By S.N. Sivanandam
ISBN-10: 0131013998
ISBN-13: 9780131013995
Fuzzy good judgment, at the present is a sizzling subject, between academicians to boot quite a few programmers. This publication is supplied to provide a extensive, in-depth assessment of the sphere of Fuzzy good judgment. the fundamental ideas of Fuzzy good judgment are mentioned intimately with a number of solved examples. the various ways and suggestions to the issues given within the e-book are good balanced and pertinent to the bushy common sense learn tasks. The functions of Fuzzy good judgment also are dealt to make the readers comprehend the idea that of Fuzzy common sense. The options to the issues are programmed utilizing MATLAB 6.0 and the simulated effects are given. 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
Fuzzy Tolerance Relation If the fuzzy relation R1 satisfies both reflexivity and symmetry then it is called ∼ as fuzzy tolerance relation R1 . A fuzzy tolerance relation can be reformed into ∼ fuzzy equivalence relation at most (n−1) compositions. This is given by: R1n−1 = R1 ◦ R1 ◦ · · · ◦ R1 = R . 8. 8 0 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ 54 3 Classical and Fuzzy Relations is reflexive and symmetric. 6) . 5) . 5. The transitivity is satisfied hence equivalence relation is also satisfied. 9. Find whether the ⎡ 1 1 0 ⎢1 1 0 ⎢ 0 0 1 R=⎢ ⎢ ⎣0 0 0 0 1 0 given matrix is reflexive or not ⎤ 0 0 0 1⎥ ⎥ 0 0⎥ ⎥ by writing an M -file.
These two laws does not hold good for fuzzy sets. Since fuzzy sets can overlap, a set and its complement also can overlap. The excluded middle law for fuzzy sets is given by − A ∪ A = X, ∼ ∼ − A ∩ A = φ. ∼ ∼ Comparing Venn diagram for classical sets and fuzzy sets for excluded middle law are shown in Figs. 12. 2 Properties of Fuzzy Sets The properties of the classical set also suits for the properties of the fuzzy sets. The important properties of fuzzy set includes: Commutativity A ∪ B = B ∪ A, ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ A∩B = B ∩A.
The Cartesian product is denoted by A1 × A2 × · · · × An . In Cartesian product the first element in each pair is a member of x and the second element is a member of y formally, x × y = {(x, y)/x ∈ X and y ∈ Y }, if x = y then x × y = y × x. 38 3 Classical and Fuzzy Relations If all the An are identical and equal to A, then the cartesian product of A1 , A2 , . . , An becomes An . 1. The elements in two sets A and B are given as A = {0, 1} and B = {e, f, g} find the Cartesian product A × B, B × A, A × A, B × B.
Introduction to Fuzzy Logic using MATLAB by S.N. Sivanandam
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