Multi-granulation rough set: from crisp to fuzzy case
نویسندگان
چکیده
Multi–granulation is an improvement of the classical rough set theory since it uses a family of binary relations instead of of a single indiscernibility relation for the constructing of approximation. In this paper, the multi–granulation rough set approach is further generalized into fuzzy environment. A family of fuzzy T–similarity relations are used to define the optimistic and pessimistic fuzzy rough sets respectively. The basic properties about these fuzzy rough sets are then discussed. Finally, the relationships among single relation based fuzzy rough set, optimistic and pessimistic multi–granulation fuzzy rough sets are addressed. 2010 AMS Classification: 94D05, 68T37
منابع مشابه
Multi-granulation fuzzy probabilistic rough sets and their corresponding three-way decisions over two universes
This article introduces a general framework of multi-granulation fuzzy probabilistic roughsets (MG-FPRSs) models in multi-granulation fuzzy probabilistic approximation space over twouniverses. Four types of MG-FPRSs are established, by the four different conditional probabilitiesof fuzzy event. For different constraints on parameters, we obtain four kinds of each type MG-FPRSs...
متن کاملMulti-granulation fuzzy rough sets
Based on analysis of Pawlak’s rough set model in the view of single equivalence relation and the theory of fuzzy set, associated with multi-granulation rough set models proposed by Qian, two types of new rough set models are constructed, which are multi-granulation fuzzy rough sets. It follows the research on the properties of the lower and upper approximations of the new multi-granulation fuzz...
متن کاملIncomplete Multigranulation Based on Rough Intuitionistic Fuzzy Sets
Rough set theory introduced by Pawlak [8] is based on equivalence relations. The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. The basic rough set model was extended to rough set model...
متن کاملMulti-granulation Fuzzy Rough Sets in a Fuzzy Tolerance Approximation Space
Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and u...
متن کاملRock mechanics modeling based on soft granulation theory
This paper describes application of information granulation theory, on the design of rock engineering flowcharts. Firstly, an overall flowchart, based on information granulation theory has been highlighted. Information granulation theory, in crisp (non-fuzzy) or fuzzy format, can take into account engineering experiences (especially in fuzzy shape-incomplete information or superfluous), or engi...
متن کامل