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Published in: Granular Computing 3/2022

12-11-2021 | Original Paper

Multiple attribute group decision-making based on generalized aggregation operators under linguistic interval-valued Pythagorean fuzzy environment

Authors: Rajkumar Verma, Nikunj Agarwal

Published in: Granular Computing | Issue 3/2022

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Abstract

The linguistic variables provide a powerful and efficient tool for describing qualitative information in many complex real-life decision situations. The notion of the linguistic interval-valued Pythagorean fuzzy sets (LIVPFSs) has been introduced to more flexibly deal with the decision–information under a qualitative environment. It generalizes the existing theories, such as linguistic Pythagorean fuzzy sets (LPFSs) and linguistic interval-valval intuitionistic fuzzy sets (LIVIFSs). The paper’s main objective is to present a detailed study of operational laws and aggregation operators (AOs) for linguistic interval-valued Pythagorean fuzzy numbers (LIVPFNs). This work uses Archimedean t-norm (ATN) and Archimedean t-conorm (ACN) to define new and generalized operational laws between LIVPFNs. The paper also proves many properties and special cases of them. Next, we define some new AOs for aggregating different LIVPFNs, such as the generalized Archimedean linguistic interval-valued Pythagorean fuzzy weighted average (GALIVPFWA) operator, the generalized Archimedean linguistic interval-valued Pythagorean fuzzy ordered weighted average (GALIVPFOWA) operator, and the generalized Archimedean linguistic interval-valued Pythagorean fuzzy ordered weighted average weighted average (GALIVPFOWAOWA) operator. The properties and special cases of developed AOs are discussed in detail. We use the linguistic scale function (LSF) to accommodate the decision-makers’ different translation requirements during the aggregation process. It is worth noting that the developed AOs have a parameter in their formulations to consider the attitudinal character of the decision-makers. The work designs a new and flexible decision-making approach utilizing the proposed AOs to solve multiple attribute group decision-making (MAGDM) problems with LIVPF information. A real-life problem of robot selection is given to illustrate the effectiveness of the developed approach in complex real-life situations. Finally, we present the sensitivity analysis and the comparison of the characteristic to show the superiority over existing methods.

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Metadata
Title
Multiple attribute group decision-making based on generalized aggregation operators under linguistic interval-valued Pythagorean fuzzy environment
Authors
Rajkumar Verma
Nikunj Agarwal
Publication date
12-11-2021
Publisher
Springer International Publishing
Published in
Granular Computing / Issue 3/2022
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI
https://doi.org/10.1007/s41066-021-00286-y

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