Catálogo de publicaciones - libros

In this paper, we discuss the most suitable “representation granularity”, keeping several types of discernibility including individually discernibility and class discernibility. In the traditional “reduction” sense, the goal is to find the smallest number of attributes such that they enable us to discern each tuple or each decision class. However, once we pay attention to the number of attribute values too, that is, the size of each attribute, another criterion is needed. Indeed, we should ask ourselves about which one is better in the following two situations: 1) we can discern them with a single attribute of size ten, and 2) we can do this with two attributes of size five. This study answers this question with some criteria. Especially, we deal with continuous attributes. If we evaluate this difference in the light of understandability, we may prefer the latter, because they give more simple descriptions. Such a combination of simple nominal description helps us as a language or as a Kansei representation. To do this, we propose some criteria and algorithms to find near-optimal solutions for those criteria. In addition, we show some results for some databases in UCI Machine Learning Repository.

In this paper, the concept of a granulation order is proposed in an information system. The positive approximation of a set under a granulation order is defined. Some properties of positive approximation are obtained. For a set of the universe in an information system, its approximation accuracy is monotonously increasing under a granulation order. This means that a proper family of granulations can be chosen for a target concept approximation according to the user requirements. An algorithm based on positive approximation is designed for decision rule mining, and its application is illustrated by an example.

Significance of granular logic, including the operational rules, studying background, is presented in this paper. This closeness relation is quoted in granular logic,and the closeness relation quoted in granular logic is defined via logical truth values. Hence, we induce several new relative properties and inference rules in the granular logic with the closeness relation. The granular logical reasoning systems with the closeness relation are also established. And this paper proves a few real examples by deductive reasoning in the systems. Significance of granular logic with closeness relation ~ is also described in the paper.

We discuss an ontological framework for approximation, i.e., to approximation of concepts and vague dependencies specified in a given ontology. The presented approach is based on different information granule calculi. We outline the rough–fuzzy approach for approximation of concepts and vague dependencies.

This paper examines the knowledge representation theory of granulations. The key strengths of rough set theory are its capabilities in representing and processing knowledge in table format. For general granulation such capabilities are unknown. For single level granulation, two initial theories have been proposed previously by one of the authors. In this paper, the theories are re-visited, a new and deeper analysis is presented: Granular information table is an incomplete representation, so computing with words is the main method of knowledge processing. However for symmetrical granulation, the pre-topological information table is a complete representation, so the knowledge processing can be formal.