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

Abstract

In this paper, a notion of L-fuzzy generalized neighborhood system is introduced and then a novel L-fuzzy rough sets based on it are defined and discussed. It is verified that 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 pessimistic L-fuzzy rough sets is studied. Later, to regain some Pawlak’s prop- erties those are lost in pessimistic L-fuzzy rough sets, the serial, reflexive, transitive and symmetric conditions for L-fuzzy general neighborhood systems are defined. Secondly, the axiomatic researches of the pessimistic L- fuzzy rough sets (include the serial, reflexive and sym- metric cases) are given. Thirdly, a reduction theory based on preserving L-fuzzy approximation operators is established. Finally, one applied in information system, i.e., a three-way decision model based on pessimistic L- fuzzy rough sets, is builded. A simple practical example to show the effectiveness of our model is also presented.