New PDF release: Applications of Fuzzy Sets Theory: 7th International

By Célia da Costa Pereira, Andrea G. B. Tettamanzi (auth.), Francesco Masulli, Sushmita Mitra, Gabriella Pasi (eds.)

ISBN-10: 354073399X

ISBN-13: 9783540733997

ISBN-10: 3540734007

ISBN-13: 9783540734000

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Read Online or Download Applications of Fuzzy Sets Theory: 7th International Workshop on Fuzzy Logic and Applications, WILF 2007, Camogli, Italy, July 7-10, 2007. Proceedings PDF

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Extra info for Applications of Fuzzy Sets Theory: 7th International Workshop on Fuzzy Logic and Applications, WILF 2007, Camogli, Italy, July 7-10, 2007. Proceedings

Sample text

Proposition 2.

Dn are, respectively, the leaves of τ . A P E k −reductant is a P E−reductant which is obtained building a depth k unfolding tree. In this section we apply the cost measures just introduced to compare the efficiency of these two semantically equivalent notions of reductants. We start with an example showing the appropriateness of our cost criteria. Example 5. 9 R4 : q(a, b)← ; The reductant for P and p(a) is: R ≡ p(a) ← @(q(a, b), 1, q(X1 , b)); 1 . 4, z)}. a. and we are going to see that their operational/interpretive costs are also the same.

Measuring the Interpretive Cost in Fuzzy Logic Computations 33 improved notion of interpretive cost, denoted Ic+ (D), is the sum of the weights of the aggregators evaluated in every interpretive step of derivation D. Example 4. Looking at the definitions given before for aggregators &P , ∨G , &L , @1 and @∗1 , it is easy to see that: W(&P ) = 1, W(&L ) = 3, W(∨G ) = 1, W(@1 ) = 2 and W(@∗1 ) = 2 + W(&L ) + W(∨G ) = 2 + 3 + 1 = 6. Consequently, we have that Ic+ (D1 ) = W(&L ) + W(∨G ) + W(@1 ) + W(&P ) = 3 + 1 + 2 + 1 = 7, and Ic+ (D1∗ ) = W(@∗1 ) + W(&P ) = 6 + 1 = 7.

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Applications of Fuzzy Sets Theory: 7th International Workshop on Fuzzy Logic and Applications, WILF 2007, Camogli, Italy, July 7-10, 2007. Proceedings by Célia da Costa Pereira, Andrea G. B. Tettamanzi (auth.), Francesco Masulli, Sushmita Mitra, Gabriella Pasi (eds.)


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