Multi-granulation rough approximations under normal distribution

Multi-granulation decision-theoretic rough set effectively combines Bayesian decision approaches with multi-granulation rough set theory, and provides an important theoretical framework for studying rough set. We mainly explore some extensional models of multi-granulation decision-theoretic rough set under the condition that the decision loss function is normally distributed. According to the 3σ rule of normal distribution, the decision loss of multi-granulation decision-theoretic rough set is transformed into a set of interval values, and the upper and lower approximations are constructed from the optimistic, weakly optimistic, pessimistic, weakly pessimistic, optimistic-pessimistic, weakly optimistic-pessimistic, pessimistic-optimistic, weakly pessimistic-optimistic viewpoints, and the decision rules of the proposed rough set models are given. The work in this paper makes the decision behavior based on multi-granulation decision-theoretic rough set more close to the actual situation.