• Honam Mathematical Journal
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• v.30 no.2
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• pp.299-310
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• 2008

The notion of interval-valued fuzzy ${\alpha}$-continuous mappings and interval-valued fuzzy contra ${\alpha}$-continuous mappings is introduced, and their characterizations are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.239-249
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• 2017

In this paper, we approximate a fuzzy almost cubic function by a cubic function in a fuzzy sense. Indeed, we investigate solutions of the following cubic functional equation $$3f(kx+y)+3f(kx-y)-kf(x+2y)-2kf(x-y)-3k(2k^2-1)f(x)+6kf(y)=0$$. and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.47-52
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• 2009

We introduce the concepts of interval-valued fuzzy M-continuity and interval-valued fuzzy M$^*$(M)-open mappings. And we study some characterizations and basic properties of such functions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10a
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• pp.124-140
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• 1995

The merit of fuzzy rule based systems stems from their capability of encoding qualitative knowledge of experts into quantitative rules. Recent advancement in automatic tuning or self-organization of fuzzy rules from experimental data further enhances their power, allowing the integration of the top-down encoding of knowledge with the bottom-up learning of rules. In this paper, methods of self-organizing fuzzy rules and of performing defuzzification and inference is presented based on a multi-resolution radial basis function network. The network learns an arbitrary input-output mapping from sample distribution as the union of hyper-ellipsoidal clusters of various locations, sizes and shapes. The hyper-ellipsoidal clusters, representing fuzzy rules, are self-organized based of global competition in such a way as to ensute uniform mapping errors. The cooperative interpolation among the multiple clusters associated with a mapping allows the network to perform a bidirectional many-to-many mapping, representing a particular from of defuzzification. Finally, an inference engine is constructed for the network to search for an optimal chain of rules or situation transitions under the constraint of transition feasibilities imposed by the learned mapping. Applications of the proposed network to skill acquisition are shown.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.257-270
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• 2009

In this paper we introduce the Henstock integral of fuzzy mappings in Banach spaces as a generalization of the Henstock integral of set-valued mappings and investigate some properties of it.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.1-14
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• 2019

We prove the generalized Hyers-Ulam-Rassias stability problem of the quadratic functional equation with involution in the fuzzy quasi ${\beta}$-normed space by using the fixed point method.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.6
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• pp.1010-1019
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• 1994

It is shown that there exists a nonlinear mapping which transforms image features and their changes to the desired camera motion without measuring of the relative distance between the camera and the object. This nonlinear mapping can eliminate several difficulties occurring in computing the inverse of the feature Jacobian as in the usual feature-based visual feedback control methods. Instead of analytically deriving the closed form of this mapping, a Fuzzy Membership Function-based Neural Network (FMFNN) incorporating a Fuzzy-Neural Interpolating Network is used to approximate the nonlinear mapping. Several FMFNN's are trained to be capable of tracking a moving object in the whole workspace along the line of sight. For an effective implementation of the proposed FMF network, an image feature selection process is investigated. Finally, several numerical examples are presented to show the validity of the proposed visual servoing method.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.388-388
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• 2000

The complexity of nonlinear systems makes it difficult to ascertain their behavior using classical methods of analysis. Many efforts have been focused on the advanced algorithms and techniques that hold the promise of improving real-time optimal control while at the same time providing higher accuracy. In this paper, a fuzzy cell mapping method of real-time optimal control far nonlinear dynamical systems is proposed. This approach combines fuzzy logic with cell mapping techniques in order to find the optimal input level and optimal time interval in the finite set which change the state of a system to achieve a desired obiective. In order to illustrate this method, we analyze the behavior of an inverted pendulum using fuzzy cell mapping.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.663-679
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• 2016

In this paper, we introduce the concepts of several types of interval-valued intuitionistic fuzzy mappings and several types of interval-valued intuitionistic fuzzy compactness in interval-valued intuitionistic smooth topological spaces and then investigate their properties.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.279-291
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• 2010

In this paper, we introduce the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces in terms of the Kurzweil-Henstock-Pettis integral of set-valued mappings and obtain some properties of the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces and the convergence theorem for Kurzweil-Henstock-Pettis integrable fuzzy mappings.