On generation of digital fuzzy parametric conjunctions

Abstract

A new method of generation of digital fuzzy parametric conjunctions by means of basic t-norms is proposed. Fuzzy conjunctions also referred to as con-junctors and semicopulas. Digital fuzzy conjunctions are defined on the set of integer membership values L={0,1,2,2m-1}, where m is a number of bits used in presentation of membership values and I = 2m-1 denotes a maximal membership value corresponding to 1 in traditional set of true values L= [0,1]. The proposed method referred to as the monotone sum of fuzzy conjunctions generalizes the method of ordinal sum of t-norms and gives possibility to construct a wide class of digital fuzzy parametric conjunctions that have effective digital hardware implementation. The classes of simplest commutative digital fuzzy parametric conjunctions obtained by this method are described. These classes of operations can constitute a part of a library of basic blocks for generation of digital fuzzy systems. © 2009 Springer-Verlag Berlin Heidelberg.