• Title/Summary/Keyword: LR fuzzy numbers

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A Note on Relationship between T-sum and T-product on LR Fuzzy Numbers

  • Hong, Dug-Hun;Kim, Kyung-Tae
    • Journal of the Korean Data and Information Science Society
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    • v.16 no.4
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    • pp.1141-1145
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    • 2005
  • In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

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NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR FUZZY LINEAR PROGRAMMING

  • Farhadinia, Bahram
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.337-349
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    • 2011
  • This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tucker conditions for a crisp linear programming problem.

T-sum of bell-shaped fuzzy intervals

  • Hong, Dug-Hun
    • 한국데이터정보과학회:학술대회논문집
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    • 2006.11a
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    • pp.81-95
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    • 2006
  • The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.

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A note on T-sum of bell-shaped fuzzy intervals

  • Hong, Dug-Hun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.6
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    • pp.804-806
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    • 2007
  • The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

Equivalence in Alpha-Level Linear Regression

  • Yoon, Jin-Hee;Jung, Hye-Young;Choi, Seung-Hoe
    • Communications for Statistical Applications and Methods
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    • v.17 no.4
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    • pp.611-624
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    • 2010
  • Several methods were suggested for constructing a fuzzy relationship between fuzzy independent and dependent variables. This paper reviews the use of the method by minimizing the square of the difference between an observed and a predicted fuzzy number in an ${\alpha}$-level linear regression model. We introduce a new distance between fuzzy numbers on the basis of a mode, a core point and a radius of an ${\alpha}$-level set of a fuzzy number an construct the fuzzy regression model using the proposed fuzzy distance. We also investigate sufficient condition for an equivalence in the ${\alpha}$-level regression model.