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| Subject: cs607 idea solution Sat Jul 10, 2010 2:55 pm | |
| Q 1) What properties do the classical logic operators posses that are not shared byfuzzy logic operators?[You must be registered and logged in to see this image.] Q 2) When combining the fuzzy numbers A and ⌐A, what fuzzy logical operatorsshould be used? Since fuzzy numbers are fuzzy sets we may perform logical operation upon them. We now construct the intersection A and ⌐A using the conventional min-max logic.The intersection of A and ⌐A is not everywhere zero as we would expect from the laws of classical logic. Similarly the union A OR ⌐A is not everywhere one. Here min logical operator will be used Q 3) When combining the fuzzy quantities A and A, what fuzzy logical operatorsshould be used? Here max logic operator will be used. Q 4) For example we have given the following prepositions: MARKS 3P = A ^ BQ = A ν BFor all crisp truth values of A and B, construct a truth table for P, Q, P ^ Q, andP ν Q. Solution: | Truth Table For P ^ Q | | P | Q | P ^ Q | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | | | | | Truth Table For P | | A | B | P | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | | | | | Truth Table For Q | | A | B | Q | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | | | | | Truth Table ForP ν Q | | P | Q | P ν Q | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | Q 5) For example we have given the following prepositions: MARKS 3P = A | |
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