• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.305-320
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• 2011

The relations among various types of continuity of fuzzy proper function on a fuzzy set and at fuzzy point belonging to the fuzzy set in the context of $\v{S}$ostak's I-fuzzy topological spaces are discussed. The projection maps are defined as fuzzy proper functions and their properties are proved.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.383-397
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• 2019

In this paper, we introduce ${\delta}$-fuzzy ideals in a pseudo complemented distributive lattice in terms of fuzzy filters. It is proved that the set of all ${\delta}$-fuzzy ideals forms a complete distributive lattice. The set of equivalent conditions are given for the class of all ${\delta}$-fuzzy ideals to be a sub-lattice of the fuzzy ideals of L. Moreover, ${\delta}$-fuzzy ideals are characterized in terms of fuzzy congruences.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.5
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• pp.705-711
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• 2013

In this paper, we introduce an design of multi-output fuzzy neural networks based on Interval Type-2 fuzzy set. The proposed Interval Type-2 fuzzy set-based fuzzy neural networks with multi-output (IT2FS-based FNNm) comprise the network structure generated by dividing the input space individually. The premise part of the fuzzy rules of the network reflects the individuality of the division space for the entire input space and the consequent part of the fuzzy rules expresses three types of polynomial functions with interval sets such as constant, linear, and modified quadratic inference for pattern recognition. The learning of fuzzy neural networks is realized by adjusting connections of the neurons in the consequent part of the fuzzy rules, and it follows a back-propagation algorithm. In addition, in order to optimize the network, the parameters of the network such as apexes of membership functions, uncertainty factor, learning rate and momentum coefficient were automatically optimized by using real-coded genetic algorithm. The proposed model is evaluated with the use of numerical experimentation.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.169-175
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• 2003

We find a G-fuzzy equivalence relation generated by the union of two G-fuzzy equivalence relations in a set, find a G-fuzzy equivalence relation generated by a fuzzy relation in a set, and find sufficient conditions for the composition ${\mu}{\circ}{\nu}$ of two G-fuzzy equivalence relations ${\mu}$ and ${\nu}$ to be a G-fuzzy equivalence relation generated by ${\mu}{\cup}{\nu}$.

• East Asian mathematical journal
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• v.29 no.3
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• pp.269-278
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• 2013

A fuzzy set A defined on a probability space (${\Omega}$, $\mathfrak{F}$, P) is called a fuzzy event. Zadeh defines the probability of the fuzzy event A using the probability P. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. We calculate the normal fuzzy probability for generalized trapezoidal fuzzy sets and give some examples.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.217-225
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• 2012

A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh defines the probability of the fuzzy event using the probability. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.316-322
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• 2008

We introduce the concept of interval-valued intuitionistic fuzzy soft sets, which is an extension of the interval-valued fuzzy soft set. We also introduce the concepts of operations for the interval-valued intuitionistic fuzzy soft sets and study basic some 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.18 no.3
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• pp.412-415
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• 2008

In this paper, we show that the concepts of null interval-valued fuzzy and absolute interval-valued fuzzy soft sets are not reasonable. Thus we introduce the modified concepts for them and study some properties. Also we introduce an operation for the interval-valued fuzzy soft set theory and study basic properties.

• 한국HCI학회:학술대회논문집
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• 2009.02a
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• pp.15-20
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• 2009

Much amount of data which demand fuzzy information system requires various analysis through the fuzzy set visualization. Therefore, this study proposes how to visualize fuzzy data set using variation of Venn diagram. For the fuzzy data which are related to many topics and have ranking of relation, this way gives results that users want by visualizing intersection, union and complementary set. That is, it visualizes the set of fuzzy data which have many topics at once, or the set of all fuzzy data which has topics, or the set of fuzzy data not related to a topic. Users control these sets by overlapping or piling them; visualized with Venn diagram, which is user-oriented. One distinct advantage of this visualization is the fact that it delivers web documents which users of search engine and web developers want much quickly. Furthermore, its possibility can be expanded to several purposes by using for information retrieval.