[Retracted] A Novel Multicriteria Decision‐Making Approach for Einstein Weighted Average Operator under Pythagorean Fuzzy Hypersoft Environment

Sunthrayuth, Pongsakorn; Jarad, Fahd; Majdoubi, Jihen; Zulqarnain, Rana Muhammad; Iampan, Aiyared; Siddique, Imran

doi:10.1155/2022/1951389

Cited by 10 publications

(13 citation statements)

References 60 publications

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“…Definition 3.1 [44] Let Jď k = aď k , bď k , Jď 11 = aď 11 , bď 11 , and Jď 12 = aď 12 , bď 12 represents the PFHSNs and ∂ is a positive real number. Then, operational laws for PFHSNs based on Einstein norms can be expressed as follows:…”

Section: Operational Laws For Pfhsnsmentioning

confidence: 99%

Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection

Zulqarnain¹,

Siddique²,

Ali³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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Hypersoft set theory is a most advanced form of soft set theory and an innovative mathematical tool for dealing with unclear complications. Pythagorean fuzzy hypersoft set (PFHSS) is the most influential and capable leeway of the hypersoft set (HSS) and Pythagorean fuzzy soft set (PFSS). It is also a general form of the intuitionistic fuzzy hypersoft set (IFHSS), which provides a better and more perfect assessment of the decision-making (DM) process. The fundamental objective of this work is to enrich the precision of decision-making. A novel mixed aggregation operator called Pythagorean fuzzy hypersoft Einstein weighted geometric (PFHSEWG) based on Einstein's operational laws has been developed. Some necessary properties, such as idempotency, boundedness, and homogeneity, have been presented for the anticipated PFHSEWG operator. Multi-criteria decision-making (MCDM) plays an active role in dealing with the complications of manufacturing design for material selection. However, conventional methods of MCDM usually produce inconsistent results. Based on the proposed PFHSEWG operator, a robust MCDM procedure for material selection in manufacturing design is planned to address these inconveniences. The expected MCDM method for material selection (MS) of cryogenic storing vessels has been established in the real world. Significantly, the planned model for handling inaccurate data based on PFHSS is more operative and consistent.

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Section: Operational Laws For Pfhsnsmentioning

confidence: 99%

Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection

Zulqarnain¹,

Siddique²,

Ali³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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“…Definition 2.4: (Sunthrayuth et al, 2022) Let J ďk = (f ďk , g ďk ), J ď11 = (f ď11 , g ď11 ), and J ď12 = (f ď12 , g ď12 ) denote the PFHSNs, and γ > 0.…”

Section: Preliminariesmentioning

confidence: 99%

“…Siddique et al (2021) delivered a creative MCDM system for PFHSSs using their developed AOs. Sunthrayuth et al (2022) and Zulqarnain et al (2022e) predicted the Einstein AOs for PFHSSs to obstinacy MCDM impediments and used them for agri-farming and material selection consistently. Zulqarnain et al (2022f) developed Einstein-ordered AOs for PFHSSs and formulated an MCDM approach to resolve DM complexities.…”

Section: Introductionmentioning

confidence: 99%

Prioritization of thermal energy storage techniques based on Einstein-ordered aggregation operators of q-rung orthopair fuzzy hypersoft sets

et al. 2023

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The capability to stock energy and manage consumption in the future is one of the keys to retrieving huge quantities of renewable energy on the grid. There are numerous techniques to stock energy, such as mechanical, electrical, chemical, electrochemical, and thermal. The q-rung orthopair fuzzy soft set (q-ROFSS) is a precise parametrization tool with fuzzy and uncertain contractions. In several environments, the attributes need to be further categorized because the attribute values are not disjointed. The existing q-rung orthopair fuzzy soft set configurations cannot resolve this state. Hypersoft sets are a leeway of soft sets (SSs) that use multi-parameter approximation functions to overcome the inadequacies of prevailing SS structures. The significance of this investigation lies in anticipating Einstein-ordered weighted aggregation operators (AOs) for q-rung orthopair fuzzy hypersoft sets (q-ROFHSSs), such as the q-rung orthopair fuzzy hypersoft Einstein-ordered weighted average (q-ROFHSEOWA) and the q-rung orthopair fuzzy hypersoft Einstein-ordered weighted geometric (q-ROFHSEOWG) operators, using the Einstein operational laws, with their requisite properties. Mathematical interpretations of decision-making constrictions are considered able to ensure the symmetry of the utilized methodology. Einstein-ordered aggregation operators, based on prospects, enable a dynamic multi-criteria group decision-making (MCGDM) approach with the most significant consequences with the predominant multi-criteria group decision techniques. Furthermore, we present the solicitation of Einstein-ordered weighted aggregation operators for selecting thermal energy-storing technology. Moreover, a numerical example is described to determine the effective use of a decision-making pattern. The output of the suggested algorithm is more authentic than existing models and the most reliable to regulate the favorable features of the planned study.

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“…Ihsan et al 26 conceptualized the structure FHSES and explained the application of DMPs with the help of the proposed algorithm. The contributions of researchers like Siddique et al 27 and Sunthrayuth et al 28 are more significant regarding the characterization pythagorean fuzzy hypersoft set, its aggregation operations and applications in decision-making. Musa and Asaad 29 discussed topological structures of hypersoft set with bipolar setting and investigated its several axioms.…”

Section: Introductionmentioning

confidence: 99%

An intelligent fuzzy parameterized multi-criteria decision-support system based on intuitionistic fuzzy hypersoft expert set for automobile evaluation

Ihsan

Saeed

Rahman

et al. 2022

Advances in Mechanical Engineering

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In every decision-making scenario, the role of parameters is pertinent but it becomes critical for the situations when parameters are ambiguous to be assessed by the experts so this sort of uncertainty is judged by assigning a fuzzy membership-grade to each parameter. The existing literature on fuzzy parameterization is unable to provide an appropriate model which may cope with hypersoft setting, multi-decisive opinions of experts and intuitionistic setting collectively. This shortcoming leads to the motivation of this study. In this paper, fuzzy parameterized intuitionistic fuzzy hypersoft expert set (FPIFHsES) is characterized which is capable to address the insufficiencies of existing models like fuzzy parameterized intuitionistic fuzzy soft expert set (FPIFSES) for the consideration of multi-argument approximate function. With the entitlement of this function, FPIFHsES tackles the real-life scenario where each attribute is meant to be further classified into its respective sub-attribute valued disjoint set. The FPIFHsES is more flexible and the reliable with the deep analysis of attributes in the decision-support system. The characterization of FPIFHsES is accomplished by employing theoretic, axiomatic, and algorithmic approaches. In order to validate the proposed model, an algorithm is proposed to study its role in decision-making while dealing with a real-world scenario.

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[Retracted] A Novel Multicriteria Decision‐Making Approach for Einstein Weighted Average Operator under Pythagorean Fuzzy Hypersoft Environment

Cited by 10 publications

References 60 publications

Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection

Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection

Prioritization of thermal energy storage techniques based on Einstein-ordered aggregation operators of q-rung orthopair fuzzy hypersoft sets

An intelligent fuzzy parameterized multi-criteria decision-support system based on intuitionistic fuzzy hypersoft expert set for automobile evaluation

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