• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.291-308
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• 2007

The motivation of this paper is to present a new and interesting notion of intuitionistic fuzzy n-normed linear space. Cauchy sequence and convergent sequence in intuitionistic fuzzy n-normed linear space are introduced and we provide some results onit. Furthermore we introduce generalized cartesian product of the intuitionistic fuzzy n-normed linear space and establish some of its properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.175-178
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• 2005

In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if $\rho_1,\;\rho_2$ are equivalent fuzzy norms on a linear space, then for every $\varepsilon\in(0.1)$, the induced crisp norms $P_\varepsilon^1,\;and\;P_\varepsilon^2$, respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let $\rho$ be a lower semicontinuous fuzzy norm on a normed linear space X, and have the bounded support. Then $\rho$ is equivalent to the fuzzy norm $\chi_B$ where B is the closed unit ball of X. The lower semi-continuity of $\rho$ is an essential condition which guarantees the continuity of $P_\varepsilon$, where 0 < e < 1. As the last result, we prove that : if $\rho$ is a fuzzy norm on a finite dimensional vector space, then $\rho$ is equivalent to $\chi_B$ if and only if the support of $\rho$ is bounded.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.447-459
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• 2007

The purpose of this paper is to introduce the notion of fuzzy n-inner product space. Ascending family of quasi ${\alpha}$-n-norms corresponding to fuzzy quasi n-norm is introduced and we provide some results on it.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.268-271
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• 2008

In this paper, we introduce the notions of a fuzzy convergence of sequences, fuzzy Cauchy sequence and the related fuzzy completeness on a fuzzy normed linear space. And we investigate some properties relative to fuzzy normed linear spaces. In particular, we prove an equivalent conditions that a fuzzy norm defined on a ordinary normed linear space is fuzzy complete.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.49-57
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• 2003

In this paper, we give some sufficient conditions for convergence of geometric mean for T-related fuzzy numbers where T is an Archimedean t-norm under some mild restrictions. These results generalize earlier results of Hong and Lee [Fuzzy Sets and Systems 116 (2000) 263-267].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.85-89
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• 2007

Many authors considered the computational aspect of sup-min convolution when applied to weighted average operations. They used a computational algorithm based on a-cut representation of fuzzy sets, nonlinear programming implementation of the extension principle, and interval analysis. It is well known that $T_W$(the weakest t-norm)-based addition and multiplication preserve the shape of L-R type fuzzy numbers. In this paper, we consider the computational aspect of the extension principle by the use of $T_W$ when the principle is applied to fuzzy weighted average operations. We give the exact solution for the case where variables and coefficients are L-L fuzzy numbers without programming or the aid of computer resources.

• East Asian mathematical journal
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• v.22 no.1
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• pp.93-109
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• 2006

The concept of intuitionistic fuzzy set was first introduced by Atanassov in 1986. In this paper, we define the intuitionistic(S,T)-fuzzy left h-ideals of a hemiring by using an s-norm S and a t-norm T and study their properties. In particular, some results of fuzzy left h-ideals in hemirings recently obtained by Jun, $\"{O}zt\"{u}rk$, Song, and others are extended and generalized to intuitionistic (S,T)-fuzzy ideals over hemirings.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.2
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• pp.231-236
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• 2003

Recently, Oussalah 〔Fuzzy Sets and Systems 128(2002) 247-260〕 investigated some theoretical results about some invariance properties concerning the relationships between the defuzzification outcomes and the arithmetic of fuzzy numbers. But, in this note we introduce some explicit calculations of the resulting fuzzy set or possibility distribution when the matter is the determination of the defuzzified value pertaining to the result of some manipulation of fuzzy quantities under t-norm based fuzzy arithmetic operations.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.447-454
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• 1999

We study a general law of large numbers for array of mu-tually T related fuzzy numbers where T is an Archimedean t-norm and generalize earlier results of Fuller(1992), Triesch(1993) and Hong (1996).

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.3
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• pp.94-98
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• 1996

The main goal of this paper is to investigate some properties in close connection with the quotient fuzzy norm $ induced by a fuzzy semi-norm $ on a linear space X and the quotient map $q:X{\rightarrow]X/W, $ where W is a subspace of X.