Fuzzy modeling in terms of surprise
The study discusses fuzzy modeling in the context of surprise. The concept of surprise is related to linguistically quantified statements and numerically quantified. The paper sets up an axiomatic framework for the notion of surprise, quantifies surprise vis-à-vis membership grades as well as connects it to operations on fuzzy sets. Considering \(d(x)\) as being a membership grade for some argument \(x\), a surprise value ``\(s\)'' relates to ``\(d\)'' via some strictly monotone decreasing transformation from \([0,\infty]\) onto the unit interval; for instance, \(d=1/(s^a+1)\) with \(a>0\). Some issues of dependence and modifiers are addressed in the context of surprise. Subsequently, fuzzy optimization is revisited in the setting of surprise minimization and specification of fuzzy functions (this being realized by means of fuzzy associative memories).
scientific article; zbMATH DE number 1915156
scientific article