• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권3호
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• pp.315-326
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• 2009

In this paper, we introduce Debreu integral of fuzzy mappings in Banach spaces in terms of the Debreu integral of set-valued mappings, investigate properties of Debreu integral of fuzzy mappings in Banach spaces and obtain the convergence theorem for Debreu integral of fuzzy mappings in Banach spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권1호
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• pp.59-64
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• 2011

In 2001, the notion of a fuzzy poset defined on a set X via a triplet (L, G, I) of functions with domain X ${\times}$ X and range [0, 1] satisfying a special condition L+G+I = 1 is introduced by J. Negger and Hee Sik Kim, where L is the 'less than' function, G is the 'greater than' function, and I is the 'incomparable to' function. Using this approach, we are able to define a special class of fuzzy posets, and define the 'skeleton' of a fuzzy poset in view of major relation. In this sense, we define the linear discrepancy of a fuzzy poset of size n as the minimum value of all maximum of I(x, y)${\mid}$f(x)-f(y)${\mid}$ for f ${\in}$ F and x, y ${\in}$ X with I(x, y) > $\frac{1}{2}$, where F is the set of all injective order-preserving maps from the fuzzy poset to the set of positive integers. We first show that the definition is well-defined. Then, it is shown that the optimality appears at the same injective order-preserving maps in both cases of a fuzzy poset and its skeleton if the linear discrepancy of a skeleton of a fuzzy poset is 1.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
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• pp.259-262
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• 2000

In this paper, an Adaptive neuro-fuzzy Inference system(ANFIS) using fuzzy min-max network(FMMN) is proposed. Fuzzy min-max network classifier that utilizes fuzzy sets as pattern classes is described. Each fuzzy set is an aggregation of fuzzy set hyperboxes. Here, the proposed method transforms the hyperboxes into gaussian menbership functions, where the transformed membership functions are inserted for generating fuzzy rules of ANFIS. Finally, we applied the proposed method to the classification problem of iris data and obtained a better performance than previous works.

• 대한수학회보
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• 제43권3호
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• pp.461-470
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• 2006

As a continuation of [4], characterizations of fuzzy implicative ideals are given. An extension property for fuzzy implicative ideals is established. We prove that the family of fuzzy implicative ideals is a completely distributive lattice. Using level subsets of a BCk-algebra X with respect to a fuzzy set $\={A}$ in X, we construct a fuzzy implicative ideal of X containing $\={A}$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권2호
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• pp.154-161
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• 2014

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.343-345
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• 2004

We propose a new category of fuzzy set-based fuzzy inference systems based on data granulation related to fuzzy space division for each variables. Data granules are viewed as linked collections of objects(data, in particular) drawn together by the criteria of proximity, similarity, or functionality. Granulation of data with the aid of Hard C-Means(HCM) clustering algorithm help determine the initial parameters of fuzzy model such as the initial apexes of the membership functions and the initial values of polyminial functions being used in the premise and consequence part of the fuzzy rules. And the initial parameters are tuned effectively with the aid of the genetic algorithms(GAs) and the least square method. Numerical example is included to evaluate the performance of the proposed model.

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.739-748
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• 2024

The intention of this paper is to acquaint domination, total domination on bipolar intuitionistic fuzzy graphs. Subsequently for bipolar intuitionistic fuzzy graphs the domination number and the total domination number are defined. Consequently we proved necessary and sufficient condition for a d-set to be minimal d-set, bounds for domination number and equality conditions for domination number and order.

• 호남수학학술지
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• 제30권1호
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• pp.171-183
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• 2008

In a previous work [18], the authors investigated autocontinuity, converse-autocontinuity, uniformly autocontinuity, uniformly converse-autocontinuity, and fuzzy multiplicativity of monotone set function defined by Choquet integral([3,4,13,14,15]) instead of fuzzy integral([16,17]). We consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. Then the interval-valued Choquet integral determines a new nonnegative monotone interval-valued set function which is a generalized concept of monotone set function defined by Choquet integral in [18]. These integrals, which can be regarded as interval-valued aggregation operators, have been used in [10,11,12,19,20]. In this paper, we investigate some characterizations of monotone interval-valued set functions defined by the interval-valued Choquet integral such as autocontinuity, converse-autocontinuity, uniform autocontinuity, uniform converse-autocontinuity, and fuzzy multiplicativity.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.435-457
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• 2013

Using the Lukasiewicz 3-valued implication operator, the notion of an (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring is introduced, where ${\alpha},{\beta}{\in}\{{\in},q,{\in}{\wedge}q,{\in}{\vee}q\}$. We define intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) and (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$)-intuitionistic fuzzy left (right) $h$-ideal of R if and only if A is an intuitionistic fuzzy left (right) $h$-ideal with thresholds (0, 1) (or (0, 0.5) or (0.5, 1)) of R respectively. It is also shown that A is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$))-intuitionistic fuzzy left (right) $h$-ideal if and only if for any $p{\in}$ (0, 1] (or $p{\in}$ (0, 0.5] or $p{\in}$ (0.5, 1] ), $A_p$ is a fuzzy left (right) $h$-ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of R if and only if for any $p{\in}(s,t]$, the cut set $A_p$ is a fuzzy left (right) $h$-ideal of R.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 춘계학술대회 학술발표 논문집
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• pp.98-103
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• 1997

Defuzzification plays a great role in fuzzy control system. Defuzzification is a process which maps from a space defined over an output universe of discourse into a space of nonfuzzy(crisp) number. But, it's impossible to convert a fuzzy set into a numeric value without losing some information during defuzzification. Also it's very hard to find a number that best represents a fuzzy set. Many methods have been used for defuzzification but most of then were problem dependent. There has been no rule which guides how to select a method that is suitable to solve given problem. Here, we have investigated most widely used methods and we have analyzed their characteristics and evaluated them. D. Driankov and Mizumoto have suggested 5 criteria which the‘ideal’defuzzification method should satisfy. But, they didn't considered about control action. Output fuzzy set if not only a fuzzy set but also a sequence of control action. We suggested 4 new criteria which describe sequence of cont ol action from some experiments. In addition, we have compared each method in simple adaptive fuzzy control. COG(Center of Gravity), or COS(Center of Sums) methods were successful in fuzzy control. However, at transition region, MOM(Mean of Maxima) was best among others in adaptive fuzzy control.