Proceedings of the International Spring School on Mathematical method of specification and synthesis of software systems '85
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Mathematical Foundations
Rough Sets: Mathematical Foundations
A set theory for rough sets: toward a formal calculus of vague statements
Fundamenta Informaticae - Special issue on theory and applications of soft computing (TASC04)
On Rough Set Logics Based on Similarity Relations
Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
Rough-fuzzy-neurocomputing based on rough mereological calculus of granules
International Journal of Hybrid Intelligent Systems - Hybrid Intelligence using rough sets
A Study in Granular Computing: On Classifiers Induced from Granular Reflections of Data
Transactions on Rough Sets IX
Reasoning about concepts by rough mereological logics
RSKT'08 Proceedings of the 3rd international conference on Rough sets and knowledge technology
Transactions on rough sets XII
Satisfiability judgement under incomplete information
Transactions on Rough Sets XI
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Rough sets carry, intuitively, a 3-valued logical structure related to the three regions into which any rough set x divides the universe., viz., the lower definable set i(x), the upper definable set c(x), and the boundary region c(x)\i(x) witnessing the vagueness of associated knowledge. In spite of this intuition, the currently known way of relating rough sets and 3-valued logics is only via 3-valued Łukasiewicz algebras (Pagliani) that endow spaces of disjoint representations of rough sets with its structure. Here, we point to a 3-valued rough logic RL of unary predicates in which values of logical formulas are given as intensions over possible worlds that are definable sets in a model of rough set theory (RZF). This logic is closely related to the Lukasiewicz 3-valued logic, i.e., its theorems are theorems of the Łukasiewicz 3-valued logic and theorems of the Łukasiewicz 3-valued logic are in one-to-one correspondence with acceptable formulas of rough logic. The formulas of rough logic have denotations and are evaluated in any universe U in which a structure of RZF has been established. RZF is introduced in this note as a variant of set theory in which elementship is defined via containment, i.e., it acquires a mereological character (for this, see the cited exposition of Lesniewski's ideas). As an application of rough logic RL, decision rules and dependencies in information systems are characterized as acceptable formulas of this logic whereas functional dependencies turn out to be theorems of rough logic RL.