Multi-criteria decision making under uncertainty via the operations of generalized intuitionistic fuzzy numbers

Abstract

Multi-criteria decision making (MCDM) is the most important approach to apply and solve many complex real-world decision-making problems where choice among alternatives is concerned. However, classical MCDM approaches are inappropriate to take decision when parameters are uncertain, imprecise or vague in nature. In such situations, fuzzy set theory comes into picture and accordingly fuzzy multi-criteria decision making (FMCDM) has been introduced to deal with such problems. Later, MCDMs have been performed using intuitionistic fuzzy set. It is encountered that FMCDM techniques are performed using arithmetic of generalized intuitionistic fuzzy numbers (GIFNs) which produce counterintuitive output more often. That is, it is found that evaluation of arithmetic operation of GIFNs is always a crucial issue. In this paper, an attempt has been made to perform FMCDM using generalized triangular Intuitionistic fuzzy numbers (GTIFNs) by devising a novel technique of arithmetic operations between GTIFNs. The major contribution of the present approach is that the arithmetic of GTIFNs produces generalized trapezoidal intuitionistic fuzzy numbers and this approach has the ability to effectively resolve the drawbacks of the conventional arithmetic operations between GTIFNs. Furthermore, it gives rational results and outperforms in all the situations.