Didier Dubois and Henri Prade. Fuzzy rules in knowledge-based systems-modelling gradedness, uncertainty and preference. In R.R. Yager and L.A. Zadeh, editors, An Introduction to Fuzzy Logic Applications in Intelligent Systems. Kluwer Acad. Publ., Dordrecht, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in cases where it is not properly treated. Several pieces of work have considered the representation of approximate temporal knowledge. Among them we would stress those based on possibility the ory [Vitek, 1983; Dutta, 1988; Dubois and Prade, 1989; Kohlas and Monney, 1990; Console et al. 1991; Dubois et al. 1992; Marin et al. 1994; Barro et al. 1994; Vila and Godo, 1995] In particular, Barro et al. 1994] propose an straight forward redefinition of generalization of the notion of metric temporal constraint based on fuzzy sets [Marin et al. 1994] In this paper we propose an approximate temporal ....

.... for a given duration variable X on T)L , we aim at finding the certainty evaluation of a fuzzy proposition XisA (the condition of a rule) being A a fuzzy subset of T)L , knowing that the values of X are restricted by a possibility distribution r (the constraint induced by the temporal fact base) Dubois and Prade [1992] have discussed this issue and they propose to use the following measure: where Z is the reciprocal of the G6del s implication, and gA i8 he membership function of he fuzzy A. k is remarkable o noice ha E(gA[ 1 iff A , and ha E(gA[ reduces, when A is non fuzzy, o N(A) i,f 1 ( A , the ....

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Didier Dubois and Henri Prade. Fuzzy rules in knowledge-based systems-modelling gradedness, uncertainty and preference. In R.R. Yager and L.A. Zadeh, editors, An Introduction to Fuzzy Logic Applications in Intelligent Systems. Kluwer Acad. Publ., Dordrecht, 1992.

....makes sense. Given a possibility distribution p x and an event A, four basic estimates can be imagined which are in agreement with the ordinal nature of p x ; namely the possibility measure (see Zadeh [9] x (A) max u A p x (u) 1) the guaranteed possibility (see Dubois and Prade [1 2]) D x (A) min u A p x (u) 2) and the similar evaluations for non A , denoted A, whose complements to 1 are taken in order to define meaningful quantities for A (p x should be normalized) namely the necessity measure N x (A) min u A (1 p x (u) 1 x ( A) 3) the ....

D. Dubois and H. Prade, "Fuzzy rules in knowledge-based systems: modelling gradedness, uncertainty and preference", in An Introduction to Fuzzy Logic Applications in Intelligent Systems, eds. R.R. Yager and L.A. Zadeh, (Kluwer Acad. Publ., Boston, 1992) pp. 45-68

....rules as follows: two certainly rules are coherent if and only if support(A 1 ) support(A 2 ) implies core(B 1 ) core(B 2 ) 31) In other words, we are back to a coherence problem in classical logic. This result generalizes to subsets of rules with coherent condition parts (Dubois and Prade, 1994a) Coherence condition (30) writes for a knowledge base made of two gradual rules 1 A form of incoherence might only appear if after defuzzification of a non convex result (obtained by disjunctive combination) the precise conclusion, thus obtained, does not belong to the support of the nonconvex fuzzy set which is ....

Dubois D., Prade H. (1992a) Fuzzy rules in knowledge-based systems ---Modelling gradedness, uncertainty and preference---. In: An introduction to Fuzzy Logic Applications in Intelligent Systems (R.R. Yager, L.A. Zadeh, eds.), Kluwer Academic Publ., Dordrecht, 45-68.

....from the certainty that A is the minimal range of our ignorance to a total lack of information whatsoever. This kind of possibility qualification goes back to [Zad78b] and [San78] The above representations (23) and (24) can be generalized to the case where A is a fuzzy set, namely we have [DP92b] i) u U, p X (u) max( A (u) 1 a) a certainty qualification) ii) u U, p X (u) min( A (u) a) a possibility qualification) It is still equivalent to N(A) a and fl(A) a provided we use the following appropriate extensions of N and fl when A is fuzzy N(A) inf u U (1 ....

D. Dubois, and H. Prade. Fuzzy rules in knowledge-based systems --- Modelling gradedness, uncertainty and preference. In R.R. Yager and L.A. Zadeh, editors. An Introduction to Fuzzy Logic Applications in Intelligent Systems, pages 45-68. Kluwer Academic Publ., Dordrecht, 1992.

....at the level A(u) if X = u, and ii) if v B, nothing is said about the minimum possibility level of value v for Y. It leads to the following constraint on the conditional possibility distribution p Y X representing the rule u U, v V, min(A(u) B(v) p Y X (v,u) See Dubois and Prade [6] for a full justification of its semantics when both A and B are fuzzy. This model of fuzzy rule is close to Mamdani [13] s original proposal in fuzzy logic based control. Since we apply the principle the more similar are s and s 0 (in the sense of S) the more possible is that t and t 0 are ....

Dubois D. and Prade H., Fuzzy rules in knowledge-based systems ---Modelling gradedness, uncertainty and preference---, in: An Introduction to Fuzzy Logic Applications in Intelligent Systems, Edited by R.R. Yager and L.A. Zadeh, Kluwer Academic Publ., Dordrecht, 1992, pp. 45-68.

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