相关论文: A Categorical Foundation of Rough Sets

Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restriction which assigns to every morphism an endomorphism of its…

In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…

In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets…

We answer the question what properties a collection $\mathcal{F}$ of three-valued functions on a set $U$ must fulfill so that there exists a quasiorder $\leq$ on $U$ such that the rough sets determined by $\leq$ coincide with the…

The integration of knowledge extracted from different models described by domain experts or from models generated by machine learning algorithms is strongly conditioned by the lack of an appropriated framework to specify and integrate…

Now a days, data mining and knowledge discovery methods are applied to a variety of enterprise and engineering disciplines to uncover interesting patterns from databases. The study of Sequential patterns is an important data mining problem…

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…

Rule-based classifier, that extract a subset of induced rules to efficiently learn/mine while preserving the discernibility information, plays a crucial role in human-explainable artificial intelligence. However, in this era of big data,…

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…

By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize those pairs of fuzzy sets which form fuzzy rough sets w.r.t. a t-similarity relation…

Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…

We study elementary theories of well-pointed toposes and pretoposes, regarded as category-theoretic or "structural" set theories in the spirit of Lawvere's "Elementary Theory of the Category of Sets". We consider weak intuitionistic and…

Rough sheets are two-parameter analogs of rough paths. In this work the theory of integration over functions of two parameters is extended to cover the case of irregular functions by developing an appropriate notion of rough sheet. The main…

Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…

In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by…

Fuzzy rough set (FRS) has a great effect on data mining processes and the fuzzy logical operators play a key role in the development of FRS theory. In order to further generalize the FRS theory to more complicated data environments, we…

Subsethood, which is to measure the degree of set inclusion relation, is predominant in fuzzy set theory. This paper introduces some basic concepts of spatial granules, coarse-fine relation, and operations like meet, join, quotient meet and…

Taxonomy Expansion, which models complex concepts and their relations, can be formulated as a set representation learning task. The generalization of set, fuzzy set, incorporates uncertainty and measures the information within a semantic…

Tree convex sets refer to a collection of sets such that each set in the collection is a subtree of a tree whose nodes are the elements of these sets. They extend the concept of row convex sets each of which is an interval over a total…

In 2004 Anna Maria Radzikowska et al \cite{RK2004} investigated the fuzzy rough sets where the set of truth values is an arbitrary residuated lattice. In this paper, we extend their work by considering a residuated multilattice $M$ as the…