Cubic Pythagorean fuzzy sets and their application to multi-attribute decision making with unknown weight information

Abbas, Syed Zaheer; Khan, Muhammad Numan; Abdullah, Saleem; Sun, Hongwei; Hussain, Fawad

doi:10.3233/jifs-18382

Cited by 43 publications

(31 citation statements)

References 16 publications

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“…Khan et al used the Dombi t-norms and t-conorms to Pythagorean fuzzy numbers and defined Pythagorean fuzzy Dombi aggregation operators [16]. e cubic Pythagorean fuzzy set (CPFS) is a well reputed structure of fuzzy sets, proposed by Abbas et al [17] in 2019 to tackle the uncertainty in decision-making problems. Talukdar and Dutta [18] presented the distance measures under CPFS information.…”

Section: Introductionmentioning

confidence: 99%

Redefined “Maclaurin Symmetric Mean Aggregation Operators Based on Cubic Pythagorean Linguistic Fuzzy Numbers”

Naeem

Ashraf

Abdullah

et al. 2021

Mathematical Problems in Engineering

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In this study, we highlight the errors in Sections 2.3, 2.4, 3, and 4 in the article by Fahmi et al. (J Ambient Intell Human Comput (2020). https://doi.org/10.1007/s12652-020-02272-9) by counter definitions and theorems. We find that the definition of cubic Pythagorean fuzzy set (CPFS) (Definition 2.3.1) and operational laws (Definition 2.3.2) violates the rules to consider the membership and nonmembership functions, and then, we redefined the corrected definition and their operations for CPFS. Furthermore, we redefine the concept of cubic Pythagorean linguistic fuzzy set (CPLFS) and their basic operational laws. In addition, we find that Sections 3 and 4 (consist of a list of Maclaurin symmetric mean (MSM) and dual MSM aggregation operators) are invalid, and then, we redefined the list of updated MSM and dual MSM aggregation operators in correct way. Finally, we established the numerical application of the proposed improved algorithm using cubic Pythagorean linguistic fuzzy information to show the applicability and effectiveness of the proposed technique.

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Section: Introductionmentioning

confidence: 99%

Redefined “Maclaurin Symmetric Mean Aggregation Operators Based on Cubic Pythagorean Linguistic Fuzzy Numbers”

Naeem

Ashraf

Abdullah

et al. 2021

Mathematical Problems in Engineering

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“…Abdullah and Mohd [20] proposed the Pythagorean fuzzy Hamacher Choquet integral (PFHCI) average (PFH-CIA) operators and PFHCI geometric PFHCIG) operators. Abbas et al [21] defined the concept of Cubic Pythagorean fuzzy numbers (CPFNs), and presented Cubic Pythagorean fuzzy (CPF) weighted averaging (CPFWA) operator, and CPF weighted geometric (CPFWG) operator. Shakeel et al [22] proposed Pythagorean trapezoidal fuzzy (PTF) ordered weighted averaging (PTFOWA) operator and PTF hybrid averaging (PTFHA) operator.…”

Section: Introductionmentioning

confidence: 99%

Interval-Valued Pythagorean Normal Fuzzy Information Aggregation Operators for Multi-Attribute Decision Making

Yang

Chang

2020

IEEE Access

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The interval-valued Pythagorean fuzzy (IVPF) sets, describing the membership and nonmembership degrees from interval values, can address uncertain information, while the normal fuzzy number (NFN) can depict normal distribution information in anthropogenic activity and natural environment. By combining the advantages of both operations, in this study, we proposed the interval-valued Pythagorean normal fuzzy (IVPNF) sets by introducing the NFN into IVPF environment. Firstly, we defined the conception, the operational laws, score function, accuracy function of IVPNF sets. Secondly, we presented four information aggregation operators to aggregate IVPNF information, including the IVPNF weighted averaging (IVPNFWA) operator, IVPNF weighted geometric (IVPNFWG) operator, the generalized IVPNFWA operator, and the generalized IVPNFWG operator. In addition, we analyzed some desirable properties of monotonicity, commutativity, and idempotency for the proposed four operators. Finally, a numerical example on multi-attribute decision-making problem is given to verify the practicality of the proposed operators, and the comparative and sensitive analysis are used to show the effectiveness and flexibility of our proposed approach. INDEX TERMS Normal fuzzy number, interval-valued Pythagorean normal fuzzy, information aggregation operators, multi-attribute decision-making.

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“…Further, the idea of cubic intuitionistic fuzzy set (CIFS) as an extension of CS was established by Kaur and Garg [23] and some CIF aggregation operators are discussed in [24]. Abbas et al [25] introduced the concept of cubic PF set (CPFS) and some CPFWA and CPFWG aggregation operators were defined by them. Wang et al [26] introduced the concept of cubic q-rung orthopair fuzzy set (Cq-ROFS) and proposed power Muirhead mean operator based on Cq-ROFNs, which can generalize both CIFS and CPFS.…”

Section: Introductionmentioning

confidence: 99%

Cubic q-Rung Orthopair Fuzzy Linguistic Set and Their Application to Multiattribute Decision-making with Muirhead Mean Operator

Garg

Mahmood

Ahmmad

et al. 2020

JAIT

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The objective of the paper is to present a new concept named as Cubic q-rung orthopair fuzzy linguistic set (Cq-ROFLS) to quantify the uncertainty in the information. The proposed Cq-ROFLS is qualitative form of cubic q-rung orthopair fuzzy set (Cq-ROFS), where membership degrees (MDs) and non-membership degrees (NMDs) are represented in terms of linguistic variables. The basic notions of Cq-ROFLS have been introduced and study their basic operations and properties. Further, to aggregate the different pairs of the preferences, we introduce the Cq-ROFL Muirhead mean, weighted Muirhead mean, dual Muirhead mean based operators. The major advantages of considering the Muirhead mean is that it considers the interrelationship between more than two arguments at a time. On the other hand, the Cq-ROFLS has the ability to describe the qualitative information in terms of linguistic variables. Several properties and relation of the derived operators are argued. Besides, we also investigate multi attribute decision making (MADM) problems under the Cq-ROFLS environment and illustrate with a numerical examples. Finally, the effectiveness and advantages of the work are established by comparing with other methods.

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Cubic Pythagorean fuzzy sets and their application to multi-attribute decision making with unknown weight information

Cited by 43 publications

References 16 publications

Redefined “Maclaurin Symmetric Mean Aggregation Operators Based on Cubic Pythagorean Linguistic Fuzzy Numbers”

Redefined “Maclaurin Symmetric Mean Aggregation Operators Based on Cubic Pythagorean Linguistic Fuzzy Numbers”

Interval-Valued Pythagorean Normal Fuzzy Information Aggregation Operators for Multi-Attribute Decision Making

Cubic q-Rung Orthopair Fuzzy Linguistic Set and Their Application to Multiattribute Decision-making with Muirhead Mean Operator

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