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

**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 resources 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**

Intuitively, given a program P and a ground atomic goal A, a P E−reductant can be constructed following these steps: i) Construct an unfolding tree5 , τ , for P 4 5 That is, there exists a θi such that A = Ci θi . An unfolding tree is a possible incomplete search tree. That is, a search tree, of the atom A in the program P, built using a breath-ﬁrst search strategy where some nodes may be let unexpanded (See [7] for a formal deﬁnition of this concept, that we omit by the lack of space). 34 P. Julián, G.

The transﬁnite chain (xi )i∈I constructed this way is increasing, therefore there is an ordinal α such that xα = xα+1 ∈ f (xα ), so xα is a ﬁxed point and xα x ✷ but by minimality of the ﬁxed point x, we have that x = xα . The usual way to approach the problem of reachability is to consider some kind of ‘continuity’ in our multi-valued functions, understanding continuity in the sense of preservation of suprema and inﬁma. But it is obvious that we have to state formally what this preservation is meant, since in complete multilattices we only have for granted the existence of sets of multi-inﬁma and sets of multisuprema.

Using Lai and Hwang’s approach [12], we substitute minimizing cm , maximizing (cm − co ), and minimizing (cp − cm ). That is, the approach used in this work involves minimizing the most possible value of the imprecise costs, cm , maximizing the possibility of lower costs (cm − co ), and minimizing the risk of obtaining higher cost (cp − cm ). The three replaced objective functions can be minimized by pushing the three prominent points towards left. In this way, our problem can be transformed into a multi-objective linear programming as follows: m m ˜ skm zjskmt + TC min z1 = i,s,t j,s,k,m,t m−o ˜ BC s p−m ˜s BC p−m ˜s HC bist + i,s,t j,s,k,m,t (13) Ijst (14) Ijst (15) j,s,t p−m ˜ skm zjskmt + TC m−o ˜ HC s bist + i,s,t j,s,k,m,t min z3 = ˜ s Ijst HC j,s,t m−o ˜ TC skm zjskmt + max z2 = m ˜ s bist + BC j,s,t In this study, we suggest Zimmermann’s fuzzy programming method with normalization process [25].

### 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.)

by Steven

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