Fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems

In this paper, we study the fuzzy reasoning based on a new fuzzy rough set. First, we define a broad family of new lower and upper approximation operators of fuzzy sets between different universes using a set of axioms. Then, based on the approximation operators above, we propose the fuzzy reasoning based on the new fuzzy rough set. By means of the above fuzzy reasoning based on the new fuzzy rough set, for a given premise, we can obtain the fuzzy reasoning consequence expressed by the fuzzy interval constructed by the above two approximations of fuzzy sets. Furthermore, through the defuzzification of the lower and upper approximations, we can get the corresponding two values constructing the interval used as the fuzzy reasoning consequence after defuzzification. Then, from the above interval, a suitable value can be selected as the final reasoning consequence so that some special constraints are satisfied as possibly. At last, we apply the fuzzy reasoning based on the new fuzzy rough set to the scheduling problems, and numerical computational results show that the fuzzy reasoning based on the new fuzzy rough set is more suitable for the scheduling problems compared with the fuzzy reasoning based on the CRI method and the III method.