We give a definition of solutions of ordinary differential equations in n containing parameters which are described by changing in time fuzzy sets. They are defined as fuzzy subsets of the space of absolutely continuous functions. We introduce a hypograph metric in the space of fuzzy sets and prove a theorem on continuous dependence of fuzzy solutions on parameters and initial conditions with respect to that metric.
In this paper we propose the new extended class of t-norm operators called the boundary weak. The aim of the extension of this operator is that the sum of the fuzzy numbers in the arithmetic based on such t-norm gives the more narrow fuzzy number if compared to arithmetic based on standard t-norm. This extension is based on the replacement of the condition T(x,1)=x by the weaker one: T(x,1)≤x, for x∈[0,1].
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