• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.541-555
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• 2009

The primary purpose of this paper is to prove the fuzzy version of Riesz theorem in n-normed linear space as a generalization of linear n-normed space. Also we study some properties of fuzzy n-norm and introduce a concept of fuzzy anti n-norm.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.279-286
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• 2007

Using t-norm T and s-norm S, we introduce the notion of intuitionistic (T, S)-normed fuzzy subalgebra in BCK/BCI-algebra, and some related properties are investigated.

• 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 Data and Information Science Society
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• v.14 no.1
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• pp.93-101
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• 2003

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy quantities based on the extension principle suggested by Mare (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous t-norm which holds the distributivity under t-norm based fuzzy arithmetic operations.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.105-111
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• 1998

In this paper a fuzzy regression model based on the weakest t-norm is introduced. The model shows a regression model which has fuzzy coefficients and fuzzy variables.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.281-286
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• 2009

In this paper, we introduce the notion of the complete fuzzy norm on a linear space. And we consider some relations between the fuzzy completeness and ordinary completeness on a linear space.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.597-606
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• 2009

In this paper, we introduce the notion of the statistically complete fuzzy norm on a linear space. And we consider some relations between the fuzzy statistical completeness and ordinary completeness on a linear space.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.22-24
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• 2002

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy Quantities based on the extension principle suggested by Mares (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous f-norm which holds the distributivity under f-norm based fuzzy arithmetic operations.

• 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.