Lógica difusa Bayesian updating and certainty theory are techniques for handling the uncertainty that arises, or is assumed to arise, from statistical variations or randomness. Possibility theory addresses a different source of uncertainty, namely vagueness in the use of language. Possibility theory, or fuzzy logic, was developed by Zadeh and builds upon his theory of fuzzy sets. Zadeh asserts that while probability theory may be appropriate for measuring the likelihood of a hypothesis, it says nothing about the meaning of the hypothesis.
Lógica difusa (cont.) Fuzzy logic is a many-valued logic, replacing the two classical truth values true (= 1) and false (= 0) by a continuum of truth values, usually represented by the unit interval [0,1]. Fuzzy sets, based on this many-valued logic, can be used to model linguistic vagueness which is intrinsically hidden in attributes like “large” and “small” and, in particular, the gradual transition between them. A main application of fuzzy logic is human-like reasoning in situations where vague, incomplete and/or (partially) contradictory knowledge is available, often in the form of rule-based systems as in fuzzy control
Fuzzy variables, fuzzy sets, operations in fuzzy sets The theory of fuzzy sets expresses imprecision quantitatively by introducing characteristic membership functions that can assume values between 0 and 1 corresponding to degrees of membership from “not a member” through to “a full member.” If F is a fuzzy set, then the membership function µF (x) measures the degree to which an absolute value x belongs to F This degree of membership is sometimes called the possibility that x is described by F.
Fuzzy variables, fuzzy sets, operations in fuzzy sets A fuzzy variable is one that can take any value from a global set (e.g., the set of all temperatures), where each value can have a degree of membership of a fuzzy set (e.g., low temperature) associated with it.
Fuzzy expert systems A fuzzy expert system is an expert system that uses fuzzy logic instead of Boolean logic. A fuzzy expert system is a collection of membership functions and rules that are used to reason about data. Unlike conventional expert systems, which are mainly symbolic reasoning engines, fuzzy expert systems are oriented toward numerical processing.
Fuzzy rules The rules in a fuzzy expert system are usually of a form similar to the following: if x is low and y is high then z = medium where x and y are input variables, z is an output variable, low is a membership function (fuzzy subset) defined on x, high is a membership function defined on y, and medium is a membership function defined on z. The antecedent describes to what degree the rule is applicable; the consequent assigns a membership function to each of one or more output variables.
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