Abstract:

Fuzzy sets conceived as mappings from X to [0,1], i. e. as a generalized characteristic functions with operations max, min, and subtraction-from-1 form a structure of De Morgan algebra, and as a such they have been introduced for the first time in 1940 by H. Weyl and independently, in much more elaborated form, by A. Kaplan and H. Schott in 1951. Recently the fuzzy sets were rediscovered by L. Zadeh and they have been developed in many directions by many researchers. An abstract De Morgan algebras have been introduced in 1935 by G. C. Moisil, generalized characteristic functions introduced in 1936 by E. Szpilrajn have been also intensively studied in fifties by H. Rasiowa and R. Sikorski.