Two Rough Set-based Software Tools for Analyzing Non-Deterministic Data

Two Rough Set-based Software Tools for Analyzing Non-Deterministic Data

Mao Wu (Kyushu Institute of Technology, Kitakyushu, Japan), Michinori Nakata (Jyosai International University, Chiba, Japan) and Hiroshi Sakai (Kyushu Institute of Technology, Kitakyushu, Japan)
Copyright: © 2014 |Pages: 16
DOI: 10.4018/ijrsda.2014010103
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Abstract

Rough Non-deterministic Information Analysis (RNIA) is a rough set-based framework for handling tables with exact and inexact data. Under this framework, the authors have coped with several issues, for example, possible equivalence relations, data dependencies, rule generation, rule stability, question-answering as well as missing and interval values as special cases of non-deterministic values. In this paper, the authors at first survey a software tool in Prolog and C for dealing issues like rule generation and question-answering, then we report the current state of our new web tool called getRNIA. The authors also propose a new issue focusing on the estimation of actual derived DIS from a Non-deterministic Information System, by employing constraints like Equivalence Classes, Data Dependency, Maximum Likelihood Estimation and Data Consistency.
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2. An Exemplary Nis And Issues In Rnia

This section reviews RNIA according to the discussion in (Sakai et al., 2008).

2.1. An Exemplary NIS

A is a quadruplet (OB,AT,{VALA | AAT},g), here OB, AT and VALA are finite sets, and g is a mapping from OBAT to the power set of ∪AATVALA. Each element in OB, AT and VALA is called an object, an attribute and an attribute value, respectively. In the mapping g, each attribute value is given as a set. We may then assume that there is an actual value in each value set but we do not know which one it is. Since each set of attribute values is finite. We might then replace each set in with an element in a set. In such a way, we would obtain a standard table. We call such tables as derived DISs from a NIS. Let DD() denote a set of all derived DISs. For in Table 1, DD()={| is a derived DIS, }, and | DD() | is 2304 (=).

Table 1.
An exemplary NIS for the suitcase data set. The values of attributes color, size, weight, price are as follows: VALcolor={red,blue,green}, VALsize={small,medium,large}, VALweight={light,heavy}, VALprice={high,low}
objectcolorsizeweightprice
1{red,blue,green}{small}{light,heavy}{low}
2{red}{small,medium}{light,heavy}{high}
3{red,blue}{small,medium}{light}{high}
4{red}{medium}{heavy}{low,high}
5{red}{small,medium,large}{heavy}{high}
6{blue,green}{large}{heavy}{low,high}

Generally, as illustrated by Figure 1, the number of derived DISs may increase exponentially. For large data sets with relatively high level of non-determinism understood as cardinalities of value sets, creation of scalable methods of data analysis requires finding a way to handle directly, with no need to considering all particular derived DISs. In the case of rule generation, we have solved this problem by using rough set-based framework. In our research, we have coped with the challenges in the following:

Figure 1.

An exemplary NIS and 2304 derived DISs

  • 1.

    Management of possible equivalence relations (Sakai & Okuma, 2004);

  • 2.

    The minimum and the maximum degrees of data dependency (Sakai, 2004);

  • 3.

    Certain and possible rules, and rule generation (Sakai et al., 2008);

  • 4.

    Stability factor of rules and calculation (Sakai et al., 2011B);

  • 5.

    Management of missing values (Sakai et al., 2008; Sakai et al., 2011A);

  • 6.

    Management of an actual value by intervals (Sakai et al., 2011A);

  • 7.

    Management of numerical patterns and figures (Sakai et al., 2008);

  • 8.

    Direct question-answering (Sakai et al., 2011B).

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