Fuzzy classifier design using genetic algorithms

A new method for design of a fuzzy-rule-based classifier using genetic algorithms (GAs) is discussed. The optimal parameters of the fuzzy classifier including fuzzy membership functions and the size and structure of fuzzy rules are extracted from the training data using GAs. This is done by introducing new representation schemes for fuzzy membership functions and fuzzy rules. An effectiveness measure for fuzzy rules is developed that allows for systematic addition or deletion of rules during the GA optimization process. A clustering method is utilized for generating new rules to be added when additions are required. The performance of the classifier is tested on two real-world databases (Iris and Wine) and a simulated Gaussian database. The results indicate that highly accurate classifiers could be designed with relatively few fuzzy rules. The performance is also compared to other fuzzy classifiers tested on the same databases.     

Deriving support threshold values and membership functions using the multiple-level cluster-based master–slave IFG approach

Today, development of e-commerce has provided many transaction databases with useful information for investigators exploring dependencies among the items. In data mining, the dependencies among different items can be shown using an association rule. The new fuzzy-genetic (FG) approach is designed to mine fuzzy association rules from a quantitative transaction database. Three important advantages are associated with using the FG approach: (1) the association rules can be extracted from the transaction database with a quantitative value; (2) extracting proper membership functions and support threshold values with the genetic algorithm will exert a positive effect on the mining process results; (3) expressing the association rules in a fuzzy representation is more understandable for humans. In this paper, we design a comprehensive and fast algorithm that mines level-crossing fuzzy association rules on multiple concept levels with learning support threshold values and membership functions using the cluster-based master–slave integrated FG approach. Mining the fuzzy association rules on multiple concept levels helps find more important, useful, accurate, and practical information.     

Discovery of fuzzy temporal association rules

We propose a data mining system for discovering interesting temporal patterns from large databases. The mined patterns are expressed in fuzzy temporal association rules which satisfy the temporal requirements specified by the user. Temporal requirements specified by human beings tend to be ill-defined or uncertain. To deal with this kind of uncertainty, a fuzzy calendar algebra is developed to allow users to describe desired temporal requirements in fuzzy calendars easily and naturally. Fuzzy operations are provided and users can define complicated fuzzy calendars to discover the knowledge in the time intervals that are of interest to them. A border-based mining algorithm is proposed to find association rules incrementally. By keeping useful information of the database in a border, candidate itemsets can be computed in an efficient way. Updating of the discovered knowledge due to addition and deletion of transactions can also be done efficiently. The kept information can be used to help save the work of counting and unnecessary scans over the updated database can be avoided. Simulation results show the effectiveness of the proposed system. A performance comparison with other systems is also given.     

Linguistic frequent pattern mining using a compressed structure

Traditional association-rule mining (ARM) considers only the frequency of items in a binary database, which provides insufficient knowledge for making efficient decisions and strategies. The mining of useful information from quantitative databases is not a trivial task compared to conventional algorithms in ARM. Fuzzy-set theory was invented to represent a more valuable form of knowledge for human reasoning, which can also be applied and utilized for quantitative databases. Many approaches have adopted fuzzy-set theory to transform the quantitative value into linguistic terms with its corresponding degree based on defined membership functions for the discovery of FFIs, also known as fuzzy frequent itemsets. Only linguistic terms with maximal scalar cardinality are considered in traditional fuzzy frequent itemset mining, but the uncertainty factor is not involved in past approaches. In this paper, an efficient fuzzy mining (EFM) algorithm is presented to quickly discover multiple FFIs from quantitative databases under type-2 fuzzy-set theory. A compressed fuzzy-list (CFL)-structure is developed to maintain complete information for rule generation. Two pruning techniques are developed for reducing the search space and speeding up the mining process. Several experiments are carried out to verify the efficiency and effectiveness of the designed approach in terms of runtime, the number of examined nodes, memory usage, and scalability under different minimum support thresholds and different linguistic terms used in the membership functions.

     

Establishing the relevancy of the bookkeeping libraries to thefunctional testing of computer implementations

We address issues related to the definition of faults, errors and failures and their separability, and attribution to the different development processes of computing systems. In particular, we deal with historical databases, which presumably contain certain data (i.e., test failure data) and describe the methodology that can be used to analyze the database and obtain the pertinent information. The validation method may be of particular importance, especially when information from the database needs to be extrapolated for a purpose other than the one for which the database was developed. Our methodology was used to evaluate the historical data collected during the development of the IBM 4381 and 9370 family of computers, and to extrapolate the faults found during the function testing     

Two-dimensional discriminant locality preserving projections (2DDLPP) and its application to feature extraction via fuzzy set

This paper presents a new method for image feature extraction, namely, the fuzzy 2D discriminant locality preserving projections (F2DDLPP) based on the 2D discriminant locality preserving projections (2DDLPP) and fuzzy set theory. Firstly, we calculate the membership degree matrix by fuzzy k-nearest neighbor (FKNN), then we incorporate the membership degree matrix into the definition of the intra-class scatter matrix and inter-class scatter matrix, respectively. Secondly, we can get the fuzzy intra-class scatter matrix and fuzzy inter-class scatter matrix, respectively. The FKNN is implemented to achieve the distribution information of original samples, and this information is utilized to redefine corresponding scatter matrices. So, F2DDLPP can extract discriminative features from overlapping (outlier) samples which is different to the conventional 2DDLPP. Finally, Experiments on the Yale, ORL face databases, USPS database and PolyU palmprint database are demonstrated to verify the effectiveness of the proposed algorithm.     

Storing and querying fuzzy XML data in relational databases

Information imprecision and uncertainty exist in many real-world applications and for this reason fuzzy data management has been extensively investigated in various database management systems. Currently, introducing native support for XML data in relational database management systems (RDBMs) has attracted considerable interest with a view to leveraging the powerful and reliable data management services provided by RDBMs. Although there is a rich literature on XML-to-relational storage, none of the existing solutions satisfactorily addresses the problem of storing fuzzy XML data in RDBMs. In this paper, we study the methodology of storing and querying fuzzy XML data in relational databases. In particular, we present an edge-based approach to shred fuzzy XML data into relational data. The unique feature of our approach is that no schema information is required for our data storage. On this basis, we present a generic approach to translate path expression queries into SQL for processing XML queries.     

Two-unit repairable systems with common-cause shock failures and fuzzy parameters: parametric programming approach

This article, proposes a procedure to construct the membership functions of the system characteristics of a two-unit repairable system in series and parallel, which is subject to individual failures and common-cause shock failures. Time to individual failure and common-cause shock failure of the operating units are assumed to follow fuzzified exponential distributions. In addition, time to repair of the failed units also follow fuzzified exponential distributions. The α-cut approach is used to extract from the fuzzy repairable system a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. A numerical example is solved successfully to illustrate the practicality of the proposed approach. Since the system characteristics are governed by the membership functions, more information is provided for use by designers and practitioners. The successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications.     

A Fuzzy Temporal Object‐Relational Database: Model and Implementation

In real world, some data have a specific temporal validity that must be appropiately managed. To deal with this kind of data, several proposals of temporal databases have been introduced. Moreover, time can also be affected by imprecision, vagueness, and/or uncertainty, since human beings manage time using temporal indications and temporal notions, which may also be imprecise. For this reason, information systems require appropriate support to accomplish this task. In this work, we present a novel possibilistic valid time model for fuzzy databases including the data structures, the integrity constraints, and the DML. Together with this model, we also present its implementation by means of a fuzzy valid time support module on top of a fuzzy object‐relational database system. The integration of these modules allows to perform queries that combines fuzzy valid time constraints together with fuzzy predicates. Besides, the model and implementation proposed support the crisp valid time model as a particular case of the fuzzy valid time support provided.     

Fuzzy rough set techniques for uncertainty processing in a relational database

This paper concerns the modeling of imprecision, vagueness, and uncertainty in databases through an extension of the relational model of data: the fuzzy rough relational database, an approach which uses both fuzzy set and rough set theories for knowledge representation of imprecise data in a relational database model. The fuzzy rough relational database is formally defined, along with a fuzzy rough relational algebra for querying. Comparisons of theoretical properties of operators in this model with those in the standard relational model are discussed. An example application is used to illustrate other aspects of this model, including a fuzzy entity–relationship type diagram for database design, a fuzzy rough data definition language, and an SQL‐like query language supportive of the fuzzy rough relational database model. This example also illustrates the ease of use of the fuzzy rough relational database, which often produces results that are better than those of conventional databases since it more accurately models the uncertainty of real‐world enterprises than do conventional databases through the use of indiscernibility and fuzzy membership values. ©2000 John Wiley & Sons, Inc.     

Reasoning of fuzzy relational databases with fuzzy ontologies

A significant interest developed regarding the problem of describing databases with expressive knowledge representation techniques in recent years, so that database reasoning may be handled intelligently. Therefore, it is possible and meaningful to investigate how to reason on fuzzy relational databases (FRDBs) with fuzzy ontologies. In this paper, we first propose a formal approach and an automated tool for constructing fuzzy ontologies from FRDBs, and then we study how to reason on FRDBs with constructed fuzzy ontologies. First, we give their respective formal definitions of FRDBs and fuzzy Web Ontology Language (OWL) ontologies. On the basis of this, we propose a formal approach that can directly transform an FRDB (including its schema and data information) into a fuzzy OWL ontology (consisting of the fuzzy ontology structure and instance). Furthermore, following the proposed approach, we implement a prototype construction tool called FRDB2FOnto. Finally, based on the constructed fuzzy OWL ontologies, we investigate how to reason on FRDBs (e.g., consistency, satisfiability, subsumption, and redundancy) through the reasoning mechanism of fuzzy OWL ontologies, so that the reasoning of FRDBs may be done automatically by means of the existing fuzzy ontology reasoner.© 2012 Wiley Periodicals, Inc.     

Feature extraction using fuzzy inverse FDA

This paper proposes a new method of feature extraction and recognition, namely, the fuzzy inverse Fisher discriminant analysis (FIFDA) based on the inverse Fisher discriminant criterion and fuzzy set theory. In the proposed method, a membership degree matrix is calculated using FKNN, then the membership degree is incorporated into the definition of the between-class scatter matrix and within-class scatter matrix to get the fuzzy between-class scatter matrix and fuzzy within-class scatter matrix. Experimental results on the ORL, FERET face databases and pulse signal database show that the new method outperforms Fisherface, fuzzy Fisherface and inverse Fisher discriminant analysis.     

Active semi-supervised fuzzy clustering

Clustering algorithms are increasingly employed for the categorization of image databases, in order to provide users with database overviews and make their access more effective. By including information provided by the user, the categorization process can produce results that come closer to user's expectations. To make such a semi-supervised categorization approach acceptable for the user, this information must be of a very simple nature and the amount of information the user is required to provide must be minimized. We propose here an effective semi-supervised clustering algorithm, active fuzzy constrained clustering (AFCC), that minimizes a competitive agglomeration cost function with fuzzy terms corresponding to pairwise constraints provided by the user. In order to minimize the amount of constraints required, we define an active mechanism for the selection of candidate constraints. The comparisons performed on a simple benchmark and on a ground truth image database show that with AFCC the results of clustering can be significantly improved with few constraints, making this semi-supervised approach an attractive alternative in the categorization of image databases.     

A systematic approach to a self-generating fuzzy rule-table forfunction approximation

In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A four-step approach to build a fuzzy system automatically is presented: Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration. Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation. Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography.     

GENERATING AUTOMATIC FUZZY SYSTEM FROM RELATIONAL DATABASE SYSTEM FOR ESTIMATING NULL VALUES

There are many methods trying to do relational database estimations with a highly estimated accuracy rate by constructing a fuzzy learning algorithm automatically. However, there exists a conflict between the degree of the interpretability and the accuracy of the approximation in a general fuzzy system. Thus, how to make the best compromise between the accuracy of the approximation and the degree of the interpretability is a significant study of the subject. In order to achieve the best compromise, this article attempts to propose a simple fuzzy learning algorithm to get a positive result in the relational database estimation on the real world database system, including partition determination, automatic membership function, and rule generation, and system approximation.     

Dealing with fuzziness in active mobile database systems

Current needs of industry required the development of advanced database models like active mobile database systems. An active mobile database system can be designed by incorporation of triggering rules into a mobile computing environment in which the users are able to access a collection of database services using mobile and non-mobile computers at any location. Fuzzy concepts are adapted to the field of databases in order to deal with ambiguous, uncertain data. Fuzziness comes into picture in active mobile databases especially with spatial queries on moving objects. Incorporating fuzziness into rules would also improve the effectiveness of active mobile databases as it provides much flexibility in defining rules for the supported application. In this paper we present some methods to adapt the concepts developed for fuzzy systems to active mobile databases.     

A design methodology for fuzzy system interfaces

Conceptually, a fuzzy system interacting with a numerical environment has three components: a numeric/linguistic interface, a linguistic processing unit, and a linguistic/numeric interface. At these interfaces, membership functions representing linguistic terms play a top role both for the linguistic meaning provided and for the pre/post information processing introduced to the fuzzy system. Considering these issues, a set of membership function properties is postulated. Furthermore, an expert-free interface design methodology able to meet these properties, and based on the concept of optimal interfaces, is proposed. This concept simply states an equivalence between information format (numeric and linguistic), thereby making the methodology appealing from the applicational point of view. An algorithm is developed, and brief notes on selected applications are outlined stressing relevant issues of the proposed methodology