Linguistic Einstein aggregation operator‐based TOPSIS for multicriteria group decision making in linguistic Pythagorean fuzzy environment

Sarkar, Biswajit; Biswas, Animesh

doi:10.1002/int.22403

Cited by 25 publications

(6 citation statements)

References 55 publications

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“…Based on strict t-norms and t-conorms, some scholars [ 29 – 33 ] have also carried out research about part of strict t-norms and t-conorms under the linguistic environment. For linguistic pythagorean fuzzy sets, a new family of aggregation operations based on Einstein t-norms and t-conorms was presented in [ 32 ]. Recently, Qiyas et al [ 33 ] developed aggregation operators for triangular linguistic cubic sets based on the Dombi t-norms and t-conorms.…”

Section: Introductionmentioning

confidence: 99%

A three-way decisions approach based on double hierarchy linguistic aggregation operators of strict t-norms and t-conorms

Zhong

Chen

et al. 2023

Int. J. Mach. Learn. & Cyber.

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With the massive increase in uncertainty of linguistic information in realistic decision making, there is a great challenge for people to make decisions in the complex linguistic environment. To overcome this challenge, this paper proposes a three-way decisions method based on aggregation operators of strict t-norms and t-conorms under double hierarchy linguistic environment. By mining the double hierarchy linguistic information, strict t-norms and t-conorms are introduced to define the operation rules and their operation examples are also given. Then, the double hierarchy linguistic weighted average (DHLWA) operator and weighted geometric (DHLWG) operator are proposed based on strict t-norms and t-conorms. Besides, some of their important properties are also proved and derived, such as idempotency, boundedness and monotonicity. Next, DHLWA and DHLWG are integrated with three-way decisions to construct our three-way decisions model. Specifically, the double hierarchy linguistic decision theoretic rough set (DHLDTRS) model is constructed by incorporating the computational model of expected loss with DHLWA and DHLWG, which can consider the various decision attitudes from decision makers more adequately. Furthermore, we also propose a novel entropy weight calculation formula to improve the entropy weight method for obtaining the weights more objectively, and integrate grey relational analysis (GRA) method to calculate the conditional probability. Based on the Bayesian minimum-loss decision rules, the solving method of our model is also propounded and the corresponding algorithm is designed. Finally, an illustrative example and experimental analysis are presented, which can validate the rationality, robustness as well as superiority of our method.

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Section: Introductionmentioning

confidence: 99%

A three-way decisions approach based on double hierarchy linguistic aggregation operators of strict t-norms and t-conorms

Zhong

Chen

et al. 2023

Int. J. Mach. Learn. & Cyber.

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“…The information representation under LPFS has been extensively explored in MAGDM methods (Ding & Liu, 2019; Liu et al, 2019; Villa Silva et al, 2021). In addition, it is also combined with a variety of classical tools to solve practical decision‐making problems, including TOPSIS (Gül & Aydoğdu, 2022; Sarkar & Biswas, 2021), TODIM (Deng & Gao, 2019), CODAS (He et al, 2020). Although many works about LPFS have been done previously, there are still some research gaps in the operational laws that the AO based on and the aggregation function.…”

Section: Introductionmentioning

confidence: 99%

Multi‐attribute group decision‐making based on linguistic Pythagorean fuzzy copula extended power average operator

Kou

Wang

et al. 2023

Expert Systems

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This paper aims to propose a novel multi‐attribute group decision‐making (MAGDM) method based on linguistic Pythagorean fuzzy copula extended power average operator. Existing researches under linguistic Pythagorean fuzzy environment lack of the ability to handle with extreme values and the flexible operational rules. To fill these two gaps, this paper first provides the definition of Archimedean copula and co‐copula operational rules under linguistic Pythagorean fuzzy environment, which can reflect the connection among arguments and provide more choices for experts to express their preferences. Then, we gather the extended power average (EPA) operator to present some new aggregation operators, which can reduce the negative influence of extreme evaluation values. To show the application of the proposed method to MAGDM problems, we apply it to handle a case of takeout O2O platform assessment problem. The numerical case and comparative analysis with other existing methods illustrate that our proposed method is more scientific and flexible.

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“…Furthermore, Garg [20] presented the concept of a linguistic Pythagorean fuzzy set (LPFS) characterized by a linguistic membership degree (LMD) and a linguistic non-membership degree (LNMD). Based on LPFS, many aggregation operators (AOs) and typical decision-making methods were extended to solve the MAGDM problem [21][22][23][24][25], and were applied in real decisionmaking environments.…”

Section: Introductionmentioning

confidence: 99%

A Novel Linguistic Interval-Valued Pythagorean Fuzzy Multi-Attribute Group Decision-Making for Sustainable Building Materials Selection

Yang

2022

Sustainability

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The linguistic interval-valued Pythagorean fuzzy (LIVPF) sets, which absorb the advantages of linguistic terms set and interval-valued Pythagorean fuzzy sets, can efficiently describe decision makers’ evaluation information in multi-attribute group decision-making (MAGDM) problems. When investigating aggregation operators of linguistic interval-valued Pythagorean fuzzy (LIVPF) information, we have to consider two important issues, viz. the operational rules of LIVPF numbers and aggregation functions. The classical Archimedean t-norm and t-conorm (ATT) are a famous t-norm and t-conorm, which can produce some special cases. Recently, ATT has been widely applied in different fuzzy decision-making information. Hence, in this paper, for the first issue, we propose some novel operational rules of LIVPF numbers based on ATT. The new operational laws are flexible and can generate some useful operations. For the second issue, we choose a powerful function, i.e., the extended power average (EPA) operator as the aggregation function. The prominent advantages of EPA are that it not only considers the relationship among input arguments, but also dynamically changes the weights of input arguments by employing a parameter. Hence, our proposed novel aggregation operators for LIVPFNs are flexible and is suitable to handle MAGDM problems in actual life. Afterward, we further present a novel MAGDM method under LIVPF conditions. The main finding of our study is a new MAGDM method, which is more powerful and flexible than existing ones. Finally, we apply the method in a sustainable building materials selection to show its effectiveness. Additionally, comparison analysis is provided to demonstrate the advantages and superiorities of the proposed method.

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Linguistic Einstein aggregation operator‐based TOPSIS for multicriteria group decision making in linguistic Pythagorean fuzzy environment

Cited by 25 publications

References 55 publications

A three-way decisions approach based on double hierarchy linguistic aggregation operators of strict t-norms and t-conorms

A three-way decisions approach based on double hierarchy linguistic aggregation operators of strict t-norms and t-conorms

Multi‐attribute group decision‐making based on linguistic Pythagorean fuzzy copula extended power average operator

A Novel Linguistic Interval-Valued Pythagorean Fuzzy Multi-Attribute Group Decision-Making for Sustainable Building Materials Selection

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