Algebraic models and mv-algebras for fuzzy reasoning

This special issue moves from the last trends of mathematical research in fuzzy logic from its unlimited ground of applications, especially in the field of many-valued reasoning. It is well known that fuzzy logic is the logic of the "vague" concepts; its enormous success stands principally in the applicational aspects, minor progress must be noted in its mathematical fundaments. Since 1986 the MV-Algebras of the sentential calculus of Lukasiewicz seems to be a powerful tool to develop a serious well-founded algebraic calculus of fuzzy set theory, just like Boolean algebras do for classical set theory. The collection of papers here presented covers a wide spectrum of applications of these algebras to the fuzzy set theory and conversely, that is usual topics dealt in fuzzy environment are read from an "MV-point of view". This is possible because the usual fuzzy algebra [0,1] x of the fuzzy set from a referential set X into [0,1] is seen as an MV-algebra. Then popular fuzzy arguments like triangular norms, fuzzy probability, fuzzy inference, etc. find a better logical collocation in this new context and of course are redefined and rediscussed. The papers of S. Ray and S. Sessa, C.S. Hoo, V. Novak, G. Georgescu and I. Leustean, M. Chakraborty and J. Sen, C.A. Drossos and P. Karazeris go along these streams of investigation. We remind the interested fuzzists to the mentioned authors for a deeper and careful reading. The remaining papers of H.T. Nguyen et al., R.S. So16 et al., L. Di Lascio et al. cover other and different interesting arguments useful in approximate reasoning. Strictly speaking, these authors, respectively, show "how" to approximate a continuous t-norm by a strict Archimedean tnorm, "how" to build possibilistic networks for the management of imprecision coming from data and "how" to fuzzify the user's behavior during the navigation in a hypermedia system. Here "how" can be understood as the synonym of "algebraic model" (to a certain extent). Thanks are due to Piero Bonissone for his availability to consent the publication of this special issue.