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Multi-Criteria Decision Making Based on Bipolar Picture Fuzzy Operators and New Distance Measures

Muhammad Riaz1, Harish Garg2, Hafiz Muhammad Athar Farid1, Ronnason Chinram3,4,*
1 Department of Mathematics, University of the Punjab, Lahore, 54590, Pakistan
2 School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, 147004, India
3 Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla, 90110, Thailand
4 Centre of Excellence in Mathematics, Bangkok, 10400, Thailand
* Corresponding Author: Ronnason Chinram. Email:
(This article belongs to this Special Issue: Intelligent Computing for Engineering Applications)

Computer Modeling in Engineering & Sciences 2021, 127(2), 771-800.

Received 06 September 2020; Accepted 21 December 2020; Issue published 19 April 2021


This paper aims to introduce the novel concept of the bipolar picture fuzzy set (BPFS) as a hybrid structure of bipolar fuzzy set (BFS) and picture fuzzy set (PFS). BPFS is a new kind of fuzzy sets to deal with bipolarity (both positive and negative aspects) to each membership degree (belonging-ness), neutral membership (not decided), and non-membership degree (refusal). In this article, some basic properties of bipolar picture fuzzy sets (BPFSs) and their fundamental operations are introduced. The score function, accuracy function and certainty function are suggested to discuss the comparability of bipolar picture fuzzy numbers (BPFNs). Additionally, the concept of new distance measures of BPFSs is presented to discuss geometrical properties of BPFSs. In the context of BPFSs, certain aggregation operators (AOs) named as “bipolar picture fuzzy weighted geometric (BPFWG) operator, bipolar picture fuzzy ordered weighted geometric (BPFOWG) operator and bipolar picture fuzzy hybrid geometric (BPFHG) operator” are defined for information aggregation of BPFNs. Based on the proposed AOs, a new multicriteria decision-making (MCDM) approach is proposed to address uncertain real-life situations. Finally, a practical application of proposed methodology is also illustrated to discuss its feasibility and applicability.


Bipolar picture fuzzy set; aggregation operators; distance measures; pattern recognition; MCDM

Cite This Article

Riaz, M., Garg, H., Muhammad, H., Chinram, R. (2021). Multi-Criteria Decision Making Based on Bipolar Picture Fuzzy Operators and New Distance Measures. CMES-Computer Modeling in Engineering & Sciences, 127(2), 771–800.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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