Comparison of fuzzy partitions based on their α-cuts

Abstract This paper proposes a measure of degree of equivalence between two fuzzy partitions. A method which allows one to find values of αϵ[0,1] at which two or more partitions are considered to be equivalent is introduced. Partial order of fuzzy partitions with respect to their sharpness is discussed. A procedure for constructing a lower α-bound and an upper α-bound of a family of fuzzy partitions is suggested. This procedure can be used in aggregation of fuzzy partitions.