Related papers: Rough concepts
We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and…
New concepts of rough natural number systems, recently introduced by the present author, are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and measures of mutual consistency of multiple…
A teacher's knowledge base consists of knowledge of mathematics content, knowledge of student epistemology, and pedagogical knowledge. It has severe implications on the understanding of student's knowledge of content, and the learning…
We present a novel method that can learn a graph representation from multivariate data. In our representation, each node represents a cluster of data points and each edge represents the subset-superset relationship between clusters, which…
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…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. In this…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
In this paper, we use theory of rough set to study graphs using the concept of orbits. We investigate the indiscernibility partitions and approximations of graphs induced by orbits of graphs. We also study rough membership functions,…
We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a…
Formal Concept Analysis has proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notions of attribute continuous formal context and continuous formal concept are introduced by…
In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering…
Pawlak rough set and neighborhood rough set are the two most common rough set theoretical models. Pawlak can use equivalence classes to represent knowledge, but it cannot process continuous data; neighborhood rough sets can process…
This paper aims to show that a simple framework, utilizing basic formalisms from set theory and category theory, can clarify and inform our theories of the relation between mind and matter.
Complex reasoning over text requires understanding and chaining together free-form predicates and logical connectives. Prior work has largely tried to do this either symbolically or with black-box transformers. We present a middle ground…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing…
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,…
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate…
We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and…
We develop two algebraic semantics for bitten rough set theory (\cite{SW}) over similarity spaces and their abstract granular versions. Connections with choice based generalized rough semantics developed in \cite{AM69} by the present author…
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…