T-norm fuzzy logics - определение. Что такое T-norm fuzzy logics
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Что (кто) такое T-norm fuzzy logics - определение


T-norm fuzzy logics         
T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that takes the real unit interval [0, 1] for the system of truth values and functions called t-norms for permissible interpretations of conjunction. They are mainly used in applied fuzzy logic and fuzzy set theory as a theoretical basis for approximate reasoning.
T-norm         
  • Graph of the bounded sum t-conorm
  • Graph of the drastic t-conorm. The function is discontinuous at the lines 1 > ''x'' = 0 and 1 > ''y'' = 0.
  • Graph of the drastic t-norm. The function is discontinuous at the lines 0 < ''x'' = 1 and 0 < ''y'' = 1.
  • Graph of the Einstein sum
  • Graph of the Hamacher product
  • Graph of the Łukasiewicz t-norm
  • Graph of the maximum t-conorm (3D and contours)
  • Graph of the minimum t-norm (3D and contours)
  • Graph of the nilpotent maximum. The function is discontinuous at the line 0 < ''x'' = 1 – ''y'' < 1.
  • Graph of the nilpotent minimum. The function is discontinuous at the line 0 < ''x'' = 1 − ''y'' < 1.
  • Graph of the probabilistic sum
  • Graph of the product t-norm
  • Standard Łukasiewicz implication.
  • Standard Gödel implication. The function is discontinuous at the line ''y'' = ''x'' < 1.
  • Residuum of the nilpotent minimum. The function is discontinuous at the line 0 &lt; ''y'' = ''x'' &lt; 1.
  • Goguen implication. The function is discontinuous at the point ''x'' = ''y'' = 0.
In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic.
fuzzy subset         
  • Some Key Developments in the Introduction of Fuzzy Set Concepts.<ref name="CADsurvey"/>
SETS WHOSE ELEMENTS HAVE DEGREES OF MEMBERSHIP
Fuzzy sets; Fuzzy set theory; Fuzzification; Fuzzy subset; Credibility(fuzzy); Fuzzy category; Goguen category; Fuzzy Sets; Fuzzy relation equation; Pythagorean fuzzy set; Degree of membership; Uncertain set
In fuzzy logic, a fuzzy subset F of a set S is defined by a "membership function" which gives the degree of membership of each element of S belonging to F.