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The fuzzy pay-off method for real option valuation (FPOM or pay-off method) [1] is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project (real
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.
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.
Type-2 fuzzy sets and systems generalize standard Type-1 fuzzy sets and systems so that more uncertainty can be handled. From the beginning of fuzzy sets, criticism was made about the fact that the membership function of a type-1 fuzzy set has no uncertainty associated with it, something that seems to contradict the word fuzzy, since that word has the connotation of much uncertainty.
Bart Andrew Kosko (born February 7, 1960) is an American writer and professor of electrical engineering and law at the University of Southern California (USC). He is a researcher and popularizer of fuzzy logic, neural networks, and noise, and the author of several trade books and textbooks on these and related subjects of machine intelligence.
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).
A systematic study of particular t-norm fuzzy logics and their classes began with Hájek's (1998) monograph Metamathematics of Fuzzy Logic, which presented the notion of the logic of a continuous t-norm, the logics of the three basic continuous t-norms (Łukasiewicz, Gödel, and product), and the 'basic' fuzzy logic BL of all continuous t-norms ...