An application of Schur-concave t-norms in pFCSP Endre Pap, Aleksandar Takaˇ ci Department of Mathematics and Informatics University of Novi Sad e-mail:pape@eunet.yu, atakaci@uns.ns.ac.yu Abstract Prioritized fuzzy constraint satisfaction problems (pFCSP’s) are used to model the concept of pri- ority in real time systems. Schur-concave t-norms are a key factor in the implementation of pFCSP. In this paper there are presented some results on the characterization of Schur-concave t-norms. There are tested two different pFCSP’s on a can- didate evaluation scenario. Using pFCSP’s, dif- ferent candidates are evaluated based on their education, experience and physical fitness for the jobs of teaching assistant and construction worker. Keywords: Schur-concavity, t-norms, priority, pFCSP. 1 Introduction In order to model real time systems sometimes it is necessary to incorporate the concept of priority into them. This can be done using Prioritized fuzzy constraint satisfaction problems (pFCSP’s). In a pFCSP, priority of constraints is considered as the global importance of a constraint among other ones. The more important the constraint is, the more impact it has on the aggregated output of the pFCSP system. They were introduced by Dubois et al. [2] (framework 1), an axiomatic framework was given in [7], and an alternative one was given in [10] (framework 2). The main difference between these two frame- works is the way they treat priority. Framework 2 favors the constraint with the larger priority regardless of its value. On the other hand, frame- work 1 favors the constraint with the larger prior- ity only when its value is smaller than the value of other less prioritized constraints. The paper has the following structure. In the sec- tion 2 some Schur-concave t-norms are introduced together with some results on their characteriza- tion. In the section 3 axiomatic frameworks 1 and 2 are presented. In the section 4 we have tested these two frameworks on a candidate evaluation scenario. 2 Schur-concave t-norms Let us recall the definition of t-norms. For more details on t-norms see [3]. Definition 1 A mapping T : [0, 1] 2 → [0, 1] is called a t-norm if the following conditions are sat- isfied for all x, y, z ∈ [0, 1]: (T1) T (x, y)= T (y,x) (T2) T (x, T (y,z )) = T (T (x, y),z ) (T3) if y ≤ z then T (x, y) ≤ T (x, z ) (T4) T (x, 1) = x. The four basic t-norms are: T M (x, y) = min(x, y) T P (x, y)= xy T L (x, y) = max(x + y − 1, 0) T D (x, y)=  0, if (x, y) ∈ [0, 1) 2 ; min(x, y), otherwise. One of the notions related to t-norms are level lines. for a continuous t-norm T they are obtained EUSFLAT - LFA 2005 380