Extension of TOPSIS and VIKOR Method for Decision-Making Problems with Picture Fuzzy Number

Abstract

In multiple criteria decision-making (MCDM) methods, the criteria are often conflicting, uncertain, imprecise and non-commensurable. Due to the presence of neutral membership degree, picture fuzzy numbers (PFN) have been successfully used to express uncertain and imprecise information. To deal with conflicting and non-commensurable criteria in MCDM problems, both VIKOR and TOPSIS methods are proven to be efficient. VIKOR and TOPSIS methods are applied in compromise ranking method which is based on aggregation functions representing closeness to the reference points. VIKOR method finds compromise solution whereas TOPSIS method finds a solution which has the shortest distance to the ideal solution and greatest distance from the negative ideal solution. This paper extends VIKOR and TOPSIS methods to solve MCDM problems using picture fuzzy information. Finally, a comparative analysis of these two methods is provided using an illustrative example.