New types of aggregation operators in intelligent systems: absorbing norms and evolutionary operators

Abstract

In this paper new types of aggregation operators, namely absorbing norms and parametric type of operator families called distance-based or evolutionary operators are introduced. Absorbing-norms are commutative, associative binary operators having an absorbing element from the unit interval. The detailed discussion of properties and structure of these operators are given in the paper. Two types of distance-based operators are defined. The maximum and minimum distance operators with respect to e have the value of the element, which is farther, or nearer to e, respectively, where e is an arbitrary element of the unit interval [0,1]. The special cases e=0 and e=1 lead to the max and min operators. The new operators are evolutionary types in the sense that if e is increasing starting from zero till e=1 the min operator is developing into the max operator, while on the other side the max is transformed into the min operator. It is shown that the evolutionary operators can be constructed by means of min and max operators, which are also special cases of the operators. The maximum distance operators are special operators called uninorms and the minimum distance ones are absorbing-norms, introduced in this paper.