A Fuzzy Rough Set Model Based on Reliability Over Dual-Universe and Its Applications

In this paper, using the weak fuzzy similarity relation, we propose a new similarity degree which describes the relationships between the 2-tuples in <inline-formula> <tex-math notation="LaTeX">$U\times V$ </tex-math></inline-formula>. In addition, we propose the reliability of each 2-tuples and use this reliability to give the calculation method of the similarity degree between the 2-tuples and the approximation set <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula>. Using this similarity degree, a new fuzzy rough set model is proposed. Furthermore, a new fuzzy rough entropy which describing the knowledge information in the dual-universe <inline-formula> <tex-math notation="LaTeX">$U\times V$ </tex-math></inline-formula> is defined. Then, we present a decision-making model to solve the problems, in which the elements in two different universes have different attributes. Finally, we give a significant algorithm which is applied to a decision-making problem in the dual-universe, and the effectiveness of this algorithm is verified by a numerical example.