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