Accession Number : ADA305715

Title :   A New Characterization of Fuzzy Logic Operators Producing Homomorphic-Like Relations with One-Point 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 one-point coverage-equivalent 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 one-point coverage-equivalent function. In turn, this is used to characterize directly the entire solution class of S to eq. (1), i.e., all one-point coverage-equivalents to h. Finally, with all of these results in place, it is shown that the only fuzzy logics admitting natural homomorphic-like relations involving arbitrary combinations of conjunctions and disjunctions, under mild assumptions, relative to all one-point 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