Hesitant fuzzy Lukasiewicz implication operation and its application to alternatives’ sorting and clustering analysis

Hesitant fuzzy set (HFS) takes several possible values as the membership degree of an element to a set to express the decision makers’ hesitance when making decisions. Since its appearance, the HFS has been widely used in many fields, such as decision making, clustering analysis. Lukasiewicz implica...

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Published in:	Soft computing (Berlin, Germany) Vol. 23; no. 2; pp. 393 - 405
Main Authors:	Wen, Miaomiao, Zhao, Hua, Xu, Zeshui
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2019 Springer Nature B.V
Subjects:	Algorithms Artificial Intelligence Cluster analysis Clustering Computational Intelligence Control Decision analysis Decision making Engineering Foundations Fuzzy logic Fuzzy sets Mathematical Logic and Foundations Mechatronics Methods Robotics Similarity measures Sorting algorithms Alternative sorting Clustering analysis Hesitant fuzzy set Hesitant fuzzy square product Lukasiewicz implication operator
ISSN:	1432-7643, 1433-7479
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Abstract	Hesitant fuzzy set (HFS) takes several possible values as the membership degree of an element to a set to express the decision makers’ hesitance when making decisions. Since its appearance, the HFS has been widely used in many fields, such as decision making, clustering analysis. Lukasiewicz implication operator, an indispensable part of implication operators, can grasp more nuances compared with the others. In this paper, we shall combine the Lukasiewicz implication operator with HFSs to realize a direct clustering analysis algorithm and a novel alternative sorting method in decision making under hesitant fuzzy environment. To do that, we first apply the Lukasiewicz implication operator to deal with HFEs by getting a hesitant fuzzy Lukasiewicz implication operator, and then construct a hesitant fuzzy triangle product and a hesitant fuzzy square product based on the new implication operator. After that, the hesitant fuzzy square product is applied to define the similarity degree between HFSs, and based on which, we develop a direct clustering algorithm for hesitant fuzzy information. Meanwhile, the hesitant fuzzy triangle product is used to induce a new alternative sorting method. Finally, two numerical examples are given to illustrate the effectiveness and practicability of our method and algorithm, one of which involves the evaluation analysis of the Arctic development risk.
AbstractList	Hesitant fuzzy set (HFS) takes several possible values as the membership degree of an element to a set to express the decision makers’ hesitance when making decisions. Since its appearance, the HFS has been widely used in many fields, such as decision making, clustering analysis. Lukasiewicz implication operator, an indispensable part of implication operators, can grasp more nuances compared with the others. In this paper, we shall combine the Lukasiewicz implication operator with HFSs to realize a direct clustering analysis algorithm and a novel alternative sorting method in decision making under hesitant fuzzy environment. To do that, we first apply the Lukasiewicz implication operator to deal with HFEs by getting a hesitant fuzzy Lukasiewicz implication operator, and then construct a hesitant fuzzy triangle product and a hesitant fuzzy square product based on the new implication operator. After that, the hesitant fuzzy square product is applied to define the similarity degree between HFSs, and based on which, we develop a direct clustering algorithm for hesitant fuzzy information. Meanwhile, the hesitant fuzzy triangle product is used to induce a new alternative sorting method. Finally, two numerical examples are given to illustrate the effectiveness and practicability of our method and algorithm, one of which involves the evaluation analysis of the Arctic development risk.
Author	Wen, Miaomiao Zhao, Hua Xu, Zeshui
Author_xml	– sequence: 1 givenname: Miaomiao surname: Wen fullname: Wen, Miaomiao organization: Department of Basic Education, PLA Army Engineering University – sequence: 2 givenname: Hua surname: Zhao fullname: Zhao, Hua organization: Department of Basic Education, PLA Army Engineering University – sequence: 3 givenname: Zeshui surname: Xu fullname: Xu, Zeshui email: xuzeshui@263.net organization: Department of Basic Education, PLA Army Engineering University
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Cites_doi	10.1016/j.asoc.2014.03.037 10.3233/IFS-151795 10.1007/s00500-015-2002-0 10.1016/S0019-9958(65)90241-X 10.1016/j.cie.2012.01.007 10.1016/S0165-0114(86)80034-3 10.1007/3-540-56735-6_47 10.1016/j.patrec.2016.11.001 10.1016/S0167-8655(99)00069-0 10.1142/S0219622013500053 10.1016/j.ijar.2010.09.002 10.1007/s00500-015-1775-5 10.1016/j.asoc.2016.06.037 10.1016/j.dss.2016.01.002 10.1016/j.ins.2015.07.057 10.1016/j.asoc.2015.12.022 10.1016/j.apm.2012.04.031 10.1080/03081078608934952 10.3233/IFS-152057 10.1007/s11766-014-3091-8 10.1016/j.knosys.2017.03.010 10.1109/FUZZY.2009.5276884 10.1109/CCDC.2014.6852948 10.3233/IFS-130978
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Keywords	Alternative sorting Clustering analysis Hesitant fuzzy set Hesitant fuzzy square product Lukasiewicz implication operator
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Snippet	Hesitant fuzzy set (HFS) takes several possible values as the membership degree of an element to a set to express the decision makers’ hesitance when making...
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StartPage	393
SubjectTerms	Algorithms Artificial Intelligence Cluster analysis Clustering Computational Intelligence Control Decision analysis Decision making Engineering Foundations Fuzzy logic Fuzzy sets Mathematical Logic and Foundations Mechatronics Methods Robotics Similarity measures Sorting algorithms
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Title	Hesitant fuzzy Lukasiewicz implication operation and its application to alternatives’ sorting and clustering analysis
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Volume	23
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