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A Study on Constructions of T-norms and Properties of T-norms-related Operators

Author: YiZhiHong
Tutor: ZuoFeng
School: Jiangxi Normal University
Course: Applied Mathematics
Keywords: Fuzzy Logic Triangular norm Construction of triangular norms Rotation Method Rotate zeroing method Fuzzy Implication R- implication S- implication QL- implication Boolean iteration law
CLC: O159
Type: Master's thesis
Year: 2008
Downloads: 93
Quote: 1
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Abstract


Triangular norm is the unit interval [ 0,1 ] in increments of 1 on the dollar exchange semigroups , it is widely used in the statistical theory of metric spaces , fuzzy logic , fuzzy set theory, information aggregation and artificial intelligence in various fields . For a long time , triangular mode theory and its application has also been one of the hot people . As a special class of algebraic structures , triangular module structure is to recognize the key triangle mode structure ; Moreover, in order to better application , it is also very concerned with the triangular norm -related function equation . This will be based on these two aspects , discuss triangular module structure and properties of triangular norm operator of the relevant Chapter 1 introduces the triangular norm and its associated operator basic concepts related to the nature of this triangular norm constructor. Chapter 2 focuses on the weak negative zero rotation method and the rotation method was constructed . First analyzed the weak negation operator 's basic nature ; Then given the weak negative rotation method on the structure , weak negation involved only one possible discontinuity points t = sup {s ∈ [0,1] | N ( s) gt; s}; Jenei the rotation method as a part of the extended form , not all are suitable for weak negative rotation method to construct , in the third quarter gives specific examples to illustrate this point ; then gives weak negative zero rotation on the structure of the law , which requires its weak negation involution point set that contains interval [a, 1] (a lt; 1). In this chapter, the final answer to the text [ 1 ] to be a problem , and proposed structure and decomposition of triangular norms on public issues . Chapter 3 discusses the relevant operator triangular norm nature . First gives S_D (T_D)-QL iteration law function implies satisfy Boolean equation I (x, y) = I (x, I (x, y)) is necessary and sufficient condition is then given Boolean equations iterative law function S (a, b) = S (T (a, b), T (S (a, b), N (T (a, b)))) two sufficient conditions for solvability .

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