Dual hesitant q ‐rung orthopair fuzzy Dombi t ‐conorm and t ‐norm based Bonferroni mean operators for solving multicriteria group decision making problems

Abstract

In this paper, Bonferroni mean (BM) and Dombi t-conorms and t-norms (Dt-CN&t-Ns) are combined under dual hesitant q-rung orthopair fuzzy (DHq-ROF) environment to produce DHq-ROF-Dombi BM, weighted Dombi BM, Dombi geometric BM, and Dombi weighted geometric BM aggregation operators (AOs). Using these operators, the decision making processes would become more flexible and also would possess the capabilities of capturing interrelationships among input arguments under imprecise decision making environments. Apart from those, a large number of AOs either already developed or not yet developed may also be derived from the proposed AOs. In the process of developing the AOs, some operational laws of DHq-ROF numbers based on Dt-CN&t-Ns are defined first. Several important properties of the developed operators are discussed. The proposed AOs are used to frame a new methodology to solve multicriteria group decision making problems under DHq-ROF contexts. Several illustrative examples are solved to demonstrate effectiveness and benefits of the developed method. Sensitivity analysis is performed to show the variations of ranking values with the change of different parameters in the decision making contexts. Finally, the introduced method is compared with several existing techniques to establish superiority and effectiveness of the proposed method.

Models for MAGDM with dual hesitant q‐rung orthopair fuzzy 2‐tuple linguistic MSM operators and their application to COVID‐19 pandemic

“…As a consequence, in real MADM implementations, DH q ‐ROF numbers could indeed describe assessment details with greater ease than other types of fuzzy numbers. Sarkar and Biswas (Sarkar & Biswas, 2021) combined the Bonferroni mean (BM) operator and Dombi t ‐norms and t ‐conorms in DH q ‐ROF environment and proposed the Dombi BM, weighted Dombi BM, Dombi geometric BM and Dombi weighted geometric BM aggregation operators with DH q ‐ROFNs.…”

Multi Label Feature Selection Through Dual Hesitant q-Rung Orthopair Fuzzy Dombi Aggregation Operators

“…Fuzzy set theory developed by Zadeh [17] and further extended to intutionistic fuzzy sets [18], Pythagorean fuzzy sets [19], q-rung orthopair fuzzy sets [20], hesitant fuzzy set [21], q-rung orthopair hesitant fuzzy sets [22], dual hesitant fuzzy sets [23], dual hesitant q-rung orthopair fuzzy sets (DHq-ROFSs) [24] etc., found their applications in diverse fields [25]- [27]. Among them, the concept of DHq-ROFSs has gained more attention recently due to its advantage of taking into account more amount of vagueness [28]- [30]. The usage of aggregation operators in different forms of fuzzy set has been able to handle the MCDM problems more efficiently.…”

“…The usage of aggregation operators in different forms of fuzzy set has been able to handle the MCDM problems more efficiently. Among the various aggregation operators, the Dombi aggregation operator has the advantage of making the process of aggregation simpler through the alteration of the Dombi parameter [30], [31]. Through altering the parameter value in the Dombi aggregation operator, we alter the working behaviour of the parameter resulting in the change of norm utilized for aggregation.…”

“…The authors of [33] handled a decision making problem in the q-rung orthopair fuzzy environment using Dombi operators. For instance, the authors of [30] implemented Dombi operators in the Bonferroni mean and used it in the DHq-ROFSs environment and applied it to a MCDM technique. In [31], Dombi operators were handled in Pythagorean fuzzy environment and were used in multi attribute decision making problem.…”

Power Muirhead Mean Operators for Interval-Valued Linear Diophantine Fuzzy Sets and Their Application in Decision-Making Strategies

“…For this reason, Yager [17] suggested q-rung orthopair FS (QROFS), with a new strategy 0 ≤ µ q D (ψ) + η q D (ψ) ≤ 1 , q ≥ 1. This approach was used in a number of further developments, such as interval-valued QROFSs [18], entropy measures [19], knowledge measures [20], a new ranking technique [21], correlation coefficient [22], connection number [23], Dombi aggregation operators [24], Maclaurin symmetric mean operators [25], and L-fuzzy sets and orbits [26].…”