Journal ArticleDOI
Clustering algorithm for intuitionistic fuzzy sets
Zeshui Xu,Jian Chen,Junjie Wu +2 more
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TLDR
This paper defines the concepts of association matrix and equivalent association matrix, and introduces some methods for calculating the association coefficients of IFSs, and proposes a clustering algorithm for IFS's, which is extended to cluster interval-valued intuitionistic fuzzy sets (IVIFSs).About:
This article is published in Information Sciences.The article was published on 2008-10-01. It has received 385 citations till now. The article focuses on the topics: Fuzzy clustering & Fuzzy associative matrix.read more
Citations
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Distance and similarity measures for hesitant fuzzy sets
Zeshui Xu,Meimei Xia +1 more
TL;DR: A variety of distance measures for hesitant fuzzy sets are proposed, based on which the corresponding similarity measures can be obtained and can alleviate the influence of unduly large deviations on the aggregation results by assigning them low (or high) weights.
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Dual Hesitant Fuzzy Sets
Bin Zhu,Zeshui Xu,Meimei Xia +2 more
TL;DR: This paper proposes dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy Sets, hesitant fuzzy set, and fuzzy multisets as special cases, and investigates the basic operations and properties of DHFSs.
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On distance and correlation measures of hesitant fuzzy information
Zeshui Xu,Meimei Xia +1 more
TL;DR: This paper defines the distance and correlation measures for hesitant fuzzy information and then discusses their properties in detail, finding that the results are the smallest ones among those when the values in two hesitant fuzzy elements are arranged in any permutations.
Journal ArticleDOI
Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis
TL;DR: The interval-valued HFSs and the corresponding correlation coefficient formulas are developed and demonstrated their application in clustering with intervals-valued hesitant fuzzy information through a specific numerical example.
Journal ArticleDOI
Choquet integrals of weighted intuitionistic fuzzy information
TL;DR: The Choquet integral is used to propose some intuitionistic fuzzy aggregation operators that not only consider the importance of the elements or their ordered positions, but also can reflect the correlations among the elements and theirordered positions.
References
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Book
Fuzzy sets
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Journal ArticleDOI
Data clustering: a review
TL;DR: An overview of pattern clustering methods from a statistical pattern recognition perspective is presented, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners.
Journal ArticleDOI
Intuitionistic fuzzy sets
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Book
Cluster Analysis
TL;DR: This fourth edition of the highly successful Cluster Analysis represents a thorough revision of the third edition and covers new and developing areas such as classification likelihood and neural networks for clustering.
Journal ArticleDOI
Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.