Tetsuro Saeki

A new rule induction method from a decision table using a statistical test

Rough Sets theory is widely used as a method for estimating and/or inducing the knowledge structure of if-then rules from various decision tables. This paper presents the results of a retest of rough set rule induction ability by the use of simulation data sets. The conventional method has two main problems: firstly the diversification of the estimated rules, and secondly the strong dependence of the estimated rules on the data set sampling from the population. We here propose a new rule induction method based on the view that the rules existing in their population cause partiality of the distribution of the decision attribute values. This partiality can be utilized to detect the rules by use of a statistical test. The proposed new method is applied to the simulation data sets. The results show the method is valid and has clear advantages, as it overcomes the above problems inherent in the conventional method.

Proposal of a statistical test rule induction method by use of the decision table

Graphical abstractDisplay Omitted We propose a new rule induction method which drastically improves the method called LEM2 proposed by Jerzy Grzymala-Busse.The new rule induction method named STRIM statistically and directly inducts if-then rules without using the concept of approximation by the conventional method.The rules inducted by STRIM have statistical assurance of the confident coefficient of the p-value, and derive accuracy and coverage indexes used in the conventional method as by-products.An algorithm for STRIM described in C language style is developed into a piece of software, implemented in a PC and confirmed to be efficient and useful for the rule induction problem by a simulation experiment. Rough sets theory is widely used as a method for estimating and/or inducing the knowledge structure of if-then rules from various decision tables. This paper presents the results of a retest of rough set rule induction ability by the use of simulation data sets. The conventional method has two main problems: firstly the diversification of the estimated rules, and secondly the strong dependence of the estimated rules on the data set sampling from the population. We here propose a new rule induction method based on the view that the rules existing in their population cause partiality of the distribution of the decision attribute values. This partiality can be utilized to detect the rules by use of a statistical test. The proposed new method is applied to the simulation data sets. The results show the method is valid and has clear advantages, as it overcomes the above problems inherent in the conventional method.

Studies on the Necessary Data Size for Rule Induction by STRIM

STRIM Statistical Test Rule Induction Method has been proposed as a method to effectively induct if-then rules from the decision table which is considered as a sample set obtained from the population of interest. Its usefulness has been confirmed by a simulation experiment specifying rules in advance, and by comparison with the conventional methods. However, there remains scope for future studies. One aspect which needs examination is determination of the size of the dataset needed for inducting true rules by simulation experiments, since finding statistically significant rules is the core of the method. This paper examines the theoretical necessary size of the dataset that STRIM needs to induct true rules with probability w [%] in connection with the rule length, and confirms the validity of this study by a simulation experiment at the rule length 2. The results provide useful guidelines for analyzing real-world datasets.

A psychological evaluation method for fluctuating random noise based on fuzzy set theory

Abstract In psychological noise evaluation, subjective judgment of the acoustical stimulus causes fuzziness. By paying special attention to the fuzziness of the subjective impression, the categorized psychological evaluation is quantitatively understood as the fuzzy event. The so-called discrete-type membership function in the field of fuzzy set theory is used as a practical method for discussing the relationship between the objective acoustical stimulus and the subjective human response. The patterns of discrete-type membership functions are determined by using the data actually observed to give the psychological impression. Next, a new method of evaluating the psychological impression is proposed for the case when subjects are exposed to the fluctuating random noise of arbitrary probability distribution. Finally, the validity and usefulness of the proposed method are confirmed experimentally by applying it to the data actually observed.

Considerations on Rule Induction Procedures by STRIM and Their Relationship to VPRS

STRIM (Statistical Test Rule Induction Method) has been proposed as a method to effectively induct if-then rules from the decision table. The method was studied independently of the conventional rough sets methods. This paper summarizes the basic notion of STRIM and the conventional rule induction methods, considers the relationship between STRIM and their conventional methods, especially VPRS (Variable Precision Rough Set), and shows that STRIM develops the notion of VPRS into a statistical principle. In a simulation experiment, we also consider the condition that STRIM inducts the true rules specified in advance. This condition has not yet been studied, even in VPRS. Examination of the condition is very important if STRIM is properly applied to a set of real-world data set.

A practical prediction method of psychological response to arbitrary non-white random noise based on simplified patterns of membership functions

In psychological noise evaluation, the fuzziness caused by the human subjective judgment for the acoustical stimulus essentially exists. By paying special attention to the fuzziness of the subjective impression, the categorized psychological evaluation is grasped quantitatively as the fuzzy event. That is, the so-called membership function in the field of fuzzy set theory is used as a method for discussing the relationship between the objective acoustical stimulus and the subjective human response. The set of eight simplified patterns of membership functions is first established by using the data obtained from an actual psychological experiment in the case when the test subjects are exposed to the octave-band-limited white noise with center frequency fcK (K = 1, 2, …, 8). Next, the membership functions for the psychological impression are estimated by use of the above set of eight simplified patterns, in a case when the test subjects are exposed to an arbitrary non-white random noise. Further, a method for evaluating the psychological response is proposed by using the concept of the fuzzy probability. Finally, the validity and the usefulness of the proposed method are confirmed experimentally by applying it to the actually observed data.

Psychological impressions and listening score when listening to audio signals composed of monosyllables and words, while subject to meaningless steady noise—introduction of weighted-mean spectral distance

Abstract A useful index for evaluating two psychological impressions of annoyance, speech audibility, and the listening score, when listening to audio signals composed of monosyllables and words, while subject to meaningless steady noise is discussed. More specifically, eight evaluation indices ( SN, AI, SIL, WSPD , etc.) are introduced that reflect the mutual relationships between the spectrum level of the speech peaks and that of the noise. After careful consideration of the relationships between these indices and the psychological impressions/listening score, WSPD can be selected as a useful index. Next, prediction problems of the psychological impressions/listening score are considered. The predicted values of the psychological impressions/listening score are compared with experimental data. The predicted values are in good agreement with the observed results.

Studies on an effective algorithm to reduce the decision matrix

In the conventional rough set theory, the decision matrix method is known as one of the method extracting the rules[1]. However, devising an efficient algorithm for the decision matrix method has seldom been reported to date. Consequently, this paper studies the process of reducing the decision matrix, finds several properties useful for the rule extraction and proposes an effective algorithm for the extraction. The algorithm is implemented in a piece of software and a simulation experiment is conducted to compare the reduced time of the software with that of LEM2[2][3]. As the results, the newly developed software is confirmed to perform exceptionally well under taxing conditions.

Proposal for a Statistical Reduct Method for Decision Tables

Rough Sets theory is widely used as a method for estimating and/or inducing the knowledge structure of if-then rules from a decision table after a reduct of the table. The concept of the reduct is that of constructing the decision table by necessary and sufficient condition attributes to induce the rules. This paper retests the reduct by the conventional methods by the use of simulation datasets after summarizing the reduct briefly and points out several problems of their methods. Then a new reduct method based on a statistical viewpoint is proposed. The validity and usefulness of the method is confirmed by applying it to the simulation datasets and a UCI dataset. Particularly, this paper shows a statistical local reduct method, very useful for estimating if-then rules hidden behind the decision table of interest.

Performance Comparison to a Classification Problem by the Second Method of Quantification and STRIM

STRIM is used for inducing if-then rules hidden behind a database called the decision table. Meanwhile, the second method of quantification is also often used as a method for summarizing and arranging such a database. This paper first summarizes both methods, next compares their performance in a learning and classification problem by applying them to a simulation dataset, and lastly considers features and clarifies differences of both methods based on the simulation results.