Rough set

Abstract: Molodtsov's soft set theory is a newly emerging tool to deal with uncertain problems. Based on the novel granulation structures called soft approximation spaces, Feng et al. initiated soft rough approximations and soft rough sets. Feng's soft rough sets can be seen as a generalized rough set model based on soft sets, which could provide better approximations than Pawlak's rough sets in some cases. This paper is devoted to establishing the relationship among soft sets, soft rough sets and topologies. We introduce the concept of topological soft sets by combining soft sets with topologies and give their properties. New types of soft sets such as keeping intersection soft sets and keeping union soft sets are defined and supported by some illustrative examples. We describe the relationship between rough sets and soft rough sets. We obtain the structure of soft rough sets and the topological structure of soft sets, and reveal that every topological space on the initial universe is a soft approximating space.

Abstract: Feature selection in incomplete decision table has gained considerable attention in recently. However many feature selection methods are mainly designed for incomplete data with categorical features. In this paper, we introduce an extended rough set model, which is based on neighborhood-tolerance relation and is applicable to incomplete data with mixed categorical and numerical features. Neighborhood-tolerance conditional entropy is proposed from this model, which is an uncertainty measure and can be used to evaluate feature subset. It is known that dependency is an important feature evaluation measure based on rough set theory. The comparison and analysis of classification complexity are made between the two measures and it is indicated that neighborhood-tolerance conditional entropy is a more effective feature evaluation criterion than dependency in incomplete decision table. Then the heuristic feature selection algorithm based on neighborhood-tolerance conditional entropy is constructed. Experimental results show that our proposal is applicable and effective to incomplete mixed data.

Abstract: The theory of three-way decision is about a philosophy of thinking in threes, a methodology of working with threes, and a mechanism of processing in threes. We approach a whole through three parts, in terms of three units, or from three perspectives. A trisecting–acting–outcome (TAO) model of three-way decision involves trisecting a whole into three parts and acting on the three parts, in order to produce an optimal outcome. In this paper, we further explore the TAO model in a set-theoretic setting and make three new contributions. The first contribution is an examination of three-way decision with nonstandard sets for representing concepts under the two kinds of objective/ontic and subjective/epistemic uncertainty. The second contribution is an introduction of an evaluation-based framework of three-way decision. We present a classification of trisections and investigate the notion of an evaluation space. The third contribution is, within the proposed framework, a systematical study of three-way decision with rough sets, interval sets, fuzzy sets, shadowed sets, rough fuzzy sets, interval fuzzy sets (or equivalently, vague sets, interval-valued fuzzy sets, intuitionistic fuzzy sets), and soft sets.

Abstract: It is increased the importance of understanding online consumers' purchase behaviors.Recommendation systems are decision aids that analyze customer's prior online behavior.This study proposes a rough set-based association rule approach.It is developed from ordinal data scale processing for customer's preference analysis.We find some patterns and rules for e-commerce platform recommendations. Increasing use of the Internet gives consumers an evolving medium for the purchase of products and services and this use means that the determinants for online consumers' purchasing behaviors are more important. Recommendation systems are decision aids that analyze a customer's prior online purchasing behavior and current product information to find matches for the customer's preferences. Some studies have also shown that sellers can use specifically designed techniques to alter consumer behavior. This study proposes a rough set based association rule approach for customer preference analysis that is developed from analytic hierarchy process (AHP) ordinal data scale processing. The proposed analysis approach generates rough set attribute functions, association rules and their modification mechanism. It also determines patterns and rules for e-commerce platforms and product category recommendations and it determines possible behavioral changes for online consumers. Display Omitted