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Interval neutrosophic multi-criteria group decision-making based on Aczel–Alsina aggregation operators

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Abstract

Considering the processing of classical information, it is an extremely difficult process to process indeterminate and inconsistent information. In addition, recently, Aczel–Alsina aggregation operators have started to gain importance in information fusion theory. However, although the fuzzy set and its extensions (e.a., the intuitionistic fuzzy set, pythagorean fuzzy, picture set and so on) have these operators, they cannot cope with the values when decision-makers have to use the structures where there is uncertainty, imprecise, incomplete and inconsistent information. Considering an integration of interval neutrosophic sets and Aczel–Alsina aggregation operators, this article presents the definitions of some new algebraic operations based on Aczel–Alsina operations for interval neutrosophic set (INS). We begin by defining the algebraic properties such as Aczel–Alsina product, Aczel–Alsina sum, and Aczel–Alsina scalar multiplication for INSs. We then apply the Aczel–Alsina operations to INSs and develop several interval neutrosophic (IN) Aczel–Alsina aggregation operators, such as the IN Aczel–Alsina weighted arithmetic average (IN-AAWAA) operator, the IN Aczel–Alsina weighted geometric average (IN-AAWGA) operator, the IN Aczel–Alsina ordered weighted average (IN-AAOWA) operator, and the IN Aczel–Alsina hybrid weighted average (IN-AAHWA) operator. We even show that these aggregation operators provide three required properties such as idempotency, boundary and monotonicity. Basically, we aim to design a new multi-criteria group decision-making (MCGDM) model based on IN Aczel–Alsina aggregation operators. In this model, while calculating the importance weights of the decision makers, both the objective and subjective evaluations of the decision makers were taken into account. In addition, the weight information of the decision criteria was determined by the DAMATEL method and included in the decision process. An operator with a parameter offers a more flexible perspective of the decision process. The approach suggested in this study is more comprehensive, exact, and concrete when we contrast the findings with those of earlier strategies. Finally, thanks to the developed model, it is aimed to solve an emerging technology selection problem. A detailed comparison analysis is provided to demonstrate the accuracy and operability of the new model.

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  1. Department of Mathematics, Faculty of Science, Ataturk University, 25240, Erzurum, Turkey

    Mesut Karabacak

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  1. Mesut Karabacak
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Correspondence to Mesut Karabacak.

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Communicated by Graçaliz Pereira Dimuro.

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Karabacak, M. Interval neutrosophic multi-criteria group decision-making based on Aczel–Alsina aggregation operators. Comp. Appl. Math. 42, 136 (2023). https://doi.org/10.1007/s40314-023-02236-7

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