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Let (G, *) be a group and A a fuzzy subset of G. Then A is a fuzzy subgroup of G if for all x, y in G, A(x*y −1) ≥ min(A(x), A(y −1)). A similar generalization principle is used, for example, for fuzzification of the transitivity property. Let R be a fuzzy relation on X, i.e. R is a fuzzy subset of X × X.
Fuzzy logic is an important concept in medical decision making. Since medical and healthcare data can be subjective or fuzzy, applications in this domain have a great potential to benefit a lot by using fuzzy-logic-based approaches. Fuzzy logic can be used in many different aspects within the medical decision making framework.
Fuzzy logic-based control systems can be found, for example, in the field of household appliances in washing machines, dish washers, microwave ovens, etc. or in the area of motor vehicles in gear transmission and braking systems.
A fuzzy control system is a control system based on fuzzy logic – a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectively).
Nowadays engineers, statisticians and programmers often represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets [13] (see also fuzzy set theory). Fuzzy logic can play a significant role in artificial intelligence programming, for example because it can model human cognitive processes more easily ...
FuzzyCLIPS is a fuzzy logic extension of the CLIPS (C Language Integrated Production System) expert system shell from NASA. It was developed by the Integrated Reasoning Group of the Institute for Information Technology of the National Research Council of Canada and has been widely distributed for a number of years. It enhances CLIPS by ...
The place of defuzzification in a fuzzy control system A particular defuzzification method. Defuzzification is the process of producing a quantifiable result in crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems.
It is the standard semantics for disjunction in Gödel fuzzy logic and for weak disjunction in all t-norm based fuzzy logics. Graph of the probabilistic sum Probabilistic sum ⊥ s u m ( a , b ) = a + b − a ⋅ b = 1 − ( 1 − a ) ⋅ ( 1 − b ) {\displaystyle \bot _{\mathrm {sum} }(a,b)=a+b-a\cdot b=1-(1-a)\cdot (1-b)} is dual to the ...