Related papers: Towards a theory of granular sets
Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas…
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…
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…
Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between…
Networks can be highly complex systems with numerous interconnected components and interactions. Granular computing offers a framework to manage this complexity by decomposing networks into smaller, more manageable components, or granules.…
Despite the increasing visibility of fine-grained recognition in our field, "fine-grained'' has thus far lacked a precise definition. In this work, building upon clustering theory, we pursue a framework for measuring dataset granularity. We…
Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…
Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…
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…
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…
Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse…
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves…
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…
The avalanche quantity of the information developed by mankind has led to concept of automation of knowledge extraction - Data Mining ([1]). This direction is connected with a wide spectrum of problems - from recognition of the fuzzy set to…
To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation…
The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental…
The concepts of rough and definite objects are relatively more determinate than those of granules and granulation in general rough set theory (RST) [1]. Representation of rough objects can however depend on the dialectical relation between…
Rough set theory is a new method that deals with vagueness and uncertainty emphasized in decision making. Data mining is a discipline that has an important contribution to data analysis, discovery of new meaningful knowledge, and autonomous…
In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article,…