Some Generalized Results on Grey Number Operations Based on Liu-Lin Axioms of Greyness Degree and Information Content

Abstract

In this manuscript, with grounding in Liu–Lin axioms of greyness degree and information content, we provide new results that relate to these concepts in consideration of a number of mathematical operations over a sequence of grey numbers. In particular, we derive greyness degree results of summation, conic combination, and convex combination of a sequence, as well as inverse of a number and normalization of a number over a sequence. Then, we turn our attention to prove information content results for the union and intersection of a sequence. We illustrate our results by using a simple Monte Carlo simulation in the multi-attribute decision-making context, and by using an interesting dice-rolling experiment. Through our analysis, we also provide some new definitions, such as for conic combination, convex combination, normalization, and union and intersection operations. The novelty of the derived results in this study is that they can help researchers and practitioners of grey systems in tracking probable intensifications and reductions in the greyness degree in successive application steps of their working methods. Moreover, researchers are provided with two results to calculate information content for the union and intersection of grey numbers in an uncomplicated manner.