Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis
Pattern Recognition LettersPublished 8 September 2006
Yanhong Li, David L. Olson, Zheng Qin
Citations278
SJR quartileQ1
SJR score1.00
SNIP1.43
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Abstract
Existing similarity measures between intuitionistic fuzzy sets/vague sets are analyzed, compared and summarized by their counter-intuitive examples in pattern recognition. The positive aspects of each similarity measure are demonstrated, along with counter cases and discussion of the conditions under which each may not work as desired. The research presented here could benefit selection and applications of similarity measures for intuitionistic fuzzy sets and vague sets in practice.
Keywords
Decision SciencesEngineering
Fuzzy Sets and SystemsIntuitionistic fuzzy sets
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IEEE Transactions on Systems Man and CyberneticsVague sets
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A vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of according to the inequality of the following type:
Fuzzy Sets and SystemsMore on intuitionistic fuzzy sets
1,488 Citations1989Krassimir Atanassov
Two news operators on intuitionistic fuzzy sets are defined and their basic properties are studied to introduce new results on intuitionism fuzzy sets.
Intuitionistic Fuzzy Sets: Theory and Applications
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Fuzzy Sets and SystemsNew operations defined over the intuitionistic fuzzy sets
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Fuzzy Sets and SystemsVague sets are intuitionistic fuzzy sets
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Fuzzy Sets and SystemsOperators over interval valued intuitionistic fuzzy sets
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The proposed similarity measures can provide a useful way for measuring IFSs more effectively and are more reasonable than some existing similarity measures in general cases.
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This paper illustrates the application of the modified similarity measure on a simple pattern recognition problem and shows how a simple modification of the Dengfeng-Chuntian operator may correct this problem.
Fuzzy Sets and SystemsMeasures of similarity between vague sets
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Information SciencesA note on similarity measures between vague sets and between elements
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It is shown by examples that the similarity measures proposed by Chen do not fit well in some cases, and a set of modified measures is proposed that turned out to be more reasonable in more general cases than the previous one.
IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)Similarity measures between vague sets and between elements
286 Citations1997Shyi‐Ming Chen
The paper presents some similarity measures between vague sets and between elements and the proposed method can provide a useful way for handling behavior analysis problems.
Fuzzy Sets and SystemsIntuitionistic fuzzy prolog
125 Citations1993Krassimir Atanassov, Christo G. Georgiev
A logic programming system which uses a theory of intuitionistic fuzzy sets to model various forms of uncertainty is presented, which allows knowledge representation and inference under uncertainty in the form of rules suitable for expert systems.
Fuzzy Sets and SystemsRemarks on the intuitionistic fuzzy sets
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The pseudo-fixed points of all operators defined over the intuitionistic fuzzy sets are determined.
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In this paper,similarity measure proposed by Chen is studied, and a modified measure is proposed that aims to improve the similarity measure between vague sets.
Fuzzy Sets and SystemsRemarks on the intuitionistic fuzzy sets — III
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Computer Engineering and ScienceBidirectional Approximate Reasoning Based on Weighted Similarity Measures of Vague Sets
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This paper introduces a new weighted similarity measure for vague sets and proposes a method for determining the similarity direction, which improves the accuracy and applicability of approximate reasoning, and also provides a useful tool for approximate reasoning in intelligent systems.
