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1.	Eklund, Patrik, et al. (författare) Categorical innovations for rough sets 2009 Ingår i: Rough set theory. - Berlin/Heidelberg : Springer Berlin/Heidelberg. - 9783540899204 - 9783540899211 ; , s. 45-69 Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract Categories arise in mathematics and appear frequently in computer science where algebraic and logical notions have powerful representations using categorical constructions. In this chapter we lean towards the functorial view involving natural transformations and monads. Functors extendable to monads, further incorporating order structure related to the underlying functor, turn out to be very useful when presenting rough sets beyond relational structures in the usual sense. Relations can be generalized with rough set operators largely maintaining power and properties. In this chapter we set forward our required categorical tools and we show how rough sets and indeed a theory of rough monads can be developed. These rough monads reveal some canonic structures, and are further shown to be useful in real applications as well. Information within pharmacological treatment can be structured by rough set approaches. In particular, situations involving management of drug interactions and medical diagnosis can be described and formalized using rough monads.

Eklund, Patrik, et al. (författare)
Categorical innovations for rough sets
2009
Ingår i: Rough set theory. - Berlin/Heidelberg : Springer Berlin/Heidelberg. - 9783540899204 - 9783540899211 ; , s. 45-69
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Categories arise in mathematics and appear frequently in computer science where algebraic and logical notions have powerful representations using categorical constructions. In this chapter we lean towards the functorial view involving natural transformations and monads. Functors extendable to monads, further incorporating order structure related to the underlying functor, turn out to be very useful when presenting rough sets beyond relational structures in the usual sense. Relations can be generalized with rough set operators largely maintaining power and properties. In this chapter we set forward our required categorical tools and we show how rough sets and indeed a theory of rough monads can be developed. These rough monads reveal some canonic structures, and are further shown to be useful in real applications as well. Information within pharmacological treatment can be structured by rough set approaches. In particular, situations involving management of drug interactions and medical diagnosis can be described and formalized using rough monads.

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