Mihir K. Chakraborty

Rough sets through algebraic logic

While studying rough equality within the framework of the modal system S 5, an algebraic structure called rough algebra [1], came up. Its features were abstracted to yield a topological quasi-Boolean algebra (tqBa). In this paper, it is observed that rough algebra is more structured than a tqBa. Thus, enriching the tqBa with additional axioms, two more structures, viz. pre-rough algebra and rough algebra, are denned. Representation theorems of these algebras are also obtained. Further, the corresponding logical systems L 1 L 2 are proposed and eventually, L 2 is proved to be sound and complete with respect to a rough set semantics.

Algebras from Rough Sets

Rough set theory has seen nearly two decades of research on both foundations and on diverse applications. A substantial part of the work done on the theory has been devoted to the study of its algebraic aspects. ‘Rough algebras’ now abound, and have been shown to be instances of various algebraic structures, both well-established and relatively new, e.g., quasi-Boolean, Stone, double Stone, Nelson, Lukasiewicz algebras, on the one hand, and topological quasi-Boolean, prerough and rough algebras, on the other. More interestingly and importantly, some of these latter algebras find a new dimension (interpretation) through representations as rough structures. An attempt is made here to present the various relationships and to discuss the representation results.

Fuzzy topology on fuzzy sets and tolerance topology

In this paper fuzzy topology has been defined on a fuzzy set. The notion of quasi-coincidence is extended in order to fit this new situation and to generalize the concept of q-neighbourhood introduced originally by Ming and Ming (1980). The generalized q-neighbourhood system has been utilized to introduce tolerance topology on a fuzzy set with a fuzzy tolerance relation.

Graded consequence: further studies

ABSTRACT The notion of graded consequence has been explored further in a more generalized framework. The agreement between the syntactic and semantic notions of consequence is fully established. A notion of degree of consistency is introduced and some of its properties have been studied.

On fuzzy equivalence I

Fuzzy reflexive, symmetric and transitive relations on fuzzy subsets are studied. Various types of reflexivities and corresponding equivalences are considered. The possible fuzzy partitioning of a fuzzy subset is investigated.

Studies in fuzzy relations over fuzzy subsets

In this paper a generalisation of fuzzy relations is introduced - fuzzy relations are defined on fuzzy subsets. Properties like ordered reflexivity, symmetry, transitity, transitive closures of such generalised relations and operations on them are discussed.

Rough Consequence and Rough Algebra

A notion of rough consequence is investigated in detail. Two algebraic structures emerge from the modal system S5. Properties of these structures, called rough algebras, have been studied. A link between rough consequence and one of the rough algebras is established.

Transactions on Rough Sets X

Every word to utter from the writer involves the element of this life. The writer really shows how the simple words can maximize how the impression of this book is uttered directly for the readers. Even you have known about the content of transactions on rough sets x so much, you can easily do it for your better connection. In delivering the presence of the book concept, you can find out the boo site here.

Fuzzy tolerance relation, fuzzy tolerance space and basis

In this paper a generalisation of tolerance relation is introduced and fuzzy tolerance relation is defined on ordinary set. Notions like pre-class, tolerance class, basis and related theorems are discussed. Algorithm for various constructions are given.

Graded Consequence and Some Metalogical Notions Generalized

The notion of graded consequence and some other metalogical notions like consistency, inconsistency, tautologihood and theoremhood to which grades have been introduced earlier by us are reviewed in the context of generalized operators. Some preliminary results regarding the relation between the notion of graded consequence and the notion of graded inconsistency are proved. The method of axiomatization is reconsidered in this general situation.