Showing papers on "Fuzzy logic published in 1972"
01 Jan 1972
TL;DR: A basic idea suggested in this paper is that a linguistic hedge such as very, more or less, much, essentially, etc. may be viewed as an operator which acts on the fuzzy set representing the meaning of its operand.
Abstract: A basic idea suggested in this paper is that a linguistic hedge such as very, more or less, much, essentially. slightly, etc. may be viewed as an operator which acts on the fuzzy set representing the meaning of its operand. For example, in the case of the composite term very tall man, the operator very acts on the fuzzy meaning of the term tall man. To represent a hedge as an operator, it is convenient to define several elementary operations on fuzzy sets from which more complicated operations may be built up by combination or composition. In this way, an approximate representation for a hedge can be expressed in terms of such operations as complementation, intersection, concentration, dilation, contrast intensification, fuzzification, accentuation, etc. Two categories of hedges are considered. In the case of hedges of Type I, e.g., very, much, more or less, slightly, etc., the hedge can be approximated by an operator acting on a single fuzzy set. In the case of hedges of Type II, e.g., technical...
882 citations
01 Jan 1972
TL;DR: In this paper, it was shown that under certain conditions a precise control goal can be attained with fuzzy observation and control as long as the observations become sufficiently precise when the goal is approached.
Abstract: A fuzzy mapping from X to Y is a fuzzy set on X × Y. The concept is extended to fuzzy mappings of fuzzy sets on X to Y, fuzzy function and its inverse, fuzzy parametric functions, fuzzy observation, and control. Set theoretical relations are obtained for fuzzy mappings, fuzzy functions, and fuzzy parametric functions. It is shown that under certain conditions a precise control goal can be attained with fuzzy observation and control as long as the observations become sufficiently precise when the goal is approached.
741 citations
TL;DR: It is proved that, in fuzzy logic, a set of clauses is unsatisfiable iff it is unsatisfiability in two-valued logic, and it is also shown that if the most unreliable clause of aSet of clauses has a truth-value a>0.5, then all the logical consequences obtained by repeatedly applying the resolution principle has truth- value never smaller than a.
Abstract: The relationship between fuzzy logic and two-valued logic in the context of the first order predicate calculus is discussed. It is proved that if every clause in a set of clauses is something more than a “half-truth” and the most reliable clause has truth-value a and the most unreliable clause has truth-value b , then we are guaranteed that all the logical consequences obtained by repeatedly applying the resolution principle will have truth-value between a and b . The significance of this theorem is also discussed.
292 citations
TL;DR: The investigation of the formal systems obtained by extending well-known connectives to continuous arguments, called ''soft algebras,'' are investigated and it is shown that every soft algebra is a bounded, distributive and symmetric lattice.
46 citations
TL;DR: An abstract model for the execution of fuzzy programs using finite-state machines is described and it is shown that the performance function λ of a fuzzy machine M can be effectively constructed so that the program searching cost of an elementary fuzzy program, a number of elementary fuzzy programs, or a regular fuzzy program is minimized.
Abstract: An abstract model for the execution of fuzzy programs using finite-state machines is described, Different ways of executing fuzzy programs are investigated. It is shown that the performance function ? of a fuzzy machine M? can be effectively constructed so that the program searching cost of an elementary fuzzy program, a number of elementary fuzzy programs, or a regular fuzzy program is minimized. Some application examples are discussed.
46 citations
01 Jan 1972
14 citations