Double Relative Quantitative Decision Theoretic Rough Sets Within Incomplete Information System

With the development of information and technology,the uncertainty of data information is becoming increasingly prominent.The rough set theory,which is used to deal with the uncertainty of data,has become a new hotspot.But the classical rough set theory is based on equivalence relations and its requirement is too strict.It is not suitable for dealing with complex information systems that are widespread in the real world.Therefore,it is a necessary to extend rough set model for solving the decision problem both theoretical analysis and practical application.Multigranulation rough sets,decision rough sets and rough sets on two universes are important research models and hotspots in rough set theory.This paper establishes two kinds of extended double relative quantitative decision theoretic rough sets models from the point of view of multigranulation and double relative quantitative information within incomplete information system.In the first place,combining generalized multigranulation decision-rough sets(GM-DTRS)and double relative quantitative decision-rough sets(Drq-DTRS),two kinds of generalized multigranulation double relative quantitative decision theoretic rough sets(GMDrq-DTRS)within incomplete information system are proposed.We define upper and lower approximations of GMDrq-DTRS by upper and lower support characteristic functions.Then important mathematical characteristics of two kinds of GMDrq-DTRS models are explored and corresponding decision rules are given.In the second place,double relative quantitative decision theoretic rough set on two universes within incomplete information system is explored based on granular rough set model over dual universes.The mathematical characteristics of proposed rough set models are discussed.What is more,the relations between the two kinds of GMDrq-DTRS and the two kinds of double relative quantitative decision theoretic rough sets on two universes are explored with an illustrative example under special parameter values.