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Statistics and Random Processes
Classical Relations and Fuzzy Relations
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A-cut algorithm alternative assigned Bezdek calculate Cartesian product Chapter classes classical cluster column control system crisp sets data points data sample data set decision defined defuzzification denoted described determine developed DSW algorithm engineering equations equivalence relation example expected utility expert expressed extension principle FIGURE focal elements fuzzy control fuzzy information fuzzy logic fuzzy numbers fuzzy output fuzzy relation fuzzy set fuzzy set theory fuzzy system fuzzy variables fuzzy vectors genetic algorithms given graphical Hence illustrated implication input variable intersection interval linguistic variables mapping matrix max-min composition maximum measure membership functions membership values method motor neural network nonlinear operations optimum parameters pattern recognition perfect information Posterior probabilities prior probabilities probability problem propositions region represented rule-based rules shown in Fig simulation singleton solution space speed strings Suppose Table temperature truth value uncertainty universe of discourse universe X voltage Zadeh zero