Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering Analysis
Hesitant fuzzy set (HFS) permits several possible values as the membership degree of an element to a set to express the decision makers' hesitance. Since its appearance, HFS has been extensively applied in multi-attribute decision making, group decision making and evaluation process. Considerin...
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doaj-1c1238ef85dd4ecc9c14565714318f802021-03-30T01:59:52ZengIEEEIEEE Access2169-35362020-01-01811999512000810.1109/ACCESS.2020.30059279129753Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering AnalysisWenyi Zeng0https://orcid.org/0000-0002-8908-3329Rong Ma1https://orcid.org/0000-0002-7828-7932Qian Yin2https://orcid.org/0000-0002-0354-5490Zeshui Xu3https://orcid.org/0000-0003-3547-2908School of Artificial Intelligence, Beijing Normal University, Beijing, ChinaSchool of Artificial Intelligence, Beijing Normal University, Beijing, ChinaSchool of Artificial Intelligence, Beijing Normal University, Beijing, ChinaBusiness School, Sichuan University, Chengdu, ChinaHesitant fuzzy set (HFS) permits several possible values as the membership degree of an element to a set to express the decision makers' hesitance. Since its appearance, HFS has been extensively applied in multi-attribute decision making, group decision making and evaluation process. Considering that the similarity measure of hesitant fuzzy sets (HFSs) is an important index in intelligent system, and the implication function can describe many subtle differences which is very suitable for dealing with hesitant fuzzy information. In this paper, we merge implication function with HFS to investigate the similarity measure of HFSs, propose some new formulas to calculate the similarity measures of HFSs which are different from the existing similarity measures of HFSs based on the distance measure, and do some comparison analysis. Meanwhile, we introduce the union and intersection operations of HFSs, the hesitant fuzzy similar relation and the hesitant fuzzy equivalent relation, and develop the hesitant fuzzy clustering algorithm. Finally, three numerical examples are used to illustrate the effectiveness and validation of our proposed method.https://ieeexplore.ieee.org/document/9129753/Hesitant fuzzy setsimilarity measureimplication functionhesitant fuzzy equivalent relationclustering analysis |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Wenyi Zeng Rong Ma Qian Yin Zeshui Xu |
spellingShingle |
Wenyi Zeng Rong Ma Qian Yin Zeshui Xu Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering Analysis IEEE Access Hesitant fuzzy set similarity measure implication function hesitant fuzzy equivalent relation clustering analysis |
author_facet |
Wenyi Zeng Rong Ma Qian Yin Zeshui Xu |
author_sort |
Wenyi Zeng |
title |
Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering Analysis |
title_short |
Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering Analysis |
title_full |
Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering Analysis |
title_fullStr |
Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering Analysis |
title_full_unstemmed |
Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering Analysis |
title_sort |
similarity measure of hesitant fuzzy sets based on implication function and clustering analysis |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2020-01-01 |
description |
Hesitant fuzzy set (HFS) permits several possible values as the membership degree of an element to a set to express the decision makers' hesitance. Since its appearance, HFS has been extensively applied in multi-attribute decision making, group decision making and evaluation process. Considering that the similarity measure of hesitant fuzzy sets (HFSs) is an important index in intelligent system, and the implication function can describe many subtle differences which is very suitable for dealing with hesitant fuzzy information. In this paper, we merge implication function with HFS to investigate the similarity measure of HFSs, propose some new formulas to calculate the similarity measures of HFSs which are different from the existing similarity measures of HFSs based on the distance measure, and do some comparison analysis. Meanwhile, we introduce the union and intersection operations of HFSs, the hesitant fuzzy similar relation and the hesitant fuzzy equivalent relation, and develop the hesitant fuzzy clustering algorithm. Finally, three numerical examples are used to illustrate the effectiveness and validation of our proposed method. |
topic |
Hesitant fuzzy set similarity measure implication function hesitant fuzzy equivalent relation clustering analysis |
url |
https://ieeexplore.ieee.org/document/9129753/ |
work_keys_str_mv |
AT wenyizeng similaritymeasureofhesitantfuzzysetsbasedonimplicationfunctionandclusteringanalysis AT rongma similaritymeasureofhesitantfuzzysetsbasedonimplicationfunctionandclusteringanalysis AT qianyin similaritymeasureofhesitantfuzzysetsbasedonimplicationfunctionandclusteringanalysis AT zeshuixu similaritymeasureofhesitantfuzzysetsbasedonimplicationfunctionandclusteringanalysis |
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