Generalized dominance rough set models for the dominance intuitionistic fuzzy information systems

Abstract

Dominance rough sets generalize classical rough sets by replacing the equivalence relation with a dominance relation. However, the existing dominance relations are still too restrictive to convenient for its practical applications because they are always considering a strict decreasing or increasing order for each attribute. In fact, in many real-world problems, we only need to employ the decreasing or increasing order in terms of partial attributes rather than all attributes or even just focus on overall evaluations of objects. Based on this phenomenon, in this paper we define two new dominance relations and obtain two generalized dominance rough set models according to define the overall evaluations and add particular requirements for some individual attributes. Meanwhile, the attribute reductions of dominance intuitionistic fuzzy decision information systems are also examined with these two models. Firstly, we define a generalized dominance relation and obtain a generalized dominance rough set model by using the intuitionistic fuzzy additive operator to aggregate individual attribute value of each object into a overall evaluation. The attribute reduction of intuitionistic fuzzy information systems with generalized dominance rough set are also explored. Secondly, we introduce another dominance relation named as generalized β-dominance relation and the generalized β-dominance rough set model by adding a parameter β ∈ [0, 1] in generalized dominance relation in order to control the number of attributes which satisfy dominance relations, from which we can induce all “at least” and “at most” decision rules. An algorithm is developed to compute the lower and upper β-dominance approximations in order to get all the lower and upper reducts of intuitionistic fuzzy decision systems. Some numerical examples are employed to substantiate the conceptual arguments.