Fuzzy logic in database

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Title: Fuzzy logic in database

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Fuzzy logic is a branch of mathematics which is a generalisation of classical logic and set theory, based on the notion of fuzzy set firstly introduced by Lotfi Zadeh in 1965 as an object with membership function of element to a set taking any values on the interval {\displaystyle [0,1]}[0, 1], not only {\displaystyle 0}{\displaystyle 0} or {\displaystyle 1}1. On the basis of this concept, various logical operations on fuzzy sets are introduced and the concept of a linguistic variable whose values are fuzzy sets is formulated. The subject of fuzzy logic is the study of reasoning under fuzzy, fuzzy conditions, similar to reasoning in the ordinary sense, and its application in computing systems. Directions for fuzzy logic research There are currently at least two main lines of research in fuzzy logic: Fuzzy logic in the broad sense (approximate computation theory); Fuzzy logic in a narrow sense (symbolic fuzzy logic). Symbolic fuzzy logic. Symbolic fuzzy logic is based on the notion of t-norm. After selecting some t-norm (and it can be entered in several different ways) it becomes possible to define the basic operations on propositional variables: conjunction, disjunction, implication, negation, and others. It is not difficult to prove the theorem that the distributivity present in classical logic is satisfied only when the Gödel t-norm is chosen as the t-norm. In addition, for certain reasons, an operation called residium is most often chosen as an implication (which, generally speaking, also depends on the choice of the t-norm). The definition of the basic operations listed above leads to a formal definition of basic fuzzy logic, which has much in common with classical Boolean logic (more precisely, with the calculus of statements). There are three main basic fuzzy logics: Lukasiewicz logic, Gödel logic and probabilistic logic. Interestingly, combining any two of the three logics listed above leads to classical Boolean logic.

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