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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Vydáno v:Soft computing (Berlin, Germany) Ročník 23; číslo 2; s. 393 - 405
Hlavní autoři: Wen, Miaomiao, Zhao, Hua, Xu, Zeshui
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2019
Springer Nature B.V
Témata:
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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Shrnutí: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.
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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-018-3359-7