• Korean Journal of Mathematics
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• v.18 no.1
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• pp.11-19
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• 2010

In this paper, several common fixed degree theorems of a sequence of fuzzy mappings defined on symmetric spaces are established.

• Proceedings of the Korean Reliability Society Conference
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• 2002.06a
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• pp.303-303
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• 2002

We obtain the necessary and sufficient condition of tightness for a sequence of random variables in the space of fuzzy sets with compact support in R.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.147-153
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• 2009

In this paper, we introduce several concepts of tightness for a sequence of random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in $R^p$ and give some characterizations of their concepts. Also, counter-examples for the relationships between the concepts of tightness are given.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.73-83
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• 2003

In this paper, we first obtain some characterizations of compact subsets of the space of level-wise continuous fuzzy numbers in R by the modulus of continuity. Using this, we establish the tightness for a sequence of level-wise continuous fuzzy random variables.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.5
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• pp.639-642
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• 2005

In this paper, we introduce the notions of the convergence in the sense of ${\alpha}$-level and the fuzzy completeness on a fuzzy normed linear space. And we investigate related properties.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.565-574
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• 2010

In this paper we introduce the concept of lacunary statistical and lacunary strongly convergence of generalized difference sequence of fuzzy real numbers. We prove some inclusion relations and also study some of their properties.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.7-7
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• 2003

We studied closed set-valued Choquet integrals in two papers(1997, 2000) and convergence theorems under some sufficient conditions in two papers(2003), for examples : (i) convergence theorems for monotone convergent sequences of Choquet integrably bounded closed set-valued functions, (ii) covergence theorems for the upper limit and the lower limit of a sequence of Choquet integrably bounded closed set-valued functions. In this presentation, we consider fuzzy number-valued functions and define Choquet integrals of fuzzy number-valued functions. But these concepts of fuzzy number-valued Choquet inetgrals are all based on the corresponding results of interval-valued Choquet integrals. We also discuss their properties which are positively homogeneous and monotonicity of fuzzy number-valued Choquet integrals. Furthermore, we will prove convergence theorems for fuzzy number-valued Choquet integrals. They will be used in the following applications : (1) Subjectively probability and expectation utility without additivity associated with fuzzy events as in Choquet integrable fuzzy number-valued functions, (2) Capacity measure which are presented by comonotonically additive fuzzy number-valued functionals, and (3) Ambiguity measure related with fuzzy number-valued fuzzy inference.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.3
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• pp.291-296
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• 2006

In context-aware computing environment, some context is characterized by a single event, but many other contexts are determined by a sequence of events which happen with some timing constraints. Therefore context inference could be conducted by monitoring the sequence of event occurrence along with checking their conformance with timing constraints. Some context could be described with fuzzy concepts instead of concrete concepts. Multiple entities may interact with a service system in the context-aware environments, and thus the context inference mechanism should be equipped to handle multiple entities in the same situation. This paper proposes a context inference model which is based on the so-called fuzzy colored timed Petri net. The model represents and handles the sequential occurrence of some events along with involving timing constraints, deals with the multiple entities using the colored Petri net model, and employs the concept of fuzzy tokens to manage the fuzzy concepts.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.657-659
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• 2006

This note gives a counterexample showing that a main theorem of Aytal and Pehliven's (Information Sciences 176 (2006) 734-744) result on statically monotonic and bounded sequences of fuzzy numbers is not valid.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.265-277
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• 2012

In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.