Fuzzy Discrete Structures - download pdf or read online

By Prof. Davender S. Malik, Prof. John N. Mordeson (auth.)

ISBN-10: 3790818380

ISBN-13: 9783790818383

ISBN-10: 3790824771

ISBN-13: 9783790824773

The topic of the e-book might be defined as fuzzy discrete buildings. The publication offers with fuzzy good judgment, fuzzy switching capabilities, fuzzy determination bushes, fuzzy networks, fuzzy petri nets, fuzzy course difficulties, fuzzy automata, and fuzzy languages. The concept of a fuzzy choice tree and a branch-bound-backtrack set of rules is gifted. within the Appendix, this set of rules is defined in C++. community movement issues of quite a few capacities are tested. Fuzzy shortest course innovations are awarded wherein there's an exact direction which corresponds to the bushy shortest direction. fresh effects on fuzzy automata and fuzzy languages also are presented.

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Sample text

Thus ! • We now consider the fuzzy logic inequality, where p E [0, 1]. Suppose that f is a fuzzy logic function in one variable. If we write f in disjunctive normal from, we have f(x) = ax + ex + d ::; p, where a, c, dE [0, IJ. ac + d::; p. ac + d::; p, then {x E [0,1] I ax + eX + d::; p} = [cap, aap]. Proof. Suppose that {x E [0,1]1 ax + ex + d ::; p} =10 0. Then 3xo E [0,1] such that axo + CXo + d ::; p. Clearly, d ::; p, axo ::; p, and cXo ::; p. Hence Xo ::; aap and Xo ~ cap. Thus cap::; aap.

Xn . (2) T' ~ T. (3) T' 1;. Pi, for any i, i = 1,2, ... ,r. 28 1. Fuzzy Logic Functions (4) No phrase exists having more literals than T' and satisfying (1), (2), and (3) above. From the definition of T', it follows that one of the variables will be missing from T'. If T' had all the set of variables appearing in it, condition (3) cannot be satisfied in the definition of T'. Suppose that the variable Xk, for some k, is missing from T'. Consider the phrase T'Xk. Clearly, T'Xk satisfies (1) and (2).

Hence acab ::; b(cab). Suppose that c > b. Then cab = b. If a ::; b, then acab ::; bcab. Suppose that a > b. Then aab = b. Since c > b, cab = b. Now aab = b. Thus by hypothesis b ::; b. Hence ab ::; bb and so a( cab) ::; b( cab). (iii)=>(i): If either a ::; bore::; b, then the result is immediate. Suppose that a > band c > b. Then cab = b. Hence ab ::; bb by hypothesis. Since a > b, it follows that b ::; b. Thus ! • We now consider the fuzzy logic inequality, where p E [0, 1]. Suppose that f is a fuzzy logic function in one variable.

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Fuzzy Discrete Structures by Prof. Davender S. Malik, Prof. John N. Mordeson (auth.)

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