Multiple criteria decision making based on bipolar picture fuzzy sets and extended TOPSIS

Volume 23, Issue 1, pp 49--57 http://dx.doi.org/10.22436/jmcs.023.01.05

Publication Date: October 02, 2020 Submission Date: May 17, 2020 Revision Date: June 24, 2020 Accteptance Date: August 17, 2020

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Authors

Muhammad Sarwar Sindhu - Department of Mathematics, Virtual University of Pakistan (VU), Lahore 54000, Pakistan. Muhammad Ahsan - Department of Mathematics, Virtual University of Pakistan (VU), Lahore 54000, Pakistan. Arif Rafiq - Department of Mathematics, Virtual University of Pakistan (VU), Lahore 54000, Pakistan. Imran Ameen Khan - Department of Management Sciences, Virtual University of Pakistan (VU), Lahore 54000, Pakistan.

Abstract

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.

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Keywords

• Picture fuzzy sets
• fuzzy sets
• B\(P_{c}\)FSs
• linear programming model

MSC

•  62C86

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