Similarity Measures of T-Spherical Fuzzy Sets Based on the Cosine Function and Their Applications in Pattern Recognition

Wu, Meiqin; Chen, Ting-You; Jian, Fan

doi:10.1109/access.2020.2997131

Cited by 29 publications

(12 citation statements)

References 50 publications

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“…From the fourth column of Table 4, the sample B 1 should have belonged to the pattern P 3 and in the sixth column of Table 4, the sample B 2 should have belonged to the pattern P 2 . The results derived by the similarity measure proposed by Zhang et al [4] are the same as decided by Chu et al [44], Julian et al [17], Tung et al [21], Li and Wan [43], Yusoff et al [45], Zeng [46], Dutta [47], Rafiq et al [48], Khan et al [49], Muthuraj et al [50], and Wu et al [51]. Our fourth example illustrates that the similarity measure proposed by Zhang et al [4] can be applied for a practical application of fault diagnosis of turbine generators.…”

Section: Examplesupporting

confidence: 61%

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The Fourth Axiom of Similarity Measures

2020

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In this research, the fourth axiom to improve the well-defined examination of similarity measures is studied, where the measures have a symmetric structure. We first provide a theoretic enhancement of three correlation coefficient similarity measures that were proposed by a source paper. Second, we use the same numerical example proposed by the source paper for pattern recognition problems to illustrate that the weighted correlation coefficient similarity measure is dependent on the set of weights. Finally, we demonstrate that the correlation coefficient similarity measure in the intuitionistic fuzzy set environment can address the issue of practical fault diagnosis when solving the turbine engine problems using similarity measures with symmetric characteristics.

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Section: Examplesupporting

confidence: 61%

“…: y ∈ Y , two T-spherical fuzzy sets, where s A (y), i A (y), d A (y) and r A (y) : X → [0, 1] are the membership, hesitancy, non-membership, and refusal degree, Wu et al [51] assumed two cosine similarity measures, TSFCS 1 (A, B) and TSFCS 2 (A, B), in the following:…”

Section: Examplementioning

confidence: 99%

The Fourth Axiom of Similarity Measures

2020

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“…In the future, we will adjust the hypothesis of complex q-rung orthopair fuzzy sets [40], complex spherical fuzzy sets [41], complex T-spherical fuzzy sets [42], linear Diophantine fuzzy sets [43], Pythagorean m-polar fuzzy sets [44], and T-spherical fuzzy sets [45][46][47][48][49][50] to advance the excellence of the created works.…”

Section: Discussionmentioning

confidence: 99%

Prioritized Muirhead Mean Aggregation Operators under the Complex Single-Valued Neutrosophic Settings and Their Application in Multi-Attribute Decision-Making

Mahmood

Ali

2021

JCCE

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Two critical tasks in multi-attribute decision making (MADM) are to describe criterion values and to aggregate the described information to generate a ranking of alternatives. A flexible and superior tool for the first task is complex single-valued neutrosophic (CSVN) setting and, a powerful device for the subsequent assignment is aggregation operator. Up until this point, almost thirty diverse aggregation operators of CSVN have been introduced. Every operator has its unmistakable qualities and can function admirably for explicit reason. Notwithstanding, there isn't yet an operator which can give helpful consensus and adaptability in conglomerating rule esteems, managing the heterogeneous interrelationships among models, and decreasing the impact of outrageous basis esteems. In genuine decision-making interaction, there are cases that the interrelationships of contentions don't exist in every one of the contentions, however in piece of the contentions. Subsequently, there is a need to parcel the contentions into various parts. For this, the technique of prioritized Muirhead mean (PMM) aggregation operator is massive dominant and more flexible is to investigate the interrelationships between any numbers of objects. The goal of this study is to initiate the CSVN setting and to determine their important algebraic laws. Moreover, to provide such an aggregation operator, the principle of CSVN PMM (CSVNPMM) operator and CSVN prioritized dual Muirhead mean (CSVNPDMM) operator is elaborated and discussed their particular cases. Further, based on these operators, we presented a new method to deal with the multi-attribute decision making problems under the fuzzy environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

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“…In this section, we make comparisons of the results using the proposed SM for TSFSs with the results using the SM for TSFSs proposed by Ullah et al [26] and Wu et al [33]. Table 3 summarizes the findings.…”

Section: Comparative Studymentioning

confidence: 98%

Similarity Measures Based on T-Spherical Fuzzy Information with Applications to Pattern Recognition and Decision Making

et al. 2022

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T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM’s validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work’s reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future.

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Similarity Measures of T-Spherical Fuzzy Sets Based on the Cosine Function and Their Applications in Pattern Recognition

Cited by 29 publications

References 50 publications

The Fourth Axiom of Similarity Measures

The Fourth Axiom of Similarity Measures

Prioritized Muirhead Mean Aggregation Operators under the Complex Single-Valued Neutrosophic Settings and Their Application in Multi-Attribute Decision-Making

Similarity Measures Based on T-Spherical Fuzzy Information with Applications to Pattern Recognition and Decision Making

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