In order to make formalization for granular computing,some kinds of formulas are constructed on a universe by a logical method. Every formula expresses a property, and can separate a semantic set which consists of all...In order to make formalization for granular computing,some kinds of formulas are constructed on a universe by a logical method. Every formula expresses a property, and can separate a semantic set which consists of all of the objects satisfying the formula.Therefore a granular space on the universe is produced based on the formulas, and the semantic sets separated by the formulas are taken as a formal definition for granules,and are called abstract granules.Furthermore,it is proved that any specific granule from an extended mathematical system can be formalized into an abstract granule,the conclusions is obtained that specific granules from approximate spaces and information systems can also be formalized into abstract granules. Based on a granular space and abstract granules,granular computing is defined,which finally realizes the goal of formalization for granular computing.展开更多
Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an...Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.展开更多
基金NaturalScienceFund ofHenan ProvinceofChina underGrant No .0611055200
文摘In order to make formalization for granular computing,some kinds of formulas are constructed on a universe by a logical method. Every formula expresses a property, and can separate a semantic set which consists of all of the objects satisfying the formula.Therefore a granular space on the universe is produced based on the formulas, and the semantic sets separated by the formulas are taken as a formal definition for granules,and are called abstract granules.Furthermore,it is proved that any specific granule from an extended mathematical system can be formalized into an abstract granule,the conclusions is obtained that specific granules from approximate spaces and information systems can also be formalized into abstract granules. Based on a granular space and abstract granules,granular computing is defined,which finally realizes the goal of formalization for granular computing.
基金Supported by the National Natural Science Foundation of China(No.61772031)the Special Energy Saving Foundation of Changsha,Hunan Province in 2017
文摘Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.
