (1986) is a generalization of the concept of fuzzy sets. Attanassov & Gargov, (1989) expanded the IFSs, using interval value to express membership and non-membership function of IFSs. Szmidt & Kacprzyk, (2002; 2003) introduced several distance functions and similarity measures for IFSs which were later used in various MAGDM problems. Many researchers have applied the IFS theory to the field of decision making. Li, (2005) presented new methods for handling MAGDM problems and the characteristics of the alternatives were represented by intuitionistic fuzzy sets. Liu, (2009), Liu et al., (2012), Wei, (2008b; 2010a; 2010b; 2010c; 2010d), Wei et al., (2011; 2012), Wei & Zhao, (2012) contributed novel approaches to the field of fuzzy decision making. Liu, (2004) and Liu & Guan, (2008; 2009) provided some new techniques for handling MAGDM problems based on vague set theory. Li, (2010a; 2010b; 2010c; 2010d) investigated MAGDM problems with intuitionistic fuzzy information and constructed several linear programming models to generate optimal weights for attributes and MADM problems in interval valued intuitionistic fuzzy sets. Wan & Li, (2014), Wan & Li, (2015) discussed several intuitionistic fuzzy programming methods and their approaches to heterogeneous multi-attribute group decision making with intuitionistic and interval valued intuitionistic fuzzy systems. Li & Ren (2015) investigated the amount and reliability of intuitionistic fuzzy information to multi-attribute decision making methods. Li, (2011; 2015) proposed application of game theory in decision making problem and correlation coefficient based on nonlinear programming method for interval valued intuitionistic fuzzy information. He et al. (2015), He & He (2016) discuss intuitionistic fuzzy interaction Bonferroni means and extensions of Atanassov’s intuitionistic fuzzy interaction Bonferroni means and applications to multiple attribute decision making. He et al., (2017) investigated robust fuzzy programming method for MRO problems. Yu et al. (2018), Li & Wan (2017), Yu & Li, (2017), Liu & Li, (2018), Li & Ye, (2018) proposed several methods in decision making problem under different types of intuitionistic fuzzy sets.

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