Related papers: Pure Rough Mereology and Counting
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…
Many techniques for handling missing data have been proposed in the literature. Most of these techniques are overly complex. This paper explores an imputation technique based on rough set computations. In this paper, characteristic…
Mereology is the study of parts and the relationships that hold between them. We introduce a behavioral approach to mereology, in which systems and their parts are known only by the types of behavior they can exhibit. Our discussion is…
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…
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…
The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification…
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…
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 set theory models uncertainty by approximating target concepts through lower and upper sets induced by indiscernibility, or more generally, by granulation relations in data tables. This perspective captures vagueness caused by limited…
Classical planning asks for a sequence of operators reaching a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored.…
Emergences of computers and information technological revolution made tremendous changes in the real world and provides a different dimension for the intelligent data analysis. Well formed fact, the information at right time and at right…
We consider a set-theoretic version of mereology based on the inclusion relation $\subseteq$ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of $\in$ from $\subseteq$, we identify…
This paper present a strong data mining method based on rough set, which can realize feature selection, classification and knowledge representation at the same time. Rough set has good interpretability, and is a popular method for feature…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the…
Mereology in its formal guise is usually couched in a language whose signature contains only one primitive binary predicate symbol representing the part of relation, either the proper or improper one. In this paper, we put forward an…
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 describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
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…
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…