Yasuo Kudo

A granularity-based framework of deduction, induction, and abduction

In this paper, we propose a granularity-based framework of deduction, induction, and abduction using variable precision rough set models proposed by Ziarko and measure-based semantics for modal logic proposed by Murai et al. The proposed framework is based on @a-level fuzzy measure models on the basis of background knowledge, as described in the paper. In the proposed framework, deduction, induction, and abduction are characterized as reasoning processes based on typical situations about the facts and rules used in these processes. Using variable precision rough set models, we consider @b-lower approximation of truth sets of nonmodal sentences as typical situations of the given facts and rules, instead of the truth sets of the sentences as correct representations of the facts and rules. Moreover, we represent deduction, induction, and abduction as relationships between typical situations.

An Evaluation Method of Relative Reducts Based on Roughness of Partitions

This paper focuses on rough set theory which provides mathematical foundations of set-theoretical approximation for concepts, as well as reasoning about data. Also presented in this paper is the concept of relative reducts which is one of the most important notions for rule generation based on rough set theory. In this paper, from the viewpoint of approximation, the authors introduce an evaluation criterion for relative reducts using roughness of partitions that are constructed from relative reducts. The proposed criterion evaluates each relative reduct by the average of coverage of decision rules based on the relative reduct, which also corresponds to evaluate the roughness of partition constructed from the relative reduct,

A Heuristic Algorithm for Attribute Reduction Based on Discernibility and Equivalence by Attributes

In this paper, we consider a heuristic method to partially calculate relative reducts with better evaluation by the evaluation criterion proposed by the authors. By considering discernibility and equivalence of elements with respect to values of condition attributes that appear in relative reducts, we introduce an evaluation criterion of condition attributes, and consider a heuristic method for calculating a relative reduct with better evaluation.

Fuzzy Multisets in Granular Hierarchical Structures Generated from Free Monoids

This paper focuses on the two definitions of fuzzy multisets by Yager and Minamoto, respectively, and examines their difference in the framework of granular hierarchical structures generated from free monoids. Then we can conclude that, in order to define the basic order on the set of multisets on interval 0,1], the Yager definition adopts the one induced just from the range i¾ź, the set of natural numbers, while the Miyamoto definition uses one generated from both the domain 0,1] and the range i¾ź through the notion of cuts.

Heuristic Algorithm for Attribute Reduction Based on Classification Ability by Condition Attributes

This chapter discusses the heuristic algorithm to computes a relative reduct candidate based on evaluating classification ability of condition attributes. Considering the discernibility and equivalence of objects for condition attributes in relative reducts, we introduce evaluation criteria for condition attributes and relative reducts. The computational complexity of the proposed algorithm is (O(|U|^2|C|^2)). Experimental results indicate that our algorithm often generates a relative reduct producing a good evaluation result.

A Heuristic Algorithm for Selective Calculation of a Better Relative Reduct in Rough Set Theory

In this paper, we consider a heuristic method to partially calculate relative reducts with better evaluation by the evaluation criterion proposed by the authors. By using the average of certainty and coverage of decision rules constructed from each condition attribute, we introduce an evaluation criterion of condition attributes, and consider a heuristic method for calculating a relative reduct with better evaluation.

Uncertainty in Future: A Paraconsistent Approach

A future event is uncertain and contingent. Since the age of Aristotle, this feature induces philosophical issues like the Master argument. In this paper, we propose to suggest interpreting future contingents, not as Aristotle did, as gappy, but as glutty in some sense using Priest’s dialectical tense logic DTL, which is a version of paraconsistent tense logic.

An Agent Control Method Based on Variable Neighborhoods

In this paper, we propose a model that an agent selects actions based on variable neighborhoods. We formulate relationships among variable neighborhoods, the agents observations, and the agents behaviors in a framework of rough set theory and topological spaces. The main task is to explore a method by which we can select sizes of neighborhoods under given contexts. We also show simulation results of the proposed method.

On a Criterion of Similarity between Partitions Based on Rough Set Theory

In this paper, we introduce a criterion of similarity between partitions. The proposed similarity criterion is a generalization of an evaluation criterion of relative reducts proposed by the authors and evaluates the similarity of partitions by correctness and roughness with each other. Moreover, for comparison of similarity scores between different universes, we also propose a normalized similarity criterion.

Rough Set Theory

This chapter describes the foundations for rough set theory. We outline Pawlak’s motivating idea and give a technical exposition. Basics of Pawlak’s rough set theory and variable precision rough set model are presented with some related topics. We also present variants and related theories.