Showing papers on "Fuzzy number published in 1972"
TL;DR: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets.
Abstract: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets. This “entropy≓ may be regarded as a measure of a quantity of information which is not necessarily related to random experiments. Some mathematical properties of this functional are analyzed and some considerations on its applicability to pattern analysis are made.
2,024 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
112 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
TL;DR: It is shown that the minimum canonical sum-of-products form of a given fuzzy function is the union of all its prime implicants.
Abstract: It is shown that the minimum canonical sum-of-products form of a given fuzzy function is the union of all its prime implicants. A reduction rule, which is necessary and sufficient, is presented that will generate all the prime implicants.
31 citations
TL;DR: The concept of fuzzy set, introduced by L. A. Zadeh, is extended to a time dependent setting and fuzzy relations are defined and discussed.
21 citations
01 Jan 1972
14 citations