Dug Hun Hong (2004)
Kybernetika
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We consider the question whether, for given fuzzy numbers, there are different pairs of -norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.
Dug Hun Hong (2003)
Kybernetika
Similarity:
Hong and Do[4] improved Mareš[7] result about additive decomposition of fuzzy quantities concerning an equivalence relation. But there still exists an open question which is the limitation to fuzzy quantities on R (the set of real numbers) with bounded supports in the presented theory. In this paper we restrict ourselves to fuzzy numbers, which are fuzzy quantities of the real line R with convex, normalized and upper semicontinuous membership function and prove this open question. ...
Milan Mareš (1995)
Kybernetika
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Congxin Wu (2008)
Banach Center Publications
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Miguel Delgado, José Luis Verdegay, M. Amparo Vila (1994)
Mathware and Soft Computing
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Two different definitions of a Fuzzy number may be found in the literature. Both fulfill Goguen's Fuzzification Principle but are different in nature because of their different starting points. The first one was introduced by Zadeh and has well suited arithmetic and algebraic properties. The second one, introduced by Gantner, Steinlage and Warren, is a good and formal representation of the concept from a topological point of view. The objective of this paper is...
Frank Klawonn, Juan Luis Castro (1995)
Mathware and Soft Computing
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Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval...
Pedro J. Burillo López, Noé Frago Paños, Ramón Fuentes González (2001)
Mathware and Soft Computing
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Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature. In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implications),...