Large Rough Sets and Modal Logics
نویسندگان
چکیده
منابع مشابه
Generalization of Rough Sets using Modal Logics
The theory of rough sets is an extension of set theory with two additional unary set-theoretic operators deened based on a binary relation on the universe. These two operators are related to the modal operators in modal logics. By exploring the relationship between rough sets and modal logics, this paper proposes and examines a number of extended rough set models. By the properties satissed by ...
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In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix)....
متن کاملThree-Valued Logics, Uncertainty Management and Rough Sets
This paper is a survey of the connections between threevalued logics and rough sets from the point of view of incomplete information management. Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such as rough sets. We then show that while such transla...
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The Kuznetsov–Index of a modal logic is the least cardinal μ such that any consistent formula has a Kripke–model of size ≤ μ if it has a Kripke–model at all. The Kuznetsov–Spectrum is the set of all Kuznetsov–Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov–Index iω+ω. Futhermore, Chagrov has constructed an extension...
متن کاملL-valued Fuzzy Rough Sets
In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches.
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ژورنال
عنوان ژورنال: Journal of Japan Society for Fuzzy Theory and Systems
سال: 2001
ISSN: 0915-647X,2432-9932
DOI: 10.3156/jfuzzy.13.6_571