The decomposition and composition of endomorphism of the fuzzy power set (F(X),boolean OR, boolean AND, c)
In [Liu, 1989], a generalized fuzzifying method was given by a homomorph of a latticee. In [Liu, 1994] we have given a portrayal of an endomorphism of a lattice (F(X),boolean OR,boolean AND) on the extension for the Zadeh's function, so to a certain extent the reasonableness about the extension of the Zadeh's function was limited, from this we know that the study about homomorphism of various algebraic structures of F(X) not only is an important part in fuzzy algebra but also has important meaning in fuzzifying. Besides the (F(X),boolean OR,boolean AND,c) which is an extension of the ordinary power set, is a soft Boolean algebra, therefore the study of its endomorphism should be a very obvious problem, but as of now no such work appears in the literature. In this paper we give the decomposition and composition theorem of endomorphism (F(X),boolean OR,boolean AND,c), such that the portrayal of endomorphism is completed. (C) 2000 Elsevier Science B.V. All rights reserved.
endomorphism fuzzy sets