5 The paper surveys the present state of knowledge on t-norm based predicate fuzzy logics with their double semantics: standard (the set of truth values being the real interval [0,1]) and general with abstract algebras of truth functions. 7 © 2009 Published by Elsevier B.V.

In this chapter, we consider particular classes of infinite-valued propositional logics which are strongly related to t-norms as conjunction connectives and to the real unit interval as set of their truth degrees, and which have their implication connectives determined via an adjointness condition. Such systems have in the last ten years been of considerable interest, and the topic of important...

A general model of judgment aggregation is presented in which judgments on propositions are not binary but come in degrees. The primitives of the model are a set of propositions, an entailment relation, and a “triangular norm” which establishes a lower bound on the degree to which a proposition is true whenever it is entailed by a set of propositions. For an important class of agendas, we ident...

In this paper we present an O(nk) procedure, Algorithm MR3, for computing k eigenvectors of an n× n symmetric tridiagonal matrix T . A salient feature of the algorithm is that a number of different LDLt products (L unit lower triangular, D diagonal) are computed. In exact arithmetic each LDLt is a factorization of a translate of T . We call the various LDLt products representations (of T ) and,...

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum infere...

In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ε. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular...

In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equations of implications. In details, by means of the section of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(x, T1(y, z)) = T2(I(x, y), I(x, z)), when T1 is a continuous but not Archimedean triangular norm, T2 is a co...

Periods of matrix power sequences in max-drast fuzzy algebra and methods of their computation are considered. Matrix power sequences occur in the theory of complex fuzzy systems with transition matrix in max-t algebra, where t is a given triangular fuzzy norm. Interpretation of a complex system in max-drast algebra reflects the situation when extreme demands are put on the reliability of the sy...

In this paper we introduce and describe two classes of aggregation functions with members that are migrative. First continuous triangular norms are studied that own the migrative property with respect to another fixed t-norm, in particular to the three prototypes minimum, product, and the Łukasiewicz t-norm. For classes of nilpotent and strict migrative t-norms the characterization and construc...