By A. R. D. Mathias, H. Rogers

ISBN-10: 354005569X

ISBN-13: 9783540055693

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**Additional info for Cambridge Summer School in Mathematical Logic, Cambridge, 1971**

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Applied Mathematics and Computation 163, 245–251 (2005) ¨ 10. : Multi-objective fuzzy regression: a general framework. Computers and Operations Research 27, 635–652 (2000) 11. : Multiobjective fuzzy linear regression analysis for fuzzy input-output data. Fuzzy Sets and Systems 47, 173–181 (1992) 12. : An ”ordewise”’ polynomial regression procedure for fuzzy data. Fuzzy Sets and Systems 130, 1–19 (2002) 13. : Fuzzy data analysis by possibilistic linear models. Fuzzy Sets and Systems 24, 363–375 (1987) 14.

Fig. 1 illustrates the case n = 4. 7]. The case n > 1 corresponds to cooperative reactions. The crisp repressor dependencies (11) are replaced by either of the equivalent forms v1 v0 1 + k x n −1 x k = v0 v1 1 + n −1 . From these expressions, it is clear that the passage from crisp to fuzzy logic is formally achieved by the replacement [[1 > λ]] −→ −1 [1 + λn ] . 5 0 0 y/l x/k Fig. 2. Fuzzy and gate Here, the dimensionless quantity λ is taken as k/x for activators and x/k for repressors. The conversion process is illustrated in the following paragraph.

In addition, we shall study syllogisms and reasoning on the basis of our approach. Finally, we plan to apply these results in data mining, quantiﬁcation in description logics and summarization. References 1. : Voting-model based evaluation of fuzzy quantified sentences: A general framework. Fuzzy Sets and Systems 146(1), 97–120 (2004) 2. : Monotonic quantified statements and fuzzy integrals. In: Proc. NAFIPS/IFIS/NASA Conference, pp. 8–12 (1994) 3. : Linguistic quantifiers based on choquet integrals.

### Cambridge Summer School in Mathematical Logic, Cambridge, 1971 by A. R. D. Mathias, H. Rogers

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