• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1049-1059
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• 2009

Continuous t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is studied. The case for bounded support, which was a conjecture suggested by Mesiar in 1997, was proved by the author in 2002 and 2008. In this paper, we give a necessary and sufficient conditions for a continuous t-norm T that induces DR-shape preserving addition of LR-fuzzy intervals with unbounded support. Some of the results can be deduced from the results given in the paper of Mesiar in 1997. But, we give direct proofs of the results.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.97-118
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• 2006

We obtain a property of distributivity in the equivalence form over LR fuzzy intervals. As an application and main result of the paper, we give a determinant method to solve systems of linear equivalentions. The expected value of the obtained solution is equal to the corresponding solution of the classical system of linear equations considering the expected values as data.

• 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.

• 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.

• 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.