General decomposition problem of fuzzy relations

Abstract

Abstract This paper deals with the problem of general max-min decomposition of binary fuzzy relations defined in the Cartesian product of finite spaces R m × R n where m and n as well as the resulting relations are not necessarily equal. The proposed algorithm guarantees decomposition within a finite sequence of steps related to the number of different non-zero membership levels in the decomposed relation. The concept of peak pattern analysis is used for this purpose. The paper also presents the potential role of the general decomposition of fuzzy relations for the needs of fuzzy logic in engineering and control modelling.