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Exercise 6

Exercise 6. 6.4

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Exercise 6

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  1. Exercise 6

  2. 6.4 • Assume four types of fuzzy predicates applicable to persons (age, height, weight, and level of education). Several specific fuzzy predicates for each of these types are represented by fuzzy sets whose membership functions are specified in Fig. 8.10. Apply these membership functions and the fuzzy truth values denned in Fig. 8.2b to some person x (perhaps yourself) to determine the truth values of various propositions such as the following: x is highly educated and not very young is very true; • x is very young, tall, not heavy, and somewhat educated is true; • x is more or less old or highly educated is fairly true; • x is very heavy or old or not highly educated is fairly true; • x is short, not very young, and highly educated is very true, In your calculations, use standard fuzzy set operators (min, max, 1 — a).

  3. 6.8 • Assume that there are ten students in a class. About half of them are young girls. Most of those young girls are good students. Using the quantifiers specified in Fig. 8.5, answer the question: Approximately how many young girls in the class are good students?

  4. 6.9 • Suppose there axe five people in a women's figure skating competition. They are Anny, Bonnie, Cathy, Diana, and Eve. Assume that their relative goodness of performance is given by a fuzzy set E = 1/Anny + .9/Bonnie + .5/Cathy + .9/Diana + ,1/Eve. Using the quantifiers specified in Figs. 8.4 and 8.5, determine the truth values of the following fuzzy propositions: (a) There are about three persons who had good performances. (b) Most of them have good performance. (c) About half of them have good performance.

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