L-fuzzy generalized neighborhood system-based pessimistic L-fuzzy rough sets and its applications

In this paper, a new type of L-fuzzy generalized neighborhood system is introduced and then novel L-fuzzy rough sets based on it are defined and discussed. It is verified that the proposed model is an extension of Pang’s generalized neighborhood system-based pessimistic rough sets and so called L-fuzzy generalized neighborhood system-based pessimistic L-fuzzy rough sets. Firstly, the basic properties of the novel model are studied. To regain some Pawlak’s properties which are lost in the novel model, the serial, reflexive, transitive and symmetric conditions for L-fuzzy general neighborhood systems are defined. Secondly, the axiomatic characterizations of the pessimistic L-fuzzy rough sets and that generated by serial, reflexive and symmetric L-fuzzy general neighborhood systems are given, respectively. Thirdly, a reduction theory preserving L-fuzzy approximation operators is established. Finally, one applied in information system, i.e., a new three-way decision model based on pessimistic L-fuzzy rough sets, is built. To show the effectiveness and reliability of our model, a practical example is presented.