• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.613-619
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• 2005

In this paper, we consider various types of convergence theorems of Choquet integral. We also show that the autocontinuity of finite fuzzy measure is equivalent to a convergence theorem with respect to convergence in measure.

• 한국지능시스템학회논문지
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• 제15권7호
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• pp.789-793
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• 2005

구간치 퍼지집합은 Gorzalczan응(1983)과 Turken(1986)에 의해 처음 제의되었다. 이를 토대로 Wang과 Li는 구간치 퍼지수에 관한 연산으로 일반화하여 연구하였다. 최근에 홍(2002)는 왕과 리의 이론을 기만적분에 의해 구간치 퍼지집합상의 거리측도에 관한 연구를 하였다. 본 논문에서 우리는 일반측도와 관련된 리만적분 대신에 퍼지측도와 관련된 쇼케이적분을 이용한 구간치 퍼지수 상의 쇼케이 거리측도를 정의하고 이와 관련된 성질들을 조사하였다.

• 전자공학회논문지B
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• 제31B권4호
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• pp.138-144
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• 1994

An inference network is proposed as a tool for bidirectional approximate reasoning. The inference network can be designed directly from the given fuzzy data(knowledge). If a fuzzy input is given for the inference netwok, then the network renders a reasonable fuzzy output after performing approximate reasoning based on an equality measure. Conversely, due to the bidirectional structure, the network can yield its corresponding reasonable fuzzy input for a given fuzzy output. This property makes it possible to perform forward and backward reasoning in the knowledge base system.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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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.

• 한국항만학회지
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• 제7권1호
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• pp.5-12
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• 1993

In complex decision making such as ill-defined system, one of the main problem is how to treat ambiguous aspect of the decision making. According to the complexity and ambiguity of the objective systems, many types of evaluation attributes are necessary for the rational decision and the relationship among the attributes become complex and fuzzy. Fuzzy integral is very effective to evalute the complex system with interaction between attributes but how to save the evaluation efforts in the decision making process of grading the membership of the objects or alternative is the problem to be tackled. Because the more object there are to evaluate, the number of decisions to made increase exponentially. Therefore, this paper aimes to propose a new evaluation algorithm based on fuzzy integral which can save the evaluator's efforts in decision making process. The proposed algorithm is constructed as follows : First, compose the fuzzy measure by introducing AHP(Analytical Hierachy Process) & mutual interaction coefficient. Second, generate fuzzy measure value of monotone family set for calculating the fuzzy integral. The effectiveness of the proposed algorithm is investigated through the example and sensitivity of interaction coefficient is illustrated.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권6호
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• pp.3121-3143
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• 2019

Segmentation plays an important role in the field of image processing and computer vision. Intuitionistic fuzzy C-means (IFCM) clustering algorithm emerged as an effective technique for image segmentation in recent years. However, standard fuzzy C-means (FCM) and IFCM algorithms are sensitive to noise and initial cluster centers, and they ignore the spatial relationship of pixels. In view of these shortcomings, an improved algorithm based on IFCM is proposed in this paper. Firstly, we propose a modified non-membership function to generate intuitionistic fuzzy set and a method of determining initial clustering centers based on grayscale features, they highlight the effect of uncertainty in intuitionistic fuzzy set and improve the robustness to noise. Secondly, an improved nonlinear kernel function is proposed to map data into kernel space to measure the distance between data and the cluster centers more accurately. Thirdly, the local spatial-gray information measure is introduced, which considers membership degree, gray features and spatial position information at the same time. Finally, we propose a new measure of intuitionistic fuzzy entropy, it takes into account fuzziness and intuition of intuitionistic fuzzy set. The experimental results show that compared with other IFCM based algorithms, the proposed algorithm has better segmentation and clustering performance.

• 한국통신학회논문지
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• 제29권7C호
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• pp.931-936
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• 2004

GPDF(Gaussian Probability Density Function)을 효율적으로 군집화할 수 있는 GBFCM(DM)(Gradient Based Fuzzy c_means with Divergence Measure) 알고리즘이 본 논문에서 제안되었다. 제안된 GBFCM(DM)은 데이터 사이의 거리 척도로 발산거리(Divergence measure)를 적용한 새로운 형태의 FCM으로, 기존의 GBFCM에 기반을 두는 알고리즘이다. 본 논문에서는 MPEG VBR 비디오 데이터를 GPDF형태의 다차원 데이터로 변형시켜 모델링 하고, 모델링 한 MPEG VBR 비디오 데이터를 영화 또는 스포츠 형태로 분류하는데 응용되었다. 본 논문의 실험에서 기존의 FCM, GBFCM과 새롭게 제안된 GBFCM(DM)을 사용하여 모델링 및 분류결과를 상호 비교하였다. 비교결과 GBFCM(DM)이 오분류율의 기준에서 기존의 다른 알고리즘들에 비해 약 5∼l5%의 향상된 성능을 보였다.

• 한국지능시스템학회논문지
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• 제19권4호
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• pp.556-561
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• 2009

In this paper, we propose new method to calculate the distance between intuitionistic fuzzy sets(IFSs) based on the three dimensional representation of IFSs and analyze the relations of similarity measure and distance measure of IFSs. Finally, we apply the proposed measures to pattern recognitions.

• 한국지능시스템학회논문지
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• 제26권1호
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• pp.76-81
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• 2016

In this paper, we present the entropy and similarity measure for generalized hesitant fuzzy information, and discuss their desirable properties. Some measure formulas are developed, and the relationships among them are investigated. We show that the similarity measure and entropy for generalized hesitant fuzzy information can be transformed by each other based on their axiomatic definitions. Furthermore, an approach of multiple attribute decision making problems where attribute weights are unknown and the evaluation values of attributes for each alternative are given in the form of GHFEs is investigated.

• 한국지능시스템학회논문지
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• 제11권3호
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• pp.270-274
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• 2001

지금까지 제안된 유사도 척도는 첫째, 기하학적 유사도 척도, 둘째, 집합론적 유사도 척도, 그리고 마지막으로 일치 함수를 이용한 유사도 척도와 같이 세 종류로 분류될 수 있다. 본 논문에서는 이러한 기존의 유사도 척도가 갖는 여러 가지 성질에 근거하여 퍼지 집합에 관한 새로운 유사도 척도를 제안하고 이의 성질을 알아본다. 마지막으로, 예제를 통하여 제안된 유사도 척도와 기존의 유사도 척도의 특성을 비교한다.