
Accession Number : ADA305715
Title : A New Characterization of Fuzzy Logic Operators Producing HomomorphicLike Relations with OnePoint Coverages of Random Sets.
Descriptive Note : Professional paper,
Corporate Author : NAVAL COMMAND CONTROL AND OCEAN SURVEILLANCE CENTER RDT AND E DIV SAN DIEGO CA
Personal Author(s) : Goodman, I. R.
Report Date : 1994
Pagination or Media Count : 28
Abstract : This paper is concerned with characterizing fuzzy logic operators via probability; in particular, through random sets. It has long been established that any fuzzy set membership function h (from D to (c,1)) has at least one, and in general, infinitely many possible random subset representations of D : S : Omega to P(D) in the onepoint coverageequivalent form P(x in S) = h(x), all x in D (1). It is shown here first, that any random set (or subset) is always determined by some copula and the random set's onepoint coverageequivalent function. In turn, this is used to characterize directly the entire solution class of S to eq. (1), i.e., all onepoint coverageequivalents to h. Finally, with all of these results in place, it is shown that the only fuzzy logics admitting natural homomorphiclike relations involving arbitrary combinations of conjunctions and disjunctions, under mild assumptions, relative to all onepoint coverages of random sets, are those determined by conjunction, disjunction being: (min, max), (prod, probsum), and any proper ordinal sum of (prod, probsum), where probsum is the usual deMorgan transform of prod(uct). (AN)
Descriptors : *STOCHASTIC PROCESSES, *PROBABILITY DISTRIBUTION FUNCTIONS, *FUZZY SETS, MATHEMATICAL MODELS, RANDOM VARIABLES, STATISTICAL INFERENCE, MATHEMATICAL LOGIC, SOLUTIONS(GENERAL), OPERATORS(MATHEMATICS), SET THEORY, MAPPING(TRANSFORMATIONS), COMPUTATIONAL LINGUISTICS, POINT THEOREM.
Subject Categories : Theoretical Mathematics
Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE