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Cubic bipolar fuzzy set with application to multi-criteria group decision making using geometric aggregation operators

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Abstract

Bipolar irrational emotions are implicated in a broad variety of individual actions. For example, two specific elements of decision making are the benefits and adverse effects. The harmony and respectful coexistence between these two elements is viewed as a cornerstone to a healthy social setting. For bipolar fuzzy characteristics of the universe of choices that rely on a small range of degrees, a bipolar fuzzy decision making method utilizing different techniques is accessible. The idea of a simplistic bipolar fuzzy set is ineffective in supplying consistency to the details about the frequency of the rating due to minimal knowledge. In this respect, we present cubic bipolar fuzzy sets (CBFSs) as a generalization of bipolar fuzzy sets. The plan of this research is to establish an innovative multi-criteria group decision making (MCGDM) based on cubic bipolar fuzzy set (CBFS) by unifying aggregation operators under geometric mean operations. The geometric mean operators are regarded to be a helpful technique, particularly in circumstances where an expert is unable to fuse huge complex unwanted information properly at the outset of the design of the scheme. We present some basic operations for CBFSs under dual order, i.e., \(\mathrm {P}\)-Order and \(\mathrm {R}\)-Order. We introduce some algebraic operations on CBFSs and some of their fundamental properties for both orders. We propose \(\mathrm {P}\)-cubic bipolar fuzzy weighted geometric (\(\mathrm {P}\)-CBFWG) operator and \(\mathrm {R}\)-cubic bipolar fuzzy weighted geometric (\(\mathrm {R}\)-CBFWG) operator to aggregate cubic bipolar fuzzy data. We also discuss the useability and efficiency of these operators in MCGDM problem. In human decisions, the second important part is ranking of alternatives obtained after evaluation. In this regard, we present an improved score and accuracy function to compare the cubic bipolar fuzzy elements (CBFEs). We also discuss a set theoretic comparison of proposed set with other theories as well as method base comparison of the proposed method with some existing techniques of bipolar fuzzy domain.

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Acknowledgements

We would like to thank the editor in chief, associate editor and anonymous reviewers for their insightful and constructive comments and suggestions that have been helpful for providing a better version of the present work.

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  1. Department of Mathematics, University of the Punjab, Lahore, Pakistan

    Muhammad Riaz & Syeda Tayyba Tehrim

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  1. Muhammad Riaz
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  2. Syeda Tayyba Tehrim
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Correspondence to Syeda Tayyba Tehrim.

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Riaz, M., Tehrim, S.T. Cubic bipolar fuzzy set with application to multi-criteria group decision making using geometric aggregation operators. Soft Comput 24, 16111–16133 (2020). https://doi.org/10.1007/s00500-020-04927-3

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