• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.2
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• pp.106-109
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• 1997

In this paper we define the t-fuzzy equivalence relation on a set and we prove some properties in connection with t-fuzzy relations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.30-35
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• 2009

We investigate the properties of fuzzy relations, metrics and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, pseudo-(quasi-) metrics induce $\bigodot$-(quasi)-equivalence relations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1317-1320
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• 1993

We are concerned with developing a robust method for comprehensive scene analysis. In particular, we address the problem of representing spatial relations between regions in a segmented 2D image. Spatial relations are modeled as fuzzy sets. The method has two aspects, symbolic and quantitative, consisting of assigning labels for spatial relations and numeric degrees to which a relation holds respectively. The procedure of deriving a spatial relation is hierarchical taking into account geometric/physical characteristics of the regions in question.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.45
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• pp.11-23
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• 1998

This paper presents a more efficient evaluation of alternatives by use of multi-criteria decision making methodlogy under fuzzy intersectional dependence relations. The performance evaluation of most systems such as weapons, enterprise systems etc. are multiple criteria decision making problems. The descriptions and judgements on these systems are usually linguistic and fuzzy. The traditional methods of Analytic Hierarchy Process(AHP) are mainly used in crisp(non-fuzzy) decision applications with a very unbalanced scale of judgements and rank reversal. To overcome these problems, we will propose a new, general decision making method for evaluation models using fuzzy AHP(FAHP) under fuzzy intersectional dependence relations. The T.M.S alternatives A, B and C will be evaluted by the Fuzzy Analytic Hierachy Process (FAHP) based on entropy weight in this study. We will use symmetric triangular fuzzy numbers to indicate the relative strength of the elements in the hierachy and degree of intersection between criteria. These problems are evaluated by five criteria : tactical criteria, technology criteria, maintenance criteria, economy criteria, advacement criteria.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.163-181
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• 2005

We study some properties of intuitionistic fuzzy equivalence relations. Also we introduce the concepts of intuitionistic fuzzy transitive closures and level sets of an intuitionistic fuzzy relation and we investigate some of their properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.895-898
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• 1993

Instead of Cartesian product for in combining multiple inputs for fuzzy logic controllers, a method using fuzzy relation in inference is proposed. Moreover, fuzzy control rule described by fuzzy relations is derived from given conventional fuzzy control rule by fitting concept. It will be shown through several examples that the proposed technique gives smoother interpolation than conventional ones.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.9-12
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• 2002

Representation and quantification of fuzziness are required for the uncertain system modelling and controller design. Conventional results show that entropy of fuzzy sets represent the fuzziness of fuzzy sets. In this literature, the relations of fuzzy enropy, distance measure and similarity measure are discussed, and distance measure is proposed. With the help of relations of fuzzy enropy, distance measure and similarity measure, fuzzy entropy is represented by the newly proposed distance measure. With simple fuzzy set, example is illustrated.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.425-431
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• 2009

By using the notion of interval-valued fuzzy relations, we forms the poset (IVFR (X), $\leq$) of interval-valued fuzzy relations on a given set X. In particular, we forms the subposet (IVFE (X), $\leq$) of interval-valued fuzzy equivalence relations on a given set X and prove that the poset (IVFE(X), $\leq$) is a complete lattice with the least element and greatest element.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.1
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• pp.145-152
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• 2011

By using the notion of interval-valued intuitionistic fuzzy relations, we form the poset (IVIR(X), $\leq$) of interval-valued intuitionistic fuzzy relations on a given set X. In particular, we form the subposet (IVIE(X), $\leq$) of interval-valued intuitionistic fuzzy equivalence relations on a given set X and prove that the poset (IVIE(X), $\leq$) is a complete lattice with the least element and greatest element.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.7-16
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• 2007

First, we investigate fuzzy equivalence relations on a set X in the sense of Youssef and Dib. Second, we discuss fuzzy congruences generated by a given fuzzy relation on a fuzzy groupoid. In particular, we obtain the characterizations of ${\rho}\;o\;{\sigma}{\in}$ FC(S) for any two fuzzy congruences ${\rho}\;and\;{\sigma}$ on a fuzzy groupoid ($S,{\odot}$). Finally, we study the lattice of fuzzy equivalence relations (congruences) on a fuzzy semigroup and give certain lattice theoretic properties.