A new distance measure based on Pythagorean hesitant fuzzy sets and its application to multi-criteria decision making

Yanru Zhong, Xiuyan Guo, Hong Gao, Meifa Huang, Yuchu Qin, Xiaonan Luo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The Pythagorean fuzzy set is characterized by five parameters, namely membership degree, non-membership degree, indeterminacy degree, strength of commitment about membership, and direction of commitment. And distance measure is an important index in Pythagorean Hesitant fuzzy (PHF) environment when solving the multicriteria decision-making problem. However, the existing distance measure considers the difference between the member ship degrees, the non-membership degrees, and the degrees of indeterminacy, but ignores the influence of the difference between the directions of PHF sets (PHFSs). The existing distance measure method may lead to unreasonable results sometimes. Inspired by above, the five parameters of PFS are extended to Pythagorean Hesitant Fuzzy set (PHFS) fully in this paper, generating new distance measures of PHFS and introducing some properties and theorems firstly. Then, the proposed method is applied in MCDM with PHF information by considering the distance between the positive ideal solution and each alternative. Finally, to validate the effectiveness of the proposed method, a pragmatic experiment is introduced for comparisons with existing methods.
Original languageEnglish
Title of host publicationThe Second International Conference on Image, Video Processing and Artificial Intelligence
Subtitle of host publicationIVPAI 2019
EditorsRuidan Su
PublisherSPIE
Number of pages8
Volume11321
ISBN (Electronic)9781510634107
ISBN (Print)9781510634091
DOIs
Publication statusPublished - 27 Nov 2019
EventThe Second International Conference on Image, Video Processing and Artifical Intelligence - Shanghai Advanced Research Institute, Shanghai, China
Duration: 23 Aug 201925 Aug 2019

Publication series

NameProceedings of SPIE
PublisherSPIE
Volume11321
ISSN (Print)0277-786X
ISSN (Electronic)1996-576X

Conference

ConferenceThe Second International Conference on Image, Video Processing and Artifical Intelligence
Abbreviated titleIVPAI 2019
CountryChina
CityShanghai
Period23/08/1925/08/19

Fingerprint

Fuzzy sets
Decision making
Ships
Experiments

Cite this

Zhong, Y., Guo, X., Gao, H., Huang, M., Qin, Y., & Luo, X. (2019). A new distance measure based on Pythagorean hesitant fuzzy sets and its application to multi-criteria decision making. In R. Su (Ed.), The Second International Conference on Image, Video Processing and Artificial Intelligence: IVPAI 2019 (Vol. 11321). [113212M] (Proceedings of SPIE; Vol. 11321). SPIE. https://doi.org/10.1117/12.2541318
Zhong, Yanru ; Guo, Xiuyan ; Gao, Hong ; Huang, Meifa ; Qin, Yuchu ; Luo, Xiaonan. / A new distance measure based on Pythagorean hesitant fuzzy sets and its application to multi-criteria decision making. The Second International Conference on Image, Video Processing and Artificial Intelligence: IVPAI 2019. editor / Ruidan Su. Vol. 11321 SPIE, 2019. (Proceedings of SPIE).
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title = "A new distance measure based on Pythagorean hesitant fuzzy sets and its application to multi-criteria decision making",
abstract = "The Pythagorean fuzzy set is characterized by five parameters, namely membership degree, non-membership degree, indeterminacy degree, strength of commitment about membership, and direction of commitment. And distance measure is an important index in Pythagorean Hesitant fuzzy (PHF) environment when solving the multicriteria decision-making problem. However, the existing distance measure considers the difference between the member ship degrees, the non-membership degrees, and the degrees of indeterminacy, but ignores the influence of the difference between the directions of PHF sets (PHFSs). The existing distance measure method may lead to unreasonable results sometimes. Inspired by above, the five parameters of PFS are extended to Pythagorean Hesitant Fuzzy set (PHFS) fully in this paper, generating new distance measures of PHFS and introducing some properties and theorems firstly. Then, the proposed method is applied in MCDM with PHF information by considering the distance between the positive ideal solution and each alternative. Finally, to validate the effectiveness of the proposed method, a pragmatic experiment is introduced for comparisons with existing methods.",
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Zhong, Y, Guo, X, Gao, H, Huang, M, Qin, Y & Luo, X 2019, A new distance measure based on Pythagorean hesitant fuzzy sets and its application to multi-criteria decision making. in R Su (ed.), The Second International Conference on Image, Video Processing and Artificial Intelligence: IVPAI 2019. vol. 11321, 113212M, Proceedings of SPIE, vol. 11321, SPIE, The Second International Conference on Image, Video Processing and Artifical Intelligence, Shanghai, China, 23/08/19. https://doi.org/10.1117/12.2541318

A new distance measure based on Pythagorean hesitant fuzzy sets and its application to multi-criteria decision making. / Zhong, Yanru; Guo, Xiuyan; Gao, Hong; Huang, Meifa; Qin, Yuchu; Luo, Xiaonan.

The Second International Conference on Image, Video Processing and Artificial Intelligence: IVPAI 2019. ed. / Ruidan Su. Vol. 11321 SPIE, 2019. 113212M (Proceedings of SPIE; Vol. 11321).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AU - Qin, Yuchu

AU - Luo, Xiaonan

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AB - The Pythagorean fuzzy set is characterized by five parameters, namely membership degree, non-membership degree, indeterminacy degree, strength of commitment about membership, and direction of commitment. And distance measure is an important index in Pythagorean Hesitant fuzzy (PHF) environment when solving the multicriteria decision-making problem. However, the existing distance measure considers the difference between the member ship degrees, the non-membership degrees, and the degrees of indeterminacy, but ignores the influence of the difference between the directions of PHF sets (PHFSs). The existing distance measure method may lead to unreasonable results sometimes. Inspired by above, the five parameters of PFS are extended to Pythagorean Hesitant Fuzzy set (PHFS) fully in this paper, generating new distance measures of PHFS and introducing some properties and theorems firstly. Then, the proposed method is applied in MCDM with PHF information by considering the distance between the positive ideal solution and each alternative. Finally, to validate the effectiveness of the proposed method, a pragmatic experiment is introduced for comparisons with existing methods.

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BT - The Second International Conference on Image, Video Processing and Artificial Intelligence

A2 - Su, Ruidan

PB - SPIE

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Zhong Y, Guo X, Gao H, Huang M, Qin Y, Luo X. A new distance measure based on Pythagorean hesitant fuzzy sets and its application to multi-criteria decision making. In Su R, editor, The Second International Conference on Image, Video Processing and Artificial Intelligence: IVPAI 2019. Vol. 11321. SPIE. 2019. 113212M. (Proceedings of SPIE). https://doi.org/10.1117/12.2541318