We survey recent developments in the program of generating proof calculi for large classes of axiomatic extensions of a non-classical logics by translating each axiom into a set of structural rules, starting from a base calculus. We will introduce three proof formalisms: the sequent calculus, the hypersequent calculus and the display calculus. The calculi that are obtained derive exactly the th...

In this paper we will investigate which fuzzy/linguistic rules are redundant in systems of such rules called linguistic descriptions. We present a formal definition of redundancy and show that rules which are seemingly redundant can be in fact indispensable. These results apply for IF-THEN rules which use evaluative linguistic expressions (e.g., small, very big, etc.) and inference method calle...

There has been a growing interest and activity in the area of multiple criteria decision making (MCDM), especially in the last 25 years. modeling and optimization methods have been developed in both crisp and fuzzy environments. The overwhelming majority of approaches for finding best compromise solutions to MCDM problems do not make use of the interdependences among the objectives. However, as...

A new approach to optimization of processes described by fuzzy rules, in which the functional relationship between the decision variables and the objective function is not completely known, is introduced in this paper. It is based on stochastic algorithms and allows to determine optimal values of state variables and to optimize fuzzy rules (parameters of membership functions). Stochastic algori...

We identify various situations in probabilistic intelligent systems in which conditionals (rules) as mathematical entities as well as their conditional logic operations are needed. In discussing Bayesian updating procedure and belief function construction, we provide a new method for modeling if ... then rules as Boolean elements, and yet, compatible with conditional probability quantifications.

Abstract A new technique for adaptation of fuzzy membership functions in a fuzzy inference system is proposed. The technique relies upon the isolation of the specific membership function that contributed to the final decision, followed by the updating of this function’s parameters using steepest descent. The error measure used is thus back propagated from output to input, through the min and ma...