On a family of billiards-inspired operators over intuitionistic fuzzy sets

Abstract

In the present work we introduce a family of geometrically inspired operators over intuitionistic fuzzy sets. In essence, if we consider the interpretational triangle as a billiards table with certain properties and each point of an intuitionistic fuzzy set as a ball propelled with a predetermined initial force, then its image after bouncing off from the boundaries of the triangle will, in general, be a new and different intuitionistic fuzzy point. The value of this image depends on the magnitude and direction of the force, which we will describe by using a parameter λ > 0 and another intuitionistic fuzzy set over the same universe.