| Intelligent control based on rough set theory need many rough functions as its basis of theory, but rough set doesn't satisfy need, so it is important to found rough function and research on its properties and application.In this paper, function rough set and rough differential equation are also generated and researched.Main contents are as follows:(1) The properties of rough function of one variable and two variables separately generated and researched, such as, intermediate value theorem and mean value theorem of integrals of rough function of one variable, necessary condition for rough extreme value theorem, mean value theorem of integrals, changing of double integral into repeated integral rough function of two variables, and so on. In addition, to make some contents concrete and understood easily, these contents are graphed and exemplified.(2) Discussing the properties and solution of rough differential equation. By analyzing rough differential equation, theorem of existence and uniqueness of rough differential equation are arrived at. Connecting the properties of rough derivative and rough integral, some methods of solving rough differential equation are arrived at.(3) Function rough set is presented; some methods of measuring the uncertainty of function rough set are defined. Introducing application theory analysis of function rough set, one application example of function rough set is presented.Creative results are as follows:Researching on rough function of two variables, defining rough extreme value of rough function of two variables, arriving at necessary condition for rough extreme value theorem,mean value theorem of integrals,changing of double integral into repeated integral rough function of two variables, and so on. Researching on rough differential equation, theorem of existence and uniqueness of rough differential equation and some methods of solving rough differential equation are arrived at. |
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