• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.550-556
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• 2007

In this paper, we introduce the concepts of fuzzy (r, s)-semi-preopen sets and fuzzy (r, s)-semi-precontinuous mappings on intuitionistic fuzzy topological spaces in ${\check{S}}ostak's$ sense. The relations among fuzzy (r, s)-semicontinuous, fuzzy (r, s)-precontinuous, and fuzzy (r, s)-semi-precontinuous mappings we discussed. The concepts of fuzzy (r, s)-semi-preinterior, fuzzy (r, s)-semi-preclosure, fuzzy (r, s)-semi-preneighborhood, and fuzzy (r, s)-quasi-semi-preneighborhood are given. Using these concepts, the characterization for the fuzzy (r, s)-semi-precontinuous mapping is obtained. Also, we introduce the notions of fuzzy (r, s)-semi-preopen and fuzzy (r, s)-semi-preclosed mappings on intuitionistic fuzzy topological spaces in ${\check{S}}ostak's$ sense, and then we investigate some of their characteristic properties.

• Journal of the Korean Institute of Intelligent Systems
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• v.1 no.1
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• pp.9-25
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• 1991

This tutorial paper has been written for biologists, physicians or beginners in fuzzy sets theory and applications. This field is introduced in the framework of medical diagnosis problems. The paper describes and illustrates with practical examples, a general methodology of special interest in the processing of borderline cases, that allows a graded assignment of diagnoses to patients. A pattern of medical knowledge consists of a tableau with linguistic entries or of fuzzy propositions. Relationships between symptoms and diagnoses are interpreted as labels of fuzzy sets. It is shown how possibility measures (soft matching) can be used and combined to derive diagnoses after measurements on collected data. The concepts and methods are illustrated in a biomedical application on inflammatory protein variations. In the case of poor diagnostic classifications, it is introduced appropriate ponderations, acting on the characterizations of proteins, in order to decrease their relative influence. As a consequence, when pattern matching is achieved, the final ranking of inflammatory syndromes assigned to a given patient might change to better fit the actual classification. Defuzzification of results (i.e. diagnostic groups assigned to patients) is performed as a non fuzzy sets partition issued from a "separating power", and not as the center of gravity method commonly employed in fuzzy control. It is then introduced a model of fuzzy connectionist expert system, in which an artificial neural network is designed to build the knowledge base of an expert system, from training examples (this model can also be used for specifications of rules in fuzzy logic control). Two types of weights are associated with the connections: primary linguistic weights, interpreted as labels of fuzzy sets, and secondary numerical weights. Cell activation is computed through MIN-MAX fuzzy equations of the weights. Learning consists in finding the (numerical) weights and the network topology. This feed forward network is described and illustrated in the same biomedical domain as in the first part.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.521-532
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• 2003

In this paper, we introduce the notions of ($T_{i},\;T_{j}$)-fuzzy (r, s)-preopen sets and fuzzy pairwise (r, s)-precontinuous mappings in smooth bitopological spaces and then we investigate some of their characteristic properties.

• Proceedings of the IEEK Conference
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• 2000.06e
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• pp.55-58
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• 2000

Previous works using a Multi-population Genetic Algorithm have divided chromosome into two components, rule sets and membership functions. However, in this case bad rule sets disturb optimization in good rule sets and membership functions. A new method for a Multi-population Genetic Algorithm suggests three components, good rule sets, bad rule sets, and membership functions. To show the effectiveness of this method, fuzzy controller is applied in a Truck Backing Problem. Results of the computer simulation show good adaptation of the proposed method for a Multi-population Genetic Algorithm.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.4
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.3
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• pp.153-164
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• 2011

Equivalence relations and mappings for crisp sets are very well known. This paper attempts an investigation of equivalence relations and mappings for fuzzy sets. We list some concepts and results related to fuzzy relations. We give some examples corresponding to the concept of fuzzy equality and fuzzy mapping introduced by Demirci [1]. In addition, we introduce the notion of preimage and quotient of fuzzy equivalence relations. Finally, we investigate relations between a fuzzy equivalence relation and a fuzzy mapping.

• 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.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.321-329
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• 1999

In this paper, we introduce a new metric on space $\mathcal{F}(R^p)$ of fuzzy sets and prove that $\mathcal{F}(R^p)$ is separable and complete.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.21-24
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• 2001

In this paper, we investigate some properties of the Skorokhod metric on the space F(R$\^$p/) of upper semicontinuous fuzzy subsets of R$\^$p/ with compact support, which include the continuity of operations, the translation inveriance and convexity.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.157-160
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• 2006

In this paper, we consider interval-valued fuzzy sets which were suggested by Wang and Li(1998) and Turksen(1986) and investigate entropy defined by Choquet integral on interval-valued fuzzy sets. Furthermore, we discuss some properties of them and give some examples related this entropy.