• Title/Summary/Keyword: interval fuzzy number

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A Note on Interval Approximation of a Fuzzy Number

  • Hong, Dug-Hun;Kim, Kyung-Tae
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.3
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    • pp.913-918
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    • 2006
  • Chanas(2001) introduced the notion of interval approximation of a fuzzy number with the condition that the width of this interval is equal to the width of the expected interval. In this note, this condition is relaxed and the resulting formulae are derived for determining the approximation interval. This interval is compared with the expected interval and approximation interval of a fuzzy number as introduced by Chanas.

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A note on the Choquet distance measures for fuzzy number-valued fuzzy numbers (퍼지수치 퍼지수 상의 쇼케이 거리측도에 관한 성질)

  • Jang Lee-Chae;Kim Won-Joo
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2006.05a
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    • pp.365-369
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    • 2006
  • 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. Using interval-valued Choquet integrals with respect to a fuzzy measure instead of Riemann integrals with respect to a classical measure, we studied some characterizations of interval-valued Choquet distance(2005). In this paper, we define Choquet distance measure for fuzzy number-valued fuzzy numbers and investigate some algebraic properties of them.

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Interval-Valued Fuzzy Cosets

  • Lee, Keon-Chang;Hur, Kul;Lim, Pyung-Ki
    • Journal of the Korean Institute of Intelligent Systems
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    • v.22 no.5
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    • pp.646-655
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    • 2012
  • First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups. Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

A study on the Choquet distance measures and their applications (쇼케이 거리측도와 응용에 관한 연구)

  • Jang, Lee-Chae;Kim, Won-Joo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.16 no.5
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    • pp.550-555
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    • 2006
  • Internal-valued fuzzy sets were suggested for the first time by Gorzalczang(1983). 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 numbers with Riemann integral. By using interval-valued Choquet integrals with respect to a fuzzy measure instead of Riemann integrals with respect to a classical measure, we studied some characterizations of interval-valued Choquet distance(2005). In this paper, we define Choquet distance measure for fuzzy number-valued fuzzy numbers and investigate some properties of them.

ON SOLVING FUZZY EQUATION

  • Hong, Dug-Hun
    • Journal of applied mathematics & informatics
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    • v.8 no.1
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    • pp.213-223
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    • 2001
  • The use of fuzzy number over interval of confidence instead of possibilitic consideration for solving fuzzy equation is proposed. This approach of solving fuzzy equation by interval arithmetic and ${\alpha}$-cuts has a considerable advantage. Through theoretical analysis, an illustrative example and computational results, we show that the proposed approach is more general and straight-forword.

Fuzzy finite element method for solving uncertain heat conduction problems

  • Chakraverty, S.;Nayak, S.
    • Coupled systems mechanics
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    • v.1 no.4
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    • pp.345-360
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    • 2012
  • In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

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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Fuzzy Test for the Fuzzy Regression Coefficient (퍼지회귀계수에 관한 퍼지검정)

  • 강만기;정지영;최규탁
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2001.05a
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    • pp.29-33
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    • 2001
  • We propose fuzzy least-squares regression analysis by few error term data and test the slop by fuzzy hypotheses membership function for fuzzy number data with agreement index. Finding the agreement index by area for fuzzy hypotheses membership function and membership function of confidence interval, we obtain the results to acceptance or reject for the test of fuzzy hypotheses.

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