<abstract><p>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.</p></abstract>
The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) is an outranking series of multi-attribute decision making used to assess a finite collection of alternatives based on conflicting criteria. One of its significant benefits is its adjustability in response to a set of acceptable preference functions that may quantify the differences between alternatives conditional on the kind and structure of the criteria. This article offers the novel approach of the PROMETHEE method, named the 2TLmF PROMETHEE method, which combines the multi-polarity with linguistic information of decision problems. The customary procedure of the offered technique begins with the normalized weights of the attributes assigned by decision-makers. After that, Gaussian and the usual preference functions are utilized to determine the preferences of the alternatives. The ultimate choice is based on the alternative's positive and negative outranking flow. The positive outranking demonstrates how one alternative outranks all other options, while the negative preference flow implies an alternative is superior to all other options.There are several modifications to the PROMETHEE approach, two of which are discussed in this article. The first is PROMETHEE I, which uses positive and negative preference flows to generate a partial ranking. Secondly, PROMETHEE II gives a comprehensive rating list based on the net flow, representing the balance of positive and negative preference flows. Further, a comprehensive flowchart is used to show the entire picture of the proposed methodology. As an application, a real-life situation related to selecting an elliptical machine for a home gym is chosen to illustrate the transparency and reliability of the presented work. Finally, a comparative study is carried out to illustrate the strength and applicability of the proposed method.
This research article is devoted to presenting the concept of 2-tuple linguistic m -polar fuzzy sets (2 TL m FSs) and introducing some fundamental operations on them. With 2 TL m FSs, we shall be able to capture imprecise information with high generality. With the appropriate operators, we shall be able to apply 2 TL m FSs in decision-making efficiently. The aggregation operators that we propose are the 2 TL m F Hamacher weighted average (2 TL m FHWA) operator, 2 TL m F Hamacher ordered weighted average (2 TL m FHOWA) operator, 2 TL m Hamacher hybrid average (2 TL m FHHA) operator, 2 TL m F Hamacher weighted geometric (2 TL m HWG) operator, 2 TL m Hamacher ordered weighted geometric (2 TL m HOWG) operator, and 2 TL m F Hamacher hybrid geometric (2 TL m FHHG) operator. We investigate their properties, including the standard cases of monotonicity, boundedness, and idempotency. Then we develop an algorithm to solve multicriteria decision-making problems formulated with 2 TL m F information. The 2 TL m F data in multiattribute decision-making are merged with the help of aggregation operators, and we consider the particular instances of the 2 TL m FHA and 2 TL m FHG operators. The influence of the parameters on the outputs is explored with a numerical simulation. Moreover, a comparative study with existing methods was performed in order to show the applicability of the proposed model and motivate the discussion about its virtues and advantages. The results confirm that the model here developed is reliable for decision-making purposes.
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