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On Fuzzifications of Discrete Dynamical Systems
, 2008
"... Let X denote a locally compact metric space and ϕ: X → X be a continuous map. In the 1970s L. Zadeh presented an extension principle, helping us to fuzzify the dynamical system (X,ϕ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, ..."
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Let X denote a locally compact metric space and ϕ: X → X be a continuous map. In the 1970s L. Zadeh presented an extension principle, helping us to fuzzify the dynamical system (X,ϕ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, Chaos, entropy and a generalized extension principle, Fuzzy Sets and Systems 61 (1994)] and we generalize Zadeh’s original extension principle. In this paper we study basic properties, such as the continuity of socalled gfuzzifications. We also show that, for any gfuzzification: (i) a uniformly convergent sequence of uniformly convergent maps on X induces a uniformly convegent sequence of continuous maps on the space of fuzzy sets, and (ii) a conjugacy (a semiconjugacy, resp.) between two discrete dynamical systems can be extended to a conjugacy (a semiconjugacy, resp.) between fuzzified dynamical systems. Moreover, at the end of this paper we show that there are connections between gfuzzifications and crisp dynamical systems via setvalued dynamical systems and skewproduct (triangular) maps. Throughout this paper we consider different topological structures in the space of fuzzy sets; namely, the sendograph, endograph and levelwise topologies.
Two Results About Optimization of Fuzzy Variable Functions
 IFSAEUSFLAT
, 2009
"... We discuss some optimization problems for fuzzy variable functions and show two interesting results. First result is related to conditions for existence of global optimal solutions for some general class of optimization problems on E n, the space of compacts, upper semicontinuous and normal fuzzy se ..."
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We discuss some optimization problems for fuzzy variable functions and show two interesting results. First result is related to conditions for existence of global optimal solutions for some general class of optimization problems on E n, the space of compacts, upper semicontinuous and normal fuzzy sets of R n. The second result is about preservation of local optimality points, via Zadeh’s principle of extension.
Article Neural Fuzzy Inference SystemBased Weather Prediction Model and Its Precipitation Predicting Experiment
, 2014
"... www.mdpi.com/journal/atmosphere ..."
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