Download PDF by S.N. Sivanandam: Introduction to fuzzy logic using MATLAB

By S.N. Sivanandam

ISBN-10: 3540357807

ISBN-13: 9783540357803

ISBN-10: 3540357815

ISBN-13: 9783540357810

This ebook presents a broad-ranging, yet distinctive evaluation of the fundamentals of Fuzzy common sense. the basics of Fuzzy common sense are mentioned intimately, and illustrated with numerous solved examples. The e-book additionally offers with purposes of Fuzzy good judgment, to aid readers extra totally comprehend the thoughts concerned. strategies to the issues are programmed utilizing MATLAB 6.0, with simulated effects. The MATLAB Fuzzy common sense toolbox is supplied for simple reference.

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Extra info for Introduction to fuzzy logic using MATLAB

Example text

This is ∼ ∼ the membership mapping and is shown in Fig. 7. 1 Fuzzy Set Operations Considering three fuzzy sets A, B and C on the universe X. For a given ∼ ∼ ∼ element x of the universe, the following function theoretic operations for the set theoretic operations unions, intersection and complement are defined for A, B and C on X: ∼ ∼ Union: ∼ µA ∪ B (x) = µA (x)VµB (x). ∼ ∼ ∼ ∼ Intersection: µA ∩ B (x) = µA (x)ΛµB (x). ∼ ∼ ∼ ∼ Complement µ− (x) = 1 − µA (x). 3 Fuzzy Sets 21 mx(x) A ⊆ X → mA (x) ~ for all x ∈ X mf (x) = 0.

7. 8 Solution. 9 ⎦ . 5 Tolerance and Equivalence Relations Relations exhibit various other properties apart from that discussed in Sects. 4. It is already said that the relation can be used in graph theory. The various other properties that are dealt here include reflexivity, symmetry, and transitivity. These are discussed in detail for the crisp and fuzzy relations and are called as equivalence relation. Apart from these, tolerance relations of both fuzzy and crisp relations are also described.

2) LHS = RHS A ∪ (B ∪ C) = (A ∪ B) ∪ C. 2) 18 2 Classical Sets and Fuzzy Sets 2. (A ∩ (B ∩ C) = (A ∩ B) ∩ C LHS (a) (B ∩ C) = {1}. (b) A ∩ (B ∩ C) = {φ}. 3) RHS (A ∩ B) ∩ C (a) (A ∩ B) = {9}. (b) (A ∩ B) ∩ C = {φ}. 4) LHS = RHS A ∩ (B ∩ C) = (A ∩ B) ∩ C. Thus associative property is proved. The distributive property is given by, 1. A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) LHS (a) B ∩ C = {1}. (b) A ∪ (B ∩ C) = {9, 5, 6, 8, 10, 1}. 5) RHS (A ∪ B) ∩ (A ∪ C) (a) (A ∪ B) = {9, 5, 6, 8, 10, 1, 2, 3, 7}. (b) (A ∪ C) = {9, 5, 6, 8, 10, 1, 0}.

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Introduction to fuzzy logic using MATLAB by S.N. Sivanandam

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