Knowledge reduction in formal concept analysis (FCA) is an important procedure for knowledge processing and data analysis. Currently, the knowledge reduction in FCA based on granular computing (GrC) provides another way to analyze and represent the structure of concept lattices. However, the granular reduction method is based on Boolean reasoning and thus is an NP-hard problem. It is therefore natural to develop some heuristic methods to deal with this problem especially for the large data. In this paper, a new framework based on graph theory is used to study the granular reduction in FCA. A graph representation for the granular reduction is first investigated. The results in this paper show that the granular reduction computation in FCA can be translated into a graph optimization problem. Two new heuristic graph-based algorithms for the granular reduction in formal contexts and formal decision contexts are then respectively presented. Furthermore, numerical experiments are conducted to evaluate the effectiveness of the proposed methods.

A graph approach for knowledge reduction in formal contexts

Characterizations of coverings for upper approximation operators being closure operators

Structure optimization based on memetic algorithm for adjusting epidemic threshold on complex networks

Develop a solution approach to resolve the hierarchical rough set problem.Explore the most specific decision attribute level by level in the level-search procedure.Apply the proposed approach to the case in the transportation industry to select green fleets.This corporation reduces pollution emissions over the long-term by choosing the green vehicles in a desired ratio. Rough set theory (RST) has been the subject of much study and numerous applications in many areas. However, most previous studies on rough sets have focused on finding rules where the decision attribute has a flat, rather than hierarchical structure. In practical applications, attributes are often organized hierarchically to represent general/specific meanings. This paper (1) determines the optimal decision attribute in a hierarchical level-search procedure, level by level, (2) merges the two stages, generating reducts and inducting decision rules, into a one-shot solution that reduces the need for memory space and the computational complexity and (3) uses a revised strength index to identify meaningful reducts and to improve their accuracy. The selection of a green fleet is used to validate the superiority of the proposed approach and its potential benefits to a decision-making process for transportation industry.

Rule induction for hierarchical attributes using a rough set for the selection of a green fleet

In this paper, We propose a condition of symmetry for the covering $$\mathscr {C}$$
 in a covering-based approximation space $$(U,\mathscr {C})$$
 . By using this condition, we obtain general, topological and intuitive characterizations of the covering $${\mathscr {C}}$$
 for two types of covering-based upper approximation operators being closure operators. We investigate axiomatic systems for $$\overline{apr}_{S}$$
 and discuss the relationships among upper approximation operators. We also give a description of $$(U,{\mathscr {C}})$$
 in terms of information exchange systems when these operators are closure ones. We also solve an open problem raised by Ge et al.

The characterizations of upper approximation operators based on coverings

This paper uses connectivity of covering approximation spaces to investigate the spread of an epidemic E in E-spread information systems. In the following diagram, if person ui is connected to a disease feature P by a line, then ui has the disease feature P. HighlightsWe introduce the E-spread information systems for an epidemic E.We take covering approximation spaces as models of E-spread information systems.We characterize connectivity of covering approximation spaces.We characterize the epidemic E spreads easily in a E-spread information system. In this paper, the author proposes some new ideas for the E-spread information systems for an epidemic E, and takes covering approximation spaces as mathematical models of E-spread information systems. By characterizations for connectivity of covering approximation spaces, the author solves the problem: How can one know that an epidemic E spreads easily or not easily in a E-spread information system? Furthermore, the author gives an example to demonstrate the usefulness, which gives a further application of rough set theory in medical sciences of the above result by logical methods and mathematical methods.

Connectivity of covering approximation spaces and its applications on epidemiological issue

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Connectivity of covering approximation spaces and its applications on epidemiological issue