Integrated decision-making methods based on 2-tuple linguistic $ m $-polar fuzzy information

Muhammad Akram; Uzma Noreen; Mohammed M. Ali Al-Shamiri; Dragan Pamucar; Muhammad Akram; Uzma Noreen; Mohammed M. Ali Al-Shamiri; Dragan Pamucar

doi:10.3934/math.2022802

AIMS Mathematics

2022, Volume 7, Issue 8: 14557-14594. doi: 10.3934/math.2022802

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Research article

Integrated decision-making methods based on 2-tuple linguistic $ m $-polar fuzzy information

1.
Department of Mathematics, University of the Punjab, New Campus, Lahore-54590, Pakistan
2.
Department of Mathematics, Faculty of science and arts, Mahayl Assir, King Khalid University, Saudi Arabia
3.
Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen
4.
Department of Logistics, , University of Defence in Belgrade, Belgrade, Serbia

Received: 02 April 2022 Revised: 26 May 2022 Accepted: 27 May 2022 Published: 07 June 2022
MSC : 03E72, 20F10

The 2-tuple linguistic $ m $-polar fuzzy sets (2TL$ m $FSs) are acknowledged to represent the multi-polar information owing to the practical structure of $ m $-polar fuzzy sets with the help of linguistic terms. The TOPSIS and ELECTRE series are efficient and widely used methods for solving multi-attribute decision-making problems. This paper aim to augment the literature on multi-attribute group decision making focusing on the the strategic approaches of TOPSIS and ELECTRE-I methods for the 2TL$ m $FSs. In the 2TL$ m $F-TOPSIS method, the relative closeness index is used to rank the alternatives. For the construction of concordance and discordance sets, the superiority and inferiority of alternatives over each other are accessed by using the score and accuracy functions. In the 2TL$ m $F ELECTRE-I, selection of the best alternative is made by the means of an outranking decision graph. At the final step of the 2TL$ m $F ELECTRE-I method, a supplementary approach is developed for the linear ranking of alternatives based on the concordance and discordance outranking indices. The structure of the proposed techniques are illustrated by using a system flow diagram. Finally, two case studies are used to demonstrate the correctness, transparency, and effectiveness of the proposed methods for selecting highway construction project manager and the best textile industry.
- 2-tuple linguistic $ m $-polar fuzzy set,
- 2-tuple linguistic $ m $-polar fuzzy number,
- accuracy function,
- TOPSIS method,
- ELECTRE-I method
Citation: Muhammad Akram, Uzma Noreen, Mohammed M. Ali Al-Shamiri, Dragan Pamucar. Integrated decision-making methods based on 2-tuple linguistic $ m $-polar fuzzy information[J]. AIMS Mathematics, 2022, 7(8): 14557-14594. doi: 10.3934/math.2022802

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Abstract

The 2-tuple linguistic $ m $-polar fuzzy sets (2TL$ m $FSs) are acknowledged to represent the multi-polar information owing to the practical structure of $ m $-polar fuzzy sets with the help of linguistic terms. The TOPSIS and ELECTRE series are efficient and widely used methods for solving multi-attribute decision-making problems. This paper aim to augment the literature on multi-attribute group decision making focusing on the the strategic approaches of TOPSIS and ELECTRE-I methods for the 2TL$ m $FSs. In the 2TL$ m $F-TOPSIS method, the relative closeness index is used to rank the alternatives. For the construction of concordance and discordance sets, the superiority and inferiority of alternatives over each other are accessed by using the score and accuracy functions. In the 2TL$ m $F ELECTRE-I, selection of the best alternative is made by the means of an outranking decision graph. At the final step of the 2TL$ m $F ELECTRE-I method, a supplementary approach is developed for the linear ranking of alternatives based on the concordance and discordance outranking indices. The structure of the proposed techniques are illustrated by using a system flow diagram. Finally, two case studies are used to demonstrate the correctness, transparency, and effectiveness of the proposed methods for selecting highway construction project manager and the best textile industry.

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