• Title/Summary/Keyword: interval-valued fuzzy sets

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Calculating Attribute Values using Interval-valued Fuzzy Sets in Fuzzy Object-oriented Data Models (퍼지객체지향자료모형에서 구간값 퍼지집합을 이용한 속성값 계산)

  • Cho Sang-Yeop;Lee Jong-Chan
    • Journal of Internet Computing and Services
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    • v.4 no.4
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    • pp.45-51
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    • 2003
  • In general, the values for attribute appearing in fuzzy object-oriented data models are represented by the fuzzy sets. If it can allow the attribute values in the fuzzy object-oriented data models to be represented by the interval-valued fuzzy sets, then it can allow the fuzzy object-oriented data models to represent the attribute values in more flexible manner. The attribute values of frames appearing in the inheritance structure of the fuzzy object-oriented data models are calculated by a prloritized conjunction operation using interval-valued fuzzy sets. This approach can be applied to knowledge and information processing in which degree of membership is represented as not the conventional fuzzy sets but the interval-valued fuzzy sets.

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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.

A note on entropy defined by Choquet integral on interval-valued fuzzy sets (구간치 퍼지집합상에서 쇼케이적분에 의해 정의된 엔트로피에 관한 연구)

  • Jang, Lee-Chae
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.2
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    • pp.149-153
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    • 2007
  • In this paper, we consider interval-valued fuzzy sets which were suggested by Wang and Li(1998) and Turksen(1986) and investigate entropy defined by Choquet integral on interval-valued fuzzy sets. Furthermore, we discuss some properties of them and give some examples related this entropy. This tool has drawn much attention due to numerous applications areas, such as decision making and information theory on interval-valued fuzzy sets.

Distances between Interval-valued Intuitionistic Fuzzy Sets (구간 값 직관적 퍼지집합들 사이의 거리)

  • Park, Jin-Han;Lim, Ki-Moon;Lee, Bu-Young;Son, Mi-Jung
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2007.04a
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    • pp.175-178
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    • 2007
  • We give a geometrical interpretation of the interval-valued fuzzy set. So, based on the geometrical background, we propose new distance measures between interval-valued fuzzy sets and compare these measures with distance measures proposed by Burillo and Bustince and Grzegorzewski, respectively. Furthermore, we extend three methods for measuring distances between interval-valued fuzzy sets to interval-valued intuitionistic fuzzy sets.

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REMARKS ON INTERVAL-VALUED FUZZY MINIMAL PRECONTINUOUS MAPPINGS AND INTERVAL-VALUED FUZZY MINIMAL PREOPEN MAPPINGS

  • Min, Won Keun;Kim, Myeong Hwan
    • Korean Journal of Mathematics
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    • v.17 no.3
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    • pp.249-255
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    • 2009
  • In [5], we introduced the concepts of IVF m-preopen sets and IVF m-precontinuous mappings on interval-valued fuzzy minimal spaces. In this paper, we introduce the concept of IVF m-preopen mapping and investigate characterizations for IVF mprecontinuous mappings and IVF m-preopen mappings.

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Some algebraic properties and a distance measure for interval-valued fuzzy numbers (쇼케이적분을 이용한 구간치 퍼지수 상의 거리측도에 관한 성질)

  • Jang, Lee-Chae;Kim, Hyun-Mee
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2005.11a
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    • pp.121-124
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    • 2005
  • Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(1986). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. In this paper, we define a distance measure on interval-valued fuzzy numbers using Choquet integral with respect to a classical measure and investigate their properties.

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ON INTERVAL VALUED INTUITIONISTIC FUZZY HYPERIDEALS OF ORDERED SEMIHYPERGROUPS

  • Lekkoksung, Somsak;Lekkoksung, Nareupanat
    • Korean Journal of Mathematics
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    • v.28 no.4
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    • pp.753-774
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    • 2020
  • We introduce the notion of interval valued intuitionistic fuzzy hyperideals, bi-hyperideals and quasi-hyperideals of an ordered semihypergroup. We characterize an interval valued intuitionistic fuzzy hyperideal of an ordered semihypergroup in terms of its level subset. Moreover, we show that interval valued intuitionistic fuzzy bi-hyperideals and quasi-hyperideals coincide only in a particular class of ordered semihypergroups. Finally, we show that every interval valued intuitionistic fuzzy quasi-hyperideal is the intersection of an interval valued intuitionistic fuzzy left hyperideal and an interval valued intuitionistic fuzzy right hyperideal.

Reliability Analysis of Fuzzy Systems Based on Interval Valued Vague Sets (구간값 모호집합에 기반을 둔 퍼지시스템의 신뢰도 분석)

  • Lee, Se-Yul;Cho, Sang-Yeop;Kim, Yong-Soo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.18 no.4
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    • pp.445-450
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    • 2008
  • In order to analyze the reliabilities of the fuzzy systems, the reliabilities of the components in the fuzzy systems are represented by real values between zero and one, fuzzy numbers, intervals of confidence, vague sets, interval valued fuzzy sets, etc in the conventional researches. In this paper, we propose a method to represent and analyze the reliabilities of the fuzzy systems based on the interval valued vague sets defined in the universe of discourse [0, 1]. In the interval valued vague sets, the upper bounds and the lower bounds of the conventional vague sets[12, 14] are represented as the intervals. Therefore, it can allow the reliabilities of a fuzzy system to represent and analyze in a more flexible manner. Because the proposed method uses the simplified arithmetic operations of the fuzzy triangular numbers rather than the complicated of the fuzzy trapezoidal numbers mentioned by Kumar[14], the execution of the proposed method is faster than the one.

On Fuzzy Inclusion in the Interval-Valued Sense

  • Park, Jin-Han;Lee, Bu-Young;Son, Mi-Jung
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2002.12a
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    • pp.63-66
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    • 2002
  • As a generalization of fuzzy sets, the concept of interval-valued fuzzy sets was introduced by Gorzalczany(GO). In this paper, we shall extend the concept of "fuzzy inclusion", introduced by Sostak[SO1], to the interval-valued fuzzy setting and study its fundamental properties for some extent.