Distance measure on intuitionistic fuzzy sets and its application in decision‐making, pattern recognition, and clustering problems

Gohain, Brindaban; Chutia, Rituparna; Dutta, Palash

doi:10.1002/int.22780

Cited by 65 publications

(21 citation statements)

References 58 publications

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“…This is a serious challenge to face up to the uncertain and fuzzy data in real-life applications involving many fields such as industry, environment science, and engineering so on. Atanassov was the first to propose the intuitionistic fuzzy sets (IFSs) [ 1 , 2 ]. IFSs are very efficient and useful mathematical techniques for dealing with ambiguous data [ 3 – 5 ], which are represented by the membership degree (MSD) and non-membership degree (NMSD), and also have the restriction that [ 6 ].…”

Section: Introductionmentioning

confidence: 99%

A new multi-attribute decision making approach based on new score function and hybrid weighted score measure in interval-valued Fermatean fuzzy environment

Qin

Peng

et al. 2023

Complex Intell. Syst.

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Interval-valued Fermatean fuzzy sets (IVFFSs) were introduced as a more effective mathematical tool for handling uncertain information in 2021. In this paper, firstly, a novel score function (SCF) is proposed based on IVFFNs that can distinguish between any two IVFFNs. And then, the novel SCF and hybrid weighted score measure were used to construct a new multi-attribute decision-making (MADM) method. Besides, three cases are used to demonstrate that our proposed method can overcome the disadvantages that the existing approaches cannot obtain the preference orderings of alternatives in some circumstances and involves the existence of division by zero error in the decision procedure. Compared with the two existing MADM methods, our proposed approach has the highest recognition index and the lowest error rate of division by zero. Our proposed method provides a better approach to dealing with the MADM problem in the interval-valued Fermatean fuzzy environment.

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Section: Introductionmentioning

confidence: 99%

A new multi-attribute decision making approach based on new score function and hybrid weighted score measure in interval-valued Fermatean fuzzy environment

Qin

Peng

et al. 2023

Complex Intell. Syst.

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“…There are partition-based [1], hierarchy-based [2], grid-based [3], model-based [4], and density-based [5] Clustering algorithms. Clustering has many applications, such as image segmentation [6,7], pattern recognition [8], recommender system [9], gene expression [10], and intrusion detection [11].…”

Section: Introductionmentioning

confidence: 99%

Density Peaks Clustering Based on Potential Model and Diffusion Strength

et al. 2022

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Density peaks clustering (DPC) is a simple and efficient density-based clustering algorithm without complex iterative procedures. However, DPC needs to manually choose clustering centers via a decision graph, which often can't identify real centers and breaks the continuous flow of the algorithm. In addition, DPC is highly sensitive to the cut-off distance and suffers from the domino chain reaction. To surmount the aforementioned deficiencies, an improved density peaks clustering based on potential model and diffusion strength (DPC-PMDS) is proposed in this paper. Firstly, we utilize the potential and centrality of data points to calculate the density instead of the cut-off distance. Secondly, inspired by the information diffusion in social networks, we define the influence of data points and the diffusion strength between data points, and realize the diffusion of label from each center to the core data points while selecting clustering centers. Through this process, the core structure of each clustering is obtained and the centers are accurately identified. Finally, the distances from the boundary points to each cluster computed based on centrality are applied to assign boundary points to avoid chain reaction. Extensive experiments on synthetic, UCI and Olivetti Faces datasets demonstrate that DPC-PMDS can achieve excellent clustering results over other state-of-art algorithms, especially on datasets with complex shapes and uneven density distribution.

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“…Similarity measures and distance measures are two important tools that are broadly used in various applications in decision‐making, pattern recognition, and clustering problems. A lot of similarity measures and distance measures are developed under the fuzzy sets and IFSs 6,7 . Since PFSs are a newer concept, not many studies are evident in similarity and distance measures of PFSs.…”

Section: Introductionmentioning

confidence: 99%

“…A lot of similarity measures and distance measures are developed under the fuzzy sets and IFSs. 6,7 Since PFSs are a newer concept, not many studies are evident in similarity and distance measures of PFSs. A brief review of such studies is followed in the next subsection.…”

Section: Introductionmentioning

confidence: 99%

Discrete similarity measures on Pythagorean fuzzy sets and its applications to medical diagnosis and clustering problems

Gohain

Chutia

Dutta

2022

Int J of Intelligent Sys

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Pythagorean fuzzy sets are an extension of intuitionistic fuzzy sets and are more efficient from an application perspective. Though the Pythagorean fuzzy sets are more informative, not much work on similarity measures is available in the literature. Furthermore, existing similarity measures are not efficient. Also, the containment property in Pythagorean fuzzy units is not correctly defined or ineffective. As a result, the existing similarity measures do not reflect appropriate information between the Pythagorean fuzzy sets. The scalar function of the Yager is mainly used for verifying the validity of similarity measures. Most of the existing similarity measures do not conform to the Yager scalar function. Hence, the existing similarity measures exhibit some discrepancies. Furthermore, the existing similarity measures are inconsistent in determining the similarity in intuitionsitic and Pythagorean fuzzy sets. In some real‐world modeling issues, past, present, and cross‐time information are essential. However, such information is missing in the existing similarity measures. Therefore, in this paper, two new measures of similarity are being developed based on the deviation of the parameters: membership degree, nonmembership degree, strength of commitment, direction of commitment, and cross‐time evaluation factors. Under this construction, the proposed similarity measures effectively measure the similarity between the Pythagorean fuzzy sets. Furthermore, the newly defined containment property is also reflected in the proposed similarity measures, which were a limitation in most cases. Moreover, Yager's scalar function is also reflected by the proposed similarity measures. The complement of given information is also essential in some real‐world problems. However, such information is incomplete in the theory of Pythagorean fuzzy sets. Hence, the complement of the Pythagorean fuzzy set is being redefined, and a few related results on similarity measures are proposed. Finally, the proposed similarity measures are tested for applicability to medical diagnosis and clustering problems through some hypothetical case studies.

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Distance measure on intuitionistic fuzzy sets and its application in decision‐making, pattern recognition, and clustering problems

Cited by 65 publications

References 58 publications

A new multi-attribute decision making approach based on new score function and hybrid weighted score measure in interval-valued Fermatean fuzzy environment

A new multi-attribute decision making approach based on new score function and hybrid weighted score measure in interval-valued Fermatean fuzzy environment

Density Peaks Clustering Based on Potential Model and Diffusion Strength

Discrete similarity measures on Pythagorean fuzzy sets and its applications to medical diagnosis and clustering problems

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