Structural approach to the analysis of fuzzy systems. II: Decision-making procedures in structured fuzzy systems (Q582241)

[For part I, see the author, Autom. Remote Control 49, No.4, 500-507 (1988); translation from Avtom. Telemekh. 1988, No.4, 128-137 (1988; Zbl 0666.93007).] The paper concerns a method determining the preimage of a fuzzy set under a given mapping. Given a fuzzy set B in \({\mathcal Y}\) and a certain mapping f: \({\mathcal X}\times {\mathcal Y}\to [0,1]\), the preimage A of B is defined as a union of all fuzzy sets whose images under ``f'' are subsets of B, namely, \[ A=\cup_{C}(C\circ f\subset B). \] Further associated results are centered around the approximation of a fuzzy relation by the cartesian power of a fuzzy set. Such problem formulation pertains to fuzzy mappings defined by many-fold fuzzy relations. Relevant theorems developed here can form a basis for algorithms. The ideas are illustrated by considering control aspects in fuzzy models in general, and modeling of a process generating the total lifecycle cost of electronic products, in particular.