A Monotonous Intuitionistic Fuzzy TOPSIS Method Under General Linear Orders via Admissible Distance Measures

Wu, Xinxing; Zhu, Zhiyi; Chen, Chuan; Chen, Guanrong; Лю, Пэйдэ

doi:10.1109/tfuzz.2022.3205435

Cited by 13 publications

(7 citation statements)

References 62 publications

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“…From Table 7 , which shows a comparison of the preference orders of the alternatives in Example 4.2 for different TOPSIS methods, we observe that although our ranking result is different from these obtained by the TOPSIS method in 25 , 35 , 43 , the most desirable mask type is always –particulate respirators (N95). Note that the scores of on the attributes , , and (by Table 5 ) are much greater than that of .…”

Section: Applicationsmentioning

confidence: 58%

“…Szmidt 24 considered IFDisMs and IFSimMs and divided them into two types of IFSs according to 2-dimensional (2D) and 3-dimensional (3D) representations. However, Wu et al 25 used some examples to show that many existing 3D IFDisMs and IFSimMs, including Euclidean DisM and SimM 24 , Minkowski DisM and SimM 26 , 27 , do not satisfy the axiomatic definitions of IFDisMs and IFSimMs. Burillo and Bustince 28 introduced the 2D Hamming IFDisM.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear strict distance and similarity measures for intuitionistic fuzzy sets with applications to pattern classification and medical diagnosis

Wu,

Tang,

Zhu

et al. 2023

Sci Rep

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In this paper, we propose a new type of nonlinear strict distance and similarity measures for intuitionistic fuzzy sets (IFSs). Our proposed methods not only have good properties, but also improve the drawbacks proposed by Mahanta and Panda (Int J Intell Syst 36(2):615–627, 2021) in which, for example, their distance value of $$d_{_{\textrm{MP}}}(\langle \mu , \nu \rangle , \langle 0, 0\rangle )$$ d MP ( ⟨ μ , ν ⟩ , ⟨ 0 , 0 ⟩ ) is always equal to the maximum value 1 for any intuitionistic fuzzy number $$\langle \mu , \nu \rangle \ne \langle 0, 0\rangle $$ ⟨ μ , ν ⟩ ≠ ⟨ 0 , 0 ⟩ . To resolve these problems in Mahanta and Panda (Int J Intell Syst 36(2):615–627, 2021), we establish a nonlinear parametric distance measure for IFSs and prove that it satisfies the axiomatic definition of strict intuitionistic fuzzy distances and preserves all advantages of distance measures. In particular, our proposed distance measure can effectively distinguish different IFSs with high hesitancy. Meanwhile, we obtain that the dual similarity measure and the induced entropy of our proposed distance measure satisfy the axiomatic definitions of strict intuitionistic fuzzy similarity measure and intuitionistic fuzzy entropy. Finally, we apply our proposed distance and similarity measures to pattern classification, decision making on the choice of a proper antivirus face mask for COVID-19, and medical diagnosis problems, to illustrate the effectiveness of the new methods.

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Section: Applicationsmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Nonlinear strict distance and similarity measures for intuitionistic fuzzy sets with applications to pattern classification and medical diagnosis

Wu,

Tang,

Zhu

et al. 2023

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, noticeably, because the indeterminacy degree is uniquely determined by the membership and nonmembership degrees, the space of all IFVs is essentially a 2-D topological structure. This indicates a serious problem that many existing distance and similarity measures via 3-D representation of IFSs, including Euclidean SimM in [42] and Minkowski SimM in ( [50,24]), do not meet the axiomatic definition of IFSimMs (see [47,Section 3]).…”

Section: Introductionmentioning

confidence: 99%

“…For 3-D IFDisMs and IFSimMs, Xu and Chen [52] suggested some IFSimMs based on the idea of TOPSIS of Hwang and Yoon [19]. Wu et al [47] pointed out that the IFSimM in [52,Eq. 14] based on the normalized Euclidean distance does not satisfy the axiomatic definition of IFSimMs.…”

Section: Introductionmentioning

confidence: 99%

Strict intuitionistic fuzzy distance/similarity measures based onJensen-Shannon divergence

Zhu

Garg

et al. 2023

Preprint

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Being a pair of dual concepts, the normalized distance and similarity measures are important tools fordecision-making and pattern recognition under an intuitionistic fuzzy set framework. A good normalizeddistance measure should ensure that its dual similarity measure satisfies the axiomatic definition in orderto be more effective for problems. In this paper, we first construct some counterexamples to illustrate thattwo existing measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures.We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values(IFVs), which can be directly judged by our intuition; (2) except for the endpoints, there exist infinitelymany pairs of IFVs, where the maximum distance 1 can be achieved under these two distances, leading tocounter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionisticfuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), andpropose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Weprove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropyis an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that ourproposed distance measure is completely superior to the existing ones.

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“…To enlarge the representing domain, Ullah et al [36] proposed the concept of complex Pythagorean fuzzy sets (CPyFSs), and Liu et al [20] introduced the concept of complex qrung orthopair fuzzy sets (Cq-ROFSs). Since then, CIFSs, CPyFSs, and Cq-ROFSs have been widely applied to various fields, such as MCDM/MADM [1][2][3][4][5][6]12,15,[20][21][22]24,25,32,38,40], medical diagnosis [13,[27][28][29]32], pattern recognition [12,13,27,36], cluster analysis [12,47], and image processing [16].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Hamming and Hausdorff 3D distance measures for complex pythagorean fuzzy sets and their applications in pattern recognition and medical diagnosis

Zhu

Ullah

et al. 2022

Complex Intell. Syst.

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Similarity measures are very effective and meaningful tool used for evaluating the closeness between any two attributes which are very important and valuable to manage awkward and complex information in real-life problems. Therefore, for better handing of fuzzy information in real life, Ullah et al. (Complex Intell Syst 6(1): 15–27, 2020) recently introduced the concept of complex Pythagorean fuzzy set (CPyFS) and also described valuable and dominant measures, called various types of distance measures (DisMs) based on CPyFSs. The theory of CPyFS is the essential modification of Pythagorean fuzzy set to handle awkward and complicated in real-life problems. Keeping the advantages of the CPyFS, in this paper, we first construct an example to illustrate that a DisM proposed by Ullah et al. does not satisfy the axiomatic definition of complex Pythagorean fuzzy DisM. Then, combining the 3D Hamming distance with the Hausdorff distance, we propose a new DisM for CPyFSs, which is proved to satisfy the axiomatic definition of complex Pythagorean fuzzy DisM. Moreover, similarly to some DisMs for intuitionistic fuzzy sets, we present some other new complex Pythagorean fuzzy DisMs. Finally, we apply our proposed DisMs to a building material recognition problem and a medical diagnosis problem to illustrate the effectiveness of our DisMs. Finally, we aim to compare the proposed work with some existing measures is to enhance the worth of the derived measures.

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A Monotonous Intuitionistic Fuzzy TOPSIS Method Under General Linear Orders via Admissible Distance Measures

Cited by 13 publications

References 62 publications

Nonlinear strict distance and similarity measures for intuitionistic fuzzy sets with applications to pattern classification and medical diagnosis

Nonlinear strict distance and similarity measures for intuitionistic fuzzy sets with applications to pattern classification and medical diagnosis

Strict intuitionistic fuzzy distance/similarity measures based onJensen-Shannon divergence

Analysis of Hamming and Hausdorff 3D distance measures for complex pythagorean fuzzy sets and their applications in pattern recognition and medical diagnosis

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