The Discussion On Some Questions Of Fuzzy Rough Sets

Nanda and Majumdar presented the concept of fuzzy rough sets in 1992. Several scholars have carried out the discussion on the theory and application of fuzzy rough sets subsequently, and have achieved fruitful outcome.These impulse the develepement of the theory of fuzzy sets infinitely.The main devotion of the paper classifies the following four parts:The first part outlines the background and development of fuzzy rough sets.The second part discusses the constructing properties of fuzzy rough sets and the properties of cut sets. On the basis of the third paper, the eight decomposition theorems are presents and we point out some decomposition theorems of the fuzzy sets of Zadeh are not generalized to the fuzzy rough sets by reason of the partial order. The unreasonableness in the third paper is proposed. Two definitions of L-nested sets are presented, utilizing the results of decomposition theorems.The third part discusses the properties of the first type of L-nested set, introduces an involutive order reversing operation in the lattice, and gives three representation theorems of rough fuzzy sets by two methods. At last, the valuable conclusions on the second type of L-nested set are presented, lay the foundation of discussing the property of fuzzy rough sets furtherly.The fourth part presents the properties of the inclusion degree and similarity degree of L-fuzzy sets. On the basis, the inclusion degree and similarity degree of fuzzy rough sets are defined. The generating methods of the inclusion degree and similarity degree of fuzzy rough sets presented, utilizing the proved properties of the inclusion degree and similarity degree. Finally, the generating problem of the strong inclusion degree and strong similarity degree is discussed furtherly from another hand by the way of constructing some functions.