• Title, Summary, Keyword: Fuzzy measure

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Similarity Measure Construction with Fuzzy Entropy and Distance Measure

  • Lee Sang-Hyuk
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.5 no.4
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    • pp.367-371
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    • 2005
  • The similarity measure is derived using fuzzy entropy and distance measure. By the elations of fuzzy entropy, distance measure, and similarity measure, we first obtain the fuzzy entropy. And with both fuzzy entropy and distance measure, similarity measure is obtained., We verify that the proposed measure become the similarity measure.

Similarity Analysis Between Fuzzy Set and Crisp Set

  • Park, Hyun-Jeong;Lee, Sang-Hyuk.
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.7 no.4
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    • pp.295-300
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    • 2007
  • The similarity analysis for fuzzy set pair or crisp set pair are carried out. The similarity measure that is based on distance measure is derived and proved. The proposed similarity measure is considered with the help of analysis for uncertainty or certainty part of the membership functions. The usefulness of proposed similarity is verified through the computation of similarity between fuzzy set and crisp set or fuzzy set and fuzzy set. Our results are also compared with those of previous similarity measure which is based on fuzzy number.

A note on distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets (구간치 퍼지집합 상에서 쇼케이적분에 의해 정의된 거리측도와 유사측도에 관한 연구)

  • Jang, Lee-Chae
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.4
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    • pp.455-459
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    • 2007
  • Interval-valued fuzzy sets were suggested for the first time by Gorzafczany(1983) and Turksen(1986). Based on this, Zeng and Li(2006) introduced concepts of similarity measure and entropy on interval-valued fuzzy sets which are different from Bustince and Burillo(1996). In this paper, by using Choquet integral with respect to a fuzzy measure, we introduce distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets and discuss some properties of them. Choquet integral is a generalization concept of Lebesgue inetgral, because the two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure.

Fuzzy Measure and Integration

  • Stojakovic, Mila
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.1418-1421
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    • 1993
  • The main purpose of this paper is to introduce and develop the notion of a fuzzy measure in separable Banach space. This definition of fuzzy measure is a natural generalization of the set-valued measure. Radon-Nikod m theorems for fuzzy measure are established.

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Mutual Information Analysis with Similarity Measure

  • Wang, Hong-Mei;Lee, Sang-Hyuk
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.3
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    • pp.218-223
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    • 2010
  • Discussion and analysis about relative mutual information has been carried out through fuzzy entropy and similarity measure. Fuzzy relative mutual information measure (FRIM) plays an important part as a measure of information shared between two fuzzy pattern vectors. This FRIM is analyzed and explained through similarity measure between two fuzzy sets. Furthermore, comparison between two measures is also carried out.

Feature extraction with distance measures and fuzzy entropy

  • Lee, Sang-Hyuk;Kim, Sung-Shin;Hyeon Bae;Kim, Youn-Tae
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.543-546
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    • 2003
  • Representation and quantification of fuzziness are required for the uncertain system modelling and controller design. Conventional results show that entropy of fuzzy sets represent the fuzziness of fuzzy sets. In this literature, the relations of fuzzy enropy, distance measure and similarity measure are discussed, and distance measure is proposed. With the help of relations of fuzzy entropy, distance measure and similarity measure, fuzzy entropy is proposed by the distance measure. Finally, proposed entropy is applied to measure the fault signal of induction machine.

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Analysis of Fuzzy Entropy and Similarity Measure for Non Convex Membership Functions

  • Lee, Sang-H.;Kim, Sang-Jin
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.9 no.1
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    • pp.4-9
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    • 2009
  • Fuzzy entropy is designed for non convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

Relation between Certainty and Uncertainty with Fuzzy Entropy and Similarity Measure

  • Lee, Sanghyuk;Zhai, Yujia
    • Journal of the Korea Convergence Society
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    • v.5 no.4
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    • pp.155-161
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    • 2014
  • We survey the relation of fuzzy entropy measure and similarity measure. Each measure represents features of data uncertainty and certainty between comparative data group. With the help of one-to-one correspondence characteristics, distance measure and similarity measure have been expressed by the complementary characteristics. We construct similarity measure using distance measure, and verification of usefulness is proved. Furthermore analysis of similarity measure from fuzzy entropy measure is also discussed.

Similarity Measure Construction for Non-Convex Fuzzy Membership Function

  • Park, Hyun-Jeong;Kim, Sung-Shin;Lee, Sang-H.
    • Journal of the Korean Institute of Intelligent Systems
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    • v.18 no.1
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    • pp.145-149
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    • 2008
  • The similarity measure is constructed for non-convex fuzzy membership function using well known Hamming distance measure. Comparison with convex fuzzy membership function is carried out, furthermore characteristic analysis for non-convex function are also illustrated. Proposed similarity measure is proved and the usefulness is verified through example. In example, usefulness of proposed similarity is pointed out.

Evaluation of certainty and uncertainty for Intuitionistic Fuzzy Sets

  • Wang, Hong-Mei;Lee, Sang-Hyuk
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.4
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    • pp.259-262
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    • 2010
  • Study about fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Unlike fuzzy set, IFSs contains uncertainty named hesistancy, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of ununified entropy definition. By considering different fuzzy entropy definitions, fuzzy entropy is designed and discussed their relation. Similarity measure was also presented and verified its usefulness to evaluate degree of similarity.