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

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

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Moreno, and J. Penabad 8. : A fuzzy Prolog database system. John Wiley & Sons, Inc, West Sussex, England (1990) 9. : Foundations of Logic Programming, 2nd edn. Springer-Verlag, Berlin (1987) 10. : Multi-adjoint logic programming with continuous semantics. , Truszczyński, M. ) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 351–364. Springer, Heidelberg (2001) 11. : Similarity-based Unification: a multiadjoint approach. Fuzzy Sets and Systems 146, 43–62 (2004) 12. : Fuzzy Logic Programming. Fuzzy Sets and Systems 124(1), 361–370 (2001) A Fixed-Point Theorem for Multi-valued Functions with an Application to Multilattice-Based Logic Programming Jes´ us Medina , Manuel Ojeda-Aciego , and Jorge Ruiz-Calvi˜ no Dept.

Indices j i s m k t P set set set set set set set of of of of of of of original grains {j = 1, 2, . . , J} blended grains {i = 1, 2, . . , I} storage sites {s = 1, 2, . . , S} transportation modes {m = RL, RD} customers {k = 1, 2, . . , K} time periods {t = 1, 2, . . , T } original and blended products {I} + {J} Parameters The full set of parameters is as follows: demand for grain i (i ∈ {I, J}), by customer k, during time period t, Dikt the amount of original grain j supplied to storage site s, Supplyjs out loading capacity at storage site s, by using transportation m, LCapsm in loading capacity at customer k, by using transportation mode m, InCapkm combined out loading capacity for storage site s, ComCaps combined in loading capacity for customer k, ComCapk minimum ratio of original grain j in blended grain i, MinBlndij MaxBlndij maximum ratio of original grain j in blended grain i, maximum blending capacity at storage site s, BCaps ˜ skm TC freight cost for route from storage site s to customer k, by using transportation mode m, ˜ s unit storage cost at each storage site s, HC ˜ s BC unit blending cost at each storage site s.

The following example highlights this fact. Example 3. 9, where [[@∗1 ]](x, y, z, w) = ([[&L ]](x, y)+ [[∨G ]](z, w))/2. Note that R∗1 has exactly the same meaning (interpretation) that R1 , although different syntax. In fact, both of them have the same sequence of atoms in their head and bodies. The differences are regarding the set of aggregators which explicitly appear in their bodies since in R∗1 we have moved &L and ∨G from the body (see R1 ) to the definition of @∗1 . 63; {X/a, Y /b, X1/a, X2 /a, Y1 /b, Y2 /b} ∗ →AS1 R1 →AS2 R2 →AS2 R3 →AS2 R4 →AS2 R5 →IS →IS Note that, since we have exploited the same atoms with the same rules (except for the first steps performed with rules R1 and R∗1 ) in both derivations, then Oc (D1 ) = Oc (D1∗ ) = 5.

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