Michinori Nakata

Rules and Apriori Algorithm in Non-deterministic Information Systems

This paper presents a framework of rule generation in Non -deterministic Information Systems (NISs ), which follows rough sets based rule generation in Deterministic Information Systems (DISs ). Our previous work about NISs coped with certain rules , minimal certain rules and possible rules . These rules are characterized by the concept of consistency . This paper relates possible rules to rules by the criteria support and accuracy in NISs . On the basis of the information incompleteness in NISs , it is possible to define new criteria, i.e., minimum support , maximum support , minimum accuracy and maximum accuracy . Then, two strategies of rule generation are proposed based on these criteria. The first strategy is Lower Approximation strategy , which defines rule generation under the worst condition. The second strategy is Upper Approximation strategy , which defines rule generation under the best condition. To implement these strategies, we extend Apriori algorithm in DISs to Apriori algorithm in NISs . A prototype system is implemented, and this system is applied to some data sets with incomplete information.

Rough sets handling missing values probabilistically interpreted

We examine methods of valued tolerance relations where the conventional methods based on rough sets are extended in order to handle incomplete information. The methods can deal with missing values probabilistically interpreted. We propose a correctness criterion to the extension of the conventional methods. And then we check whether or not the correctness criterion is satisfied in a method of valued tolerance relations. As a result, we conclude that the method does not satisfy the correctness criterion. Therefore, we show how to revise the method of valued tolerance relations so that the correctness criterion can be satisfied.

Lower and upper approximations in data tables containing possibilistic information

An extended method of rough sets, called a method of weighted equivalence classes, is applied to a data table containing imprecise values expressed in a possibility distribution. An indiscerniblity degree between objects is calculated. A family of weighted equivalence classes is obtained via indiscernible classes from a binary relation for indiscernibility between objects. Each equivalence class in the family is accompanied by a possibilistic degree to which it is an actual one. By using the family of weighted equivalence classes we derive a lower approximation and an upper approximation. These approximations coincide with those obtained from methods of possible worlds. Therefore, the method of weighted equivalence classes is justified.

Stable rule extraction and decision making in rough non-deterministic information analysis

Rough Non-deterministic Information Analysis (RNIA) is a rough set-based data analysis framework for Non-deterministic Information Systems (NISs). RNIA-related algorithms and software tools developed so far for rule generation provide good characteristics of NISs and can be successfully applied to decision making based on non-deterministic data. In this paper, we extend RNIA by introducing stability factor that enables to evaluate rules in a more flexible way and by developing a question-answering functionality that enables decision makers to analyze data gathered in NISs in case there are no pre-extracted rules that may address specified conditions.

Twofold rough approximations under incomplete information

Abstract A method using possible equivalence classes has been developed on information tables with missing values. The method essentially differs from the other methods in having the two features. One is to directly deal with missing values by using not actual but possible equivalence classes. The other is to consider both aspects of discernibility and indiscernibility of a missing value from another value. When information tables contain incomplete information, rough approximations are not unique. We have lower and upper bounds of the actual rough approximations. The lower and upper bounds correspond to certain and possible rough approximations, respectively. Therefore, rough approximations are twofold under incomplete information. The certain and possible rough approximations are linked with each other. The method creates the same rough approximations as the method of possible worlds. This justifies the method of possible equivalence classes. The method is free from the difficulty of computational complexity for the growth of the number of missing values. Furthermore, the method is free from the restriction that missing values may occur for only some specified attributes. Therefore, we can efficiently obtain certain and possible rough approximations between arbitrary sets of attributes having missing values.

Granular Reasoning Using Zooming In & Out

The concept of granular computing is applied to propositional reasoning. Such kind of reasoning is called granular reasoning in this paper. For the purpose, two operations called zooming in & out is introduced to reconstruct granules of possible worlds.

Applying Rough Sets to Information Tables Containing Probabilistic Values

Rough sets are applied to information tables containing imprecise values that are expressed in a probability distribution. A family of weighted equivalence classes is obtained where each equivalence class is accompanied by the probability to which it is an actual one. By using the family of weighted equivalence classes, we derive lower and upper approximations. The lower and upper approximations coincide with ones obtained from methods of possible worlds. Therefore, the method of weighted equivalence classes is justified. In addition, this method is applied to missing values interpreted probabilistically. Using weighted equivalence classes correctly derives a lower approximation, even in the case where the method of Kryszkiewicz does not derive any lower approximation.

Checking whether or not rough-set-based methods to incomplete data satisfy a correctness criterion

Methods based on rough sets to data containing incomplete information are examined for whether a correctness criterion is satisfied or not. It is clarified that the methods proposed so far do not satisfy the correctness criterion. Therefore, we show a new formula that satisfies the correctness criterion in methods by valued tolerance relations.

A Note on Filtration and Granular Reasoning

The filtration method in modal logic is considered to develop a way of formulating an aspect of granular reasoning, which, roughly speaking, means human reasoning based on granularity. The method, however, originates in purely logical problems like decidability. Then, for our purpose, an extended concept of relative filtration is newly introduced using lower and upper approximations in rough set theory. An example of reasoning process using the relative filtration is illustrated.

An Overview of the getRNIA System for Non-deterministic Data☆

Abstract In Perception-Based Computing (PBC), we face several problems, and the management of incomplete information and inexact data is an important issue to address. We have proposed a framework Rough Non-deterministic Information Analysis (RNIA) for handling tables with non-deterministic information as a kind of incomplete information. Under this framework, we coped with several rough sets-based concepts, and extended the Apriori algorithm to tables with non-deterministic information. We named this algorithm NIS -Apriori. This paper reports the overview of RNIA, NIS -Apriori and our new software getRNIA. This getRNIA gives us to generate rules through the web browser easily.