Fuzzy Values in Fuzzy Logic* zy cb JIH L. Godo zyxwvu KJIHGF C. €.A. B.IC.S.I.C., Cami Sta. Barbara, 17300 Blanes, Girona, Spain J. Jacas E.T.S.A. Barcelona, Univ. Polit. Catalunya, Diagonal 649, 08028 Barcelona, Spain L. Valverde Dep. Cienc. Mat., Univ. llles Balears, Ctra. Valldemosa Km zyx EDC 7,5, 07071 Palma Mallorca, Spain zyxwv HGFE One of the main features of Fuzzy Logic is its capability to deal with the concept of compatibility between two propositions, in such a way that the inference process mod- eled through the Compositional Rule of Inference is independent from the particular possibility distributions involved. It is in this context that the compatibility functions can be considered as fuzzy truth values, labels or qualifications, playing the same role the values true and false play in the Classical Logic, where the meaning of propositions is nothing but its truth value. In this article we consider a restricted family of labels having the following desirable properties: (a) easy parametric representation, (b) eas semantic interpretation, (c) to allow a gradation in the family according to the modifica- tions performed by each label, and (d) to be closed under inference processes (FR- functions), and also under some suitable and meaningful operations between them. zy JI 1. INTRODUCTION AND PRELIMINARIES It is known that one of the main features of Fuzzy Logic is its capability to deal with the concept of compatibility between two propositions like zy IH “X is A ” and “X is A”’, where A and A’ are linguistic terms represented by fuzzy subsets of a given universe of discourse zyxw ONM U , inducing, respectively, possibility distributions on the values of the variable X. Such a compatibility is usually estimated by the so-called “inverse-tru functional modification” proposed by Baldwin’ in the following way Sup{A’(ir)lu E A-’({u})} if A-’({u}) # 0; otherwise. P A A ~ Q ) = *Research partially supported by the CSIC-CAICYT. project No. 836. INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, VOL. 6, 199-212 (1991) zyx 0 1991 John Wiley & Sons, Inc. CCC 0884-8173/91/020199- 14$04.00