arXiv subjects

Qingguo Li

Publications and source records attributed to Qingguo Li.

43 records · Page 3Linked to original sources

arXiv2018

Domains via approximation operators

In this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators offer a fresh perspective to existing concepts and results in domain theory, but also reveal ways to establishing novel domain-theoretic results. For instance, (1) the well-known interpolation property of the way-below relation on a continuous poset is equivalent to the idempotence of a certain set-operator; (2) the continuity of a poset can be characterized by the coincidence of the Scott closure operator and the upper approximation operator induced by the way below relation; (3) meet-continuity can be established from a certain property of the topological closure operator. Additionally, we show how, to each approximating relation, an associated order-compatible topology can be defined in such a way that for the case of a continuous poset the topology associated to the way-below relation is exactly the Scott topology. A preliminary investigation is carried out on this new topology.

cs.LO↗

arXiv2015

On $(α+uβ)$-constacyclic codes of length $p^sn$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$

Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and $R=\mathbb{F}_{p^m}[u]/\langle u^2\rangle=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ $(u^2=0)$, where $p$ is an odd prime and $m$ is a positive integer. For any $α,β\in \mathbb{F}_{p^m}^{\times}$, the aim of this paper is to represent all distinct $(α+uβ)$-constacyclic codes over $R$ of length $p^sn$ and their dual codes, where $s$ is a nonnegative integer and $n$ is a positive integer satisfying ${\rm gcd}(p,n)=1$. Especially, all distinct $(2+u)$-constacyclic codes of length $6\cdot 5^t$ over $\mathbb{F}_{3}+u\mathbb{F}_3$ and their dual codes are listed, where $t$ is a positive integer.

cs.IT↗

arXiv2015

Compression of dynamic fuzzy relation information systems

This paper further investigates the data compression of fuzzy relation information systems. First, we introduce an algorithm for constructing the homomorphism between fuzzy relation information systems. Then, we discuss that how to compress the dynamic fuzzy relation information systems by utilizing the compression of the original systems. Afterwards, several illustrative examples are employed to show that the data compression of fuzzy relation information systems and dynamic fuzzy relation information systems can be simplified significantly by our proposed

cs.IT↗

arXiv2013

Generalized fuzzy rough sets based on fuzzy coverings

This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation of fuzzy coverings for fuzzy covering rough sets, the concepts of fuzzy subcoverings, the reducible and intersectional elements, the union and intersection operations are provided and their properties are discussed in detail. Afterwards, we introduce the concepts of consistent functions and fuzzy covering mappings and provide a basic theoretical foundation for the communication between fuzzy covering information systems. In addition, the notion of homomorphisms is proposed to reveal the relationship between fuzzy covering information systems. We show how large-scale fuzzy covering information systems and dynamic fuzzy covering information systems can be converted into small-scale ones by means of homomorphisms. Finally, an illustrative example is employed to show that the attribute reduction can be simplified significantly by our proposed approach.

cs.IT↗

arXiv2012

Some new similarity measures for hesitant fuzzy sets and their applications in multiple attribute decision making

Similarity measure is a very important topic in fuzzy set theory. Torra (2010) proposed the notion of hesitant fuzzy set(HFS), which is a generalization of the notion of Zadeh' fuzzy set. In this paper, some new similarity measures for HFSs are developed. Based on the proposed similarity measures, a method of multiple attribute decision making under hesitant fuzzy environment is also introduced. Additionally, a numerical example is given to illustrate the application of the proposed similarity measures of HFSs to decision-making.

cs.IT↗

arXiv2012

The construction of characteristic matrixes of dynamic coverings using an incremental approach

The covering approximation space evolves in time due to the explosion of the information, and the characteristic matrixes of coverings viewed as an effective approach to approximating the concept should update with time for knowledge discovery. This paper further investigates the construction of characteristic matrixes without running the matrix acquisition algorithm repeatedly. First, we present two approaches to computing the characteristic matrixes of the covering with lower time complexity. Then, we investigate the construction of the characteristic matrixes of the dynamic covering using the incremental approach. We mainly address the characteristic matrix updating from three aspects: the variations of elements in the covering, the immigration and emigration of objects and the changes of attribute values. Afterwards, several illustrative examples are employed to show that the proposed approach can effectively compute the characteristic matrixes of the dynamic covering for approximations of concepts.

cs.IT↗

arXiv2012

Data compression of dynamic set-valued information systems

This paper further investigates the set-valued information system. First, we bring forward three tolerance relations for set-valued information systems and explore their basic properties in detail. Then the data compression is investigated for attribute reductions of set-valued information systems. Afterwards, we discuss the data compression of dynamic set-valued information systems by utilizing the precious compression of the original systems. Several illustrative examples are employed to show that attribute reductions of set-valued information systems can be simplified significantly by our proposed approach.

cs.IT↗