Related papers: Algebraic Semantics of Similarity-Based Bitten Rou…
Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation…
Antichain based semantics for general rough sets were introduced recently by the present author. In her paper two different semantics, one for general rough sets and another for general approximation spaces over quasi-equivalence relations,…
A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in \cite{AM699} by the present author. The focus of our investigation is on elucidating the minimal conditions…
Rough sets over generalized transitive relations like proto-transitive ones had been initiated by the present author in the year 2012. Subsequently, approximation of proto-transitive relations by other relations was investigated and the…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…
In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional…
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…
Rough set theory is an important mathematical tool for dealing with uncertain or vague information. This paper studies some new topologies induced by a binary relation on universe with respect to neighborhood opera- tors. Moreover, the…
The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…
Rough sets are approximations of concrete sets. The theory of rough sets has been used widely for data-mining. While it is well-known that adjunctions are underlying in rough approximations, such adjunctions are not enough for…
Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this…
In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
Lattice-theoretic ideals have been used to define and generate non granular rough approximations over general approximation spaces over the last few years by few authors. The goal of these studies, in relation based rough sets, have been to…
Soft set theory and rough set theory are mathematical tools to deal with uncertainties. In [3], authors combined these concepts and introduced soft rough sets. In this paper, we introduce the concepts of soft rough graphs, vertex and edge…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak's original…