Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

Ruan, Chuan-Yang; Chen, Xiangjing; Lv, Han

doi:10.32604/cmc.2023.035480

Cited by 5 publications

(5 citation statements)

References 60 publications

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“…Definition 2 [19]. Let X be a non-empty set, then a Fermatean hesitant fuzzy set (FHFS) H defined on X is given as:…”

Section: Fermatean Fuzzy Setsmentioning

confidence: 99%

“…In reality, the attributes involved in the decision-making process are not always independent of each other and often have certain correlations. Therefore, considering the n ∑ i=1 p i l > (19) where ω = (ω 1 , ω 2 , . .…”

Section: Hamacher Choquet Integral Aggregation Operators Of Pivfhfssmentioning

confidence: 99%

“…( ) 1 ( ) [0.5, 0.7], 0.5) be two PIVFHFEs and ω = (0.7, 0.3) T be the weighting vector of M i (i = 1, 2). Assume that δ = 1.5 , then calculate PIVFHFHWA (M 1 , M 2 ) by Equation (19).…”

Section: Hamacher Choquet Integral Aggregation Operators Of Pivfhfssmentioning

confidence: 99%

“…Kirisci [18] presented an extended version of the ELimination Et Choix Traduisant la REalité (ELECTRE) I method under the Fermatean fuzzy environment for solving multi-criteria group decision-making (MCGDM) problems. To solve the problem of multiple membership degrees under Fermatean fuzzy environment, Ruan et al [19] introduced the concept of Fermatean hesitant fuzzy set (FHFS) and proposed a prioritized Heronian mean operator for FHFSs. Mishra [20] defined several distance measures of FHFSs and developed the remoteness index-based Fermatean hesitant fuzzy-VIKOR MADM method.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Interval-Valued Fermatean Hesitant Fuzzy Set and Its Application to Multi-Attribute Decision Making

Ruan,

Chen

2023

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It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and interval values into Fermatean hesitant fuzzy set (FHFS) and creatively proposes the probabilistic interval-valued Fermatean hesitant fuzzy set (PIVFHFS) to deal with information loss. This new fuzzy set allows decision makers to use interval-valued information with probability to express their quantitative evaluation, which broadens the range of information expression, effectively reflects the important degree of different membership degrees, and can describe uncertain information more completely and accurately. Under the probabilistic interval-valued Fermatean hesitant fuzzy environment, several new aggregation operators based on Hamacher operation are proposed, including the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher weighted averaging (PIVFHFHWA) operator and geometric (PIVFHFHWG) operator, and their basic properties and particular forms are studied. Then, considering the general correlation between different attributes, this paper defines the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher Choquet integral averaging (PIVFHFHCIA) operator and geometric (PIVFHFHCIG) operator and discusses related properties. Finally, a multi-attribute decision-making (MADM) method is presented and applied to the decision-making problem of reducing carbon emissions of manufacturers in the supply chain. The stability and feasibility of this method are demonstrated by sensitivity analysis and comparative analysis. The proposed new operators can not only consider the correlation between various factors but also express the preference information of decision makers more effectively by using probability, thus avoiding information loss in decision-making progress to some extent.

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“…Definition 2 [19]. Let X be a non-empty set, then a Fermatean hesitant fuzzy set (FHFS) H defined on X is given as:…”

Section: Fermatean Fuzzy Setsmentioning

confidence: 99%

Section: Hamacher Choquet Integral Aggregation Operators Of Pivfhfssmentioning

confidence: 99%

“…( ) 1 ( ) [0.5, 0.7], 0.5) be two PIVFHFEs and ω = (0.7, 0.3) T be the weighting vector of M i (i = 1, 2). Assume that δ = 1.5 , then calculate PIVFHFHWA (M 1 , M 2 ) by Equation (19).…”

Section: Hamacher Choquet Integral Aggregation Operators Of Pivfhfssmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Probabilistic Interval-Valued Fermatean Hesitant Fuzzy Set and Its Application to Multi-Attribute Decision Making

Ruan,

Chen

2023

Axioms

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“…Pérez-Arellano et al [37] introduced a prioritized induced probabilistic (PIP) operator. Ruan et al [38] defined a new Fermatean hesitant fuzzy prioritized Heronian mean operator (FHFPHM) and applied it to solving MADM problems.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Interval Ordering Prioritized Averaging Operator and Its Application in Bank Investment Decision Making

Ruan,

Gong,

Chen

2023

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Probabilistic interval ordering, as a helpful tool for expressing positive and negative information, can effectively address multi-attribute decision-making (MADM) problems in reality. However, when dealing with a significant number of decision-makers and decision attributes, the priority relationships between different attributes and their relative importance are often neglected, resulting in deviations in decision outcomes. Therefore, this paper combines probability interval ordering, the prioritized aggregation (PA) operator, and the Gauss–Legendre algorithm to address the MADM problem with prioritized attributes. First, considering the significance of interval priority ordering and the distribution characteristics of attribute priority, the paper introduces probability interval ordering elements that incorporate attribute priority, and it proposes the probabilistic interval ordering prioritized averaging (PIOPA) operator. Then, the probabilistic interval ordering Gauss–Legendre prioritized averaging operator (PIOGPA) is defined based on the Gauss–Legendre algorithm, and various excellent properties of this operator are explored. This operator considers the priority relationships between attributes and their importance level, making it more capable of handling uncertainty. Finally, a new MADM method is constructed based on the PIOGPA operator using probability intervals and employs the arithmetic–geometric mean (AGM) algorithm to compute the weight of each attribute. The feasibility and soundness of the proposed method are confirmed through a numerical example and comparative analysis. The MADM method introduced in this paper assigns higher weights to higher-priority attributes to establish fixed attribute weights, and it reduces the impact of other attributes on decision-making results. It also utilizes the Gauss AGM algorithm to streamline the computational complexity and enhance the decision-making effectiveness.

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Intuitionistic Hesitant Fuzzy Partitioned Maclaurin Symmetric Mean Aggregation Operators-Based Algorithm and Its Application in Decision Making

Azeem,

Ali,

Ali

et al. 2023

IEEE Access

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Intuitionistic hesitant fuzzy sets, which enable the representation of an element's membership and non-membership as a set of multiple possible values, offer significant utility in describing uncertainty in various aspects of people's daily lives. Fundamental mathematical techniques known as intuitionistic hesitant fuzzy aggregation operators are employed to merge multiple inputs into a single result based on predetermined criteria. However, conventional approaches that rely on classic intuitionistic hesitant fuzzy aggregation operators have faced criticism due to their limited understanding of criteria characterization. We introduce two novel operators, namely the intuitionistic hesitant fuzzy partitioned Maclaurin symmetric mean (IHFPMSM) and intuitionistic hesitant fuzzy weighted partitioned Maclaurin symmetric mean (IHFWPMSM), which draw inspiration from the partitioned Maclaurin symmetric mean concept. Subsequently, we thoroughly examine various characteristics and special cases of these operators. Building upon the IHFWPMSM operator, we propose a novel multiple-criteria decision-making (MCDM) method that effectively selects the most suitable alternative from a set of options. To demonstrate the effectiveness of our proposed approach, we discuss a systematic methodology for selecting the optimal location for shoe company construction. Lastly, we demonstrate the superior prevalence and effectiveness of the developed approach through comprehensive comparative and sensitivity analyses, surpassing the capabilities of existing approaches.INDEX TERMS Intuitionistic hesitant fuzzy set, Maclaurin symmetric mean, partitioned Maclaurin symmetric mean, multiple criteria decision-making.

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Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

Cited by 5 publications

References 60 publications

Probabilistic Interval-Valued Fermatean Hesitant Fuzzy Set and Its Application to Multi-Attribute Decision Making

Probabilistic Interval-Valued Fermatean Hesitant Fuzzy Set and Its Application to Multi-Attribute Decision Making

Probabilistic Interval Ordering Prioritized Averaging Operator and Its Application in Bank Investment Decision Making

Intuitionistic Hesitant Fuzzy Partitioned Maclaurin Symmetric Mean Aggregation Operators-Based Algorithm and Its Application in Decision Making

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