Applications of nth Power Root Fuzzy Sets in Multicriteria Decision Making

Ibrahim, Hariwan Z.; Al-shami, Tareq M.; Mhemdi, Abdelwaheb

doi:10.1155/2023/1487724

Cited by 13 publications

(3 citation statements)

References 28 publications

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“…Here, we use our data in accordance with the hybrid model by which we must compare our proposed model in order to verify the accuracy and efficacy of our generated hybrid model. Table 5 provides a summary of the computed results using the currently used square-root fuzzy weighted power average (SR-FWPA) operator [15], the n th power root fuzzy weighted power average (nPR-FWPA) operator [35], the Fermatean fuzzy weighted power average (FFWPA) operator [34], and the n,m-rung orthopair fuzzy weighted power average (n,m-ROFWPA) operator [16]. Therefore, the SR-FWPA, 3PR-FWPA, FFWPA, and n,m-ROFWPA operators are applied to our application and yield identical optimal results, which are presented in Table 6.…”

Section: Comparison Analysis and Discussionmentioning

confidence: 99%

“…Ibrahim and Alshammari [16] proposed the n,m-rung orthopair fuzzy weighted power average. Ibrahim et al [35] developed a new weighted aggregated operator via n th power root fuzzy sets.…”

Section: Introductionmentioning

confidence: 99%

“…It is clear that one of the n,m-th power root fuzzy set's main advantages is that it can be used in a wide range of decision-making situations. In Section 5, we provide a comparative analysis of the proposed FWPA n m operator with other popular operators such as the SR-FWPA operator [15], nPR-FWPA operator [35], FFWPA operator [34], and n,m-ROFWPA operator [16]. In the final section, we summarize the paper's main achievements and make some recommendations for future research.…”

Section: Introductionmentioning

confidence: 99%

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Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator

Hamadneh,

Ibrahim,

Abualhomos

et al. 2023

Symmetry

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A significant addition to fuzzy set theory for expressing uncertain data is an n,m-th power root fuzzy set. Compared to the nth power root, Fermatean, Pythagorean, and intuitionistic fuzzy sets, n,m-th power root fuzzy sets can cover more uncertain situations due to their greater range of displayed membership grades. When discussing the symmetry between two or more objects, the innovative concept of an n,m-th power root fuzzy set over dual universes is more flexible than the current notion of an intuitionistic fuzzy set, a Pythagorean fuzzy set, and a nth power root fuzzy set. In this study, we demonstrate a number of additional operations on n,m-th power root fuzzy sets along with a number of their special aspects. Additionally, to deal with choice information, we create a novel weighted aggregated operator called the n,m-th power root fuzzy weighted power average (FWPAmn) across n,m-th power root fuzzy sets and demonstrate some of its fundamental features. To rank n,m-th power root fuzzy sets, we also define the score and accuracy functions. Moreover, we use this operator to identify the countries with the best standards of living and show how we can select the best option by contrasting aggregate results using score values. Finally, we contrast the results of the FWPAmn operator with the square-root fuzzy weighted power average (SR-FWPA), the nth power root fuzzy weighted power average (nPR-FWPA), the Fermatean fuzzy weighted power average (FFWPA), and the n,m-rung orthopair fuzzy weighted power average (n,m-ROFWPA) operators.

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Section: Comparison Analysis and Discussionmentioning

confidence: 99%

“…Ibrahim and Alshammari [16] proposed the n,m-rung orthopair fuzzy weighted power average. Ibrahim et al [35] developed a new weighted aggregated operator via n th power root fuzzy sets.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator

Hamadneh,

Ibrahim,

Abualhomos

et al. 2023

Symmetry

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Roughness of linear Diophantine fuzzy sets by intuitionistic fuzzy relations over dual universes with decision-making applications

Gul,

Ayub,

Shabir

et al. 2024

Comp. Appl. Math.

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$$k^{n}_{m}$$-Rung picture fuzzy information in a modern approach to multi-attribute group decision-making

Ibrahim,

Al-shami,

Arar

et al. 2023

Complex Intell. Syst.

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A useful tool for expressing fuzziness and uncertainty is the recently developed n,m-rung orthopair fuzzy set (n,m-ROFS). Due to their superior ability to manage uncertain situations compared to theories of q-rung orthopair fuzzy sets, the n,m-rung orthopair fuzzy sets have variety of applications in decision-making in daily life. To deal with ambiguity and unreliability in multi-attribute group decision-making, this study introduces a novel tool called $$k^{n}_{m}$$ k m n -rung picture fuzzy set ($$k^{n}_{m}$$ k m n -RPFS). The suggested $$k^{n}_{m}$$ k m n -RPFS incorporates all of the benefits of n,m-ROFS and represents both the quantitative and qualitative analyses of the decision-makers. The presented model is a fruitful advancement of the q-rung picture fuzzy set (q-RPFS). Furthermore, numerous of its key notions, including as complement, intersection, and union are explained and illustrated with instances. In many decision-making situations, the main benefit of $$k^{n}_{m}$$ k m n -rung picture fuzzy sets is the ability to express more uncertainty than q-rung picture fuzzy sets. Then, along with their numerous features, we discover the basic set of operations for the $$k^{n}_{m}$$ k m n -rung picture fuzzy sets. Importantly, we present a novel operator, $$k^{n}_{m}$$ k m n -rung picture fuzzy weighted power average ($$k^{n}_{m}$$ k m n -RPFWPA) over $$k^{n}_{m}$$ k m n -rung picture fuzzy sets, and use it to multi-attribute decision-making issues for evaluating alternatives with $$k^{n}_{m}$$ k m n -rung picture fuzzy information. Additionally, we use this operator to pinpoint the countries with the highest expat living standards and demonstrate how to choose the best option by comparing aggregate findings and applying score values. Finally, we compare the outcomes of the q-RPFEWA, SFWG, PFDWA, SFDWA, and SFWA operators to those of the $$k^{n}_{m}$$ k m n -RPFWPA operator.

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Applications of nth Power Root Fuzzy Sets in Multicriteria Decision Making

Cited by 13 publications

References 28 publications

Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator

Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator

Roughness of linear Diophantine fuzzy sets by intuitionistic fuzzy relations over dual universes with decision-making applications

$$k^{n}_{m}$$-Rung picture fuzzy information in a modern approach to multi-attribute group decision-making

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