Multiple criteria decision making based on bipolar picture fuzzy sets and extended TOPSIS
Muhammad Sarwar Sindhu, Muhammad Ahsan, Arif Rafiq, Imran Ameen Khan · Journal of Mathematics and Computer Science · 2020
The notion of bipolar fuzzy sets (\(B_{p}\)FSs) has got much attention from the experts or decision-makers (DMs). \(B_{p}\)FSs have ample information in the form of two degrees called the positive belonging degree (\(P_{v}\)BD) and a negative belonging degree (\(N_{v}\)BD). In this article, we introduced the concept of bipolar picture fuzzy sets (B\(P_{c}\)FSs) by connecting the concepts of \(B_{p}\)FSs and picture fuzzy sets (\(P_{c}\)FSs). Firstly, we presented the concept, operational rules, score, and accuracy functions of B\(P_{c}\)FSs. Secondly, a distance measure is formulated for the B\(P_{c}\)FSs and then implemented for the extension of TOPSIS. Thirdly, a multiple criteria decision making (MCDM) model is proposed to handle the uncertain MCDM problems. Lastly, a practical example related to the sum of money's investment is exemplified to validate and effectiveness of the proposed model.