On Computation of the Compositional Rule of Inference Under Triangular Norms

This paper is devoted to the derivation of exact calculation formulas for the compositional rule of inference under Archimedean t-norms, when both the observation and the relation parts are given by Hellendoorn's #-function [6]. Keywords: Triangular norm, compositional rule of inference, Lagrange's multipliers method, 1 Introduction The inference process from imprecise or vague premises is becoming more and more important for knowledge-based systems, especially for fuzzy expert systems [9,12,13,15]. In approximate reasoning there are several kinds of inference rules, which deal with the problem of deduction of conclusions in an imprecise setting. An important problem is the (approximate) computation of the membership function of the conclusion in these schemes [1,4,6,7,8,10]. This paper deals with the derivation of exact calculation formulas for the compositional rule of inference, which has the global scheme [14] Observation: x has property P Relation: x and y have relation W Conc..

Stability in Multiobjective Possibilistic Linear Programs with Weakly Noninteractive Fuzzy Number Coefficients

Stability and sensitivity analysis becomes more and more attractive also in the area of multiple objective mathematical programming (for excellent surveys see e.g. [Gal86] and [Rios90]). Publications on this topic usually investigate the impact of parameter changes (in the righthand side or/and the objective function or/and the 'A-matrix' or/and the domination structure) on the solution in various models of vectormaximization problems, e.g. linear or non-linear, deterministic or stochastic, static or dynamic (see e.g. [Dev79, Rari83, Rios91]). There are only few paper dealing with stability or sensitivity analysis in fuzzy mathematical programming (e.g. [Ham78, Tan86, Ful89, Fed92, Fef92, Dut92]). In this paper, generalizing the earlier results [Fed92,Fef92] of the second and third co-authors', we show that the possibility distribution of the objectives of an Multiobjective Possibilistic Linear Program (MPLP) under continuous triangular norms is stable under small changes in the member..