A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators

Sumera Naz; Muhammad Akram; Mohammed M. Ali Al-Shamiri; Mohammed M. Khalaf; Gohar Yousaf; Sumera Naz; Muhammad Akram; Mohammed M. Ali Al-Shamiri; Mohammed M. Khalaf; Gohar Yousaf

doi:10.3934/mbe.2022177

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 4: 3843-3878. doi: 10.3934/mbe.2022177

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A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators

1.
Department of Mathematics, Division of Science and Technology, University of Eduction, Lahore, Pakistan
2.
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
3.
Department of Mathematics, Faculty of Science and Arts, Muhayl Asser, King Khalid University, Kingdom of Saudi Arabia
4.
Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen
5.
Faculty of Engineering, Arab Academy for Science & Technology and Maritime Transport (AASTMT), Aswan Branch, Egypt
6.
School of Mathematics, Minhaj University Lahore, Pakistan

Academic Editor: Alessio Martino

Received: 28 November 2021 Revised: 24 December 2022 Accepted: 25 January 2022 Published: 10 February 2022

In this article, we introduce the 2-tuple linguistic bipolar fuzzy set (2TLBFS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into bipolar fuzzy set. The 2TLBFS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the 2-tuple linguistic bipolar fuzzy weighted averaging (2TLBFWA) operator and the 2-tuple linguistic bipolar fuzzy weighted geometric (2TLBFWG) operator are presented to fuse the 2TLBF numbers (2TLBFNs). The Heronian mean (HM) operator, which can reflect the internal correlation between attributes and their influence on decision results, is integrated into the 2TLBF environment to analyze the effect of the correlation between decision factors on decision results. Initially, the generalized 2-tuple linguistic bipolar fuzzy Heronian mean (G2TLBFHM) operator and generalized 2-tuple linguistic bipolar fuzzy weighted Heronian mean (G2TLBFWHM) operator are proposed and properties are explained. Further, 2-tuple linguistic bipolar fuzzy geometric Heronian mean (2TLBFGHM) operator and 2-tuple linguistic bipolar weighted geometric Heronian mean (2TLBFWGHM) operator are proposed along with some of their desirable properties. Then, an approach to multi-attribute group decision-making (MAGDM) based on the proposed aggregation operators under the 2TLBF framework is developed. At last, a numerical illustration is provided for the selection of the best photovoltaic cell to demonstrate the use of the generated technique and exhibit its adequacy.
- 2-tuple linguistic bipolar fuzzy set,
- generalized HM operator,
- geometric HM operator,
- MAGDM,
- photovoltaic cells
Citation: Sumera Naz, Muhammad Akram, Mohammed M. Ali Al-Shamiri, Mohammed M. Khalaf, Gohar Yousaf. A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 3843-3878. doi: 10.3934/mbe.2022177

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Abstract

In this article, we introduce the 2-tuple linguistic bipolar fuzzy set (2TLBFS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into bipolar fuzzy set. The 2TLBFS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the 2-tuple linguistic bipolar fuzzy weighted averaging (2TLBFWA) operator and the 2-tuple linguistic bipolar fuzzy weighted geometric (2TLBFWG) operator are presented to fuse the 2TLBF numbers (2TLBFNs). The Heronian mean (HM) operator, which can reflect the internal correlation between attributes and their influence on decision results, is integrated into the 2TLBF environment to analyze the effect of the correlation between decision factors on decision results. Initially, the generalized 2-tuple linguistic bipolar fuzzy Heronian mean (G2TLBFHM) operator and generalized 2-tuple linguistic bipolar fuzzy weighted Heronian mean (G2TLBFWHM) operator are proposed and properties are explained. Further, 2-tuple linguistic bipolar fuzzy geometric Heronian mean (2TLBFGHM) operator and 2-tuple linguistic bipolar weighted geometric Heronian mean (2TLBFWGHM) operator are proposed along with some of their desirable properties. Then, an approach to multi-attribute group decision-making (MAGDM) based on the proposed aggregation operators under the 2TLBF framework is developed. At last, a numerical illustration is provided for the selection of the best photovoltaic cell to demonstrate the use of the generated technique and exhibit its adequacy.

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