# Lesson 31 - Module 11 Reasoning with uncertainty-Fuzzy...

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Module 11 Reasoning with uncertainty-Fuzzy Reasoning Version 1 CSE IIT, Kharagpur

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Lesson 31 Fuzzy Set Representation Version 1 CSE IIT, Kharagpur
11.3 Fuzzy Sets: BASIC CONCEPTS The notion central to fuzzy systems is that truth values (in fuzzy logic) or membership values (in fuzzy sets) are indicated by a value on the range [0.0, 1.0], with 0.0 representing absolute Falseness and 1.0 representing absolute Truth. For example, let us take the statement: "Jane is old." If Jane's age was 75, we might assign the statement the truth value of 0.80. The statement could be translated into set terminology as follows: "Jane is a member of the set of old people." This statement would be rendered symbolically with fuzzy sets as: mOLD(Jane) = 0.80 where m is the membership function, operating in this case on the fuzzy set of old people, which returns a value between 0.0 and 1.0. At this juncture it is important to point out the distinction between fuzzy systems and probability. Both operate over the same numeric range, and at first glance both have similar values: 0.0 representing False (or non- membership), and 1.0 representing True (or membership). However, there is a distinction to be made between the two statements: The probabilistic approach yields the natural-language statement, "There is an 80% chance that Jane is old," while the fuzzy terminology corresponds to "Jane's degree of membership within the set of old people is 0.80." The semantic difference is significant: the first view supposes that Jane is or is not old (still caught in the Law of the Excluded Middle); it is just that we only have an 80% chance of knowing which set she is in. By contrast, fuzzy terminology supposes that Jane is "more or less" old, or some other term corresponding to the value of 0.80. Further distinctions arising out of the operations will be noted below. The next step in establishing a complete system of fuzzy logic is to define the operations

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Lesson 31 - Module 11 Reasoning with uncertainty-Fuzzy...

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