Dug Hun Hong (2004)
Kybernetika
Similarity:
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
Similarity:
Miguel Delgado, José Luis Verdegay, M. Amparo Vila (1994)
Mathware and Soft Computing
Similarity:
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
Similarity:
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...
Popov, Antony (2010)
Serdica Journal of Computing
Similarity:
This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncertainties exist. ...