• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.121-124
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• 2005

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(1986). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. In this paper, we define a distance measure on interval-valued fuzzy numbers using Choquet integral with respect to a classical measure and investigate their properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.3
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• pp.196-199
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• 2005

Recently, many types of set-valued fuzzy integrals are studied by many authors. In this paper, we consider various types of convergence theorems of Choquet integrals of interval-valued function with respect to an autocontinuous fuzzy measure.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1041-1044
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• 2005

Recently, Zhang et al.(Fuzzy Sets and Systems 147(2004) 475-485) proved Fatou's lemma and Lebesgue dominated convergence theorem under some conditions of fuzzy measure. In this note, we show that these conditions of fuzzy measure is essential to prove Fatou's lemma and Lebesgue dominated convergence theorem by examples

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.787-790
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• 1997

This paper proposes a method which selects essential elements in a human evaluation model using the Choquet integral based on fuzzy measures, and applies the model to the evaluation of human interface. Three kinds of concepts are defined to select essential elements. Increment Degree implies the increment degree from fuzzy measures of composed elements to the fuzzy measure of a combined element. Average of Increment Degree of an element means the relative possibility of superadditivity of the fuzzy measure of each combined element. Necessity Degree means the selection degree of each combined element as a result of the human evaluation. A task experiment, which consists of a static work and two dynamic works, is performed by the use of some human interfaces. In the experiment, (1) a warning sound which gives an attention to subjects, (2) a color vision which can be distinguished easily or not, (3) the size of working area and (4) a response of confirmation that is given from an interface, are considered as human interface elements. Subjects answer the questionnaire after the experiment. From the data of the questionnaire, fuzzy measures are identified and are applied to the proposed model. Effectiveness of the proposed model is confirmed by the comparison of human interface elements extracted from the proposed model and those from the questionnaire.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.5
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• pp.550-555
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• 2006

Internal-valued fuzzy sets were suggested for the first time by Gorzalczang(1983). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy numbers with Riemann integral. By using interval-valued Choquet integrals with respect to a fuzzy measure instead of Riemann integrals with respect to a classical measure, we studied some characterizations of interval-valued Choquet distance(2005). In this paper, we define Choquet distance measure for fuzzy number-valued fuzzy numbers and investigate some properties of them.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.269-274
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• 2009

Measuring uncertainty for fuzzy sets has been carried out by calculating fuzzy entropy. Fuzzy entropy of fuzzy set is derived with the help of distance measure. The distance proportional value between the fuzzy set and the corresponding crisp set is designed as the fuzzy entropy. The usefulness is verified by proving the proposed entropy. Generally, fuzzy entropy contains the complementary characteristics that the fuzzy entropies of fuzzy set and complementary fuzzy set have the same entropies. Discrepancy that low fuzzy entropy did not guarantee the data certainty was overcome by modifying fuzzy entropy formulation. Obtained fuzzy entropy is analyzed and discussed through simple example.

• The Journal of the Korea Contents Association
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• v.5 no.5
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• pp.140-144
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• 2005

In this paper, an almost everywhere convergence theorem for seminormed fuzzy co-integrals is showed provided that the fuzzy measure is null-additive.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.6
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• pp.583-588
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• 2002

Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. Tt is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of $F\bigcapF^c and F\bigcupF^c$, while applying the Hamming distances. In this note, while applying the Euclidean distances, it is also shown that the proposed measure can be defined in terms of the ratio of some function of intuitionistic fuzzy cardinalities: of $F\bigcapF^c and F\bigcupF^c$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.13-16
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• 2002

Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] Proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. It is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F∩F$\^$c/ and F∪F$\^$c/, while applying the Hamming distances. In this note, while applying the Euclidean distances, it is also shown that the proposed measure can be defined in terms of the ratio of some function of intuitionistic fuzzy cardinalities: of F∩F$\^$c/ and F∪F$\^$c/.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.257-261
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• 2008

In this Paper we derived fuzzy entropy that is based on similarity measure. Similarity measure represents the degree of similarity between two informations, those informations characteristics are not important. First we construct similarity measure between two informations, and derived entropy functions with obtained similarity measure. Obtained entropy is verified with proof. With the help of one-to-one similarity is also obtained through distance measure, this similarity measure is also proved in our paper.