Normalization and lossless join decomposition of similarity‐based fuzzy relational databases

Fuzzy relational database models generalize the classical relational database model by allowing uncertain and imprecise information to be represented and manipulated. In this article, we introduce fuzzy extensions of the normal forms for the similarity‐based fuzzy relational database model. Within this framework of fuzzy data representation, similarity, conformance of tuples, the concept of fuzzy functional dependencies, and partial fuzzy functional dependencies are utilized to define the fuzzy key notion, transitive closures, and the fuzzy normal forms. Algorithms for dependency preserving and lossless join decompositions of fuzzy relations are also given. We include examples to show how normalization, dependency preserving, and lossless join decomposition based on the fuzzy functional dependencies of fuzzy relation are done and applied to some real‐life applications. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 885–917, 2004.     

Fuzzy multi‐attribute cost–benefit analysis of e‐services

E‐service evaluation is a complex problem in which many qualitative attributes must be considered. These kinds of attributes make the evaluation process hard and vague. Cost–benefit analyses applied to various areas are usually based on the data under certainty or risk. In case of uncertain, vague, and/or linguistic data, the fuzzy set theory can be used to handle the analysis. In this article, after the evaluation attributes of e‐services and the fuzzy multi‐attribute decision‐making methods are introduced, a fuzzy hierarchical TOPSIS model is developed and applied to an e‐service provider selection problem with some sensitivity analyses. The developed model is a useful tool for the companies that prefer outsourcing for e‐activities. It is shown that service systems can be effectively evaluated by the proposed method. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 547–565, 2007.     

An alternative approach to fuzzy control charts: Direct fuzzy approach

The major contribution of fuzzy set theory lies in its capability of representing vague data. Fuzzy logic offers a systematic base to deal with situations, which are ambiguous or not well defined. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. In this paper, some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of α-cut to provide the ability of determining the tightness of the inspection: the higher the value of α the tighter inspection. A new alternative approach “Direct Fuzzy Approach (DFA)” is also developed in this paper. In contrast to the existing fuzzy control charts, the proposed approach is quite different in the sense it does not require the use of the defuzziffication. This prevents the loss of information included by the samples. It directly compares the linguistic data in fuzzy space without making any transformation. We use some numeric examples to illustrate the performance of the method and interpret its results.     

A C‐OWA operator‐based approach to decision making with interval fuzzy preference relation

Yager [IEEE Trans Syst Man Cybern B 2004;34:1952–1963] introduced a continuous interval argument OWA (C‐OWA) operator, which extends the ordered weighted averaging (OWA) operator, introduced by Yager [IEEE Trans Syst Man Cybern B 1988;18:183–190], to the case in which the given argument is a continuous valued interval rather than a finite set of values. In this article, we utilize the C‐OWA operator to derive the priority vector of an interval fuzzy preference relation and then develop a practical approach to solving the decision‐making problem with interval fuzzy preference relation. Finally, a numerical example is provided to demonstrate the practicability and efficiency of the developed approach. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 1289–1298, 2006.     

A new approach to mining fuzzy databases using nearest neighbor classification by exploiting attribute hierarchies

Data classification is a well‐organized operation in the field of data mining. This article presents an application of the k‐nearest neighbor classification technique for mining a fuzzy database. We consider a data set in which attribute values have certain similarities in nature and analyze the observations for the domain of each attribute, on the basis of fuzzy similarity relations. The proposed technique is general and the presented case study demonstrates the suitability of using this fuzzy approach for mining fuzzy databases, especially when the database contains various levels of abstraction. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1277–1290, 2004.     

Construction of quality control charts by using probability and fuzzy approaches and an application in a textile company

A method that uses statistical techniques to monitor and control product quality is called statistical process control (SPC), where control charts are test tools frequently used for monitoring the manufacturing process. In this study, statistical quality control and the fuzzy set theory are aimed to combine. As known, fuzzy sets and fuzzy logic are powerful mathematical tools for modeling uncertain systems in industry, nature and humanity; and facilitators for common-sense reasoning in decision making in the absence of complete and precise information. In this basis for a textile firm for monitoring the yarn quality, control charts proposed by Wang and Raz are constructed according to fuzzy theory by considering the quality in terms of grades of conformance as opposed to absolute conformance and nonconformance. And then with the same data for textile company, the control chart based on probability theory is constructed. The results of control charts based on two different approaches are compared. It’s seen that fuzzy theory performs better than probability theory in monitoring the product quality.     

On Algebraic Structure of L‐Fuzzy Bags

This study introduces a revised definition for fuzzy bags. It is based on the definition of bags given by Delgado et al. (Int J Intell Syst 2009;24:706–721) in which each bag has two parts: function and summary information. The new definition is given as a special case of L‐fuzzy bags, where L is a complete lattice. By some examples, the new concept is illustrated. Furthermore, the algebraic structure of L‐fuzzy bags is studied and the concept of α‐cuts, L‐fuzzy bag relations, and related theorems are given.     

Updating extended possibility‐based fuzzy relational databases

Two kinds of fuzziness in attribute values of the fuzzy relational databases can be distinguished: one is that attribute values are possibility distributions and the other is that there are resemblance relations in attribute domains. The fuzzy relational databases containing these two kinds of fuzziness simultaneously are called extended possibility‐based fuzzy relational databases. In this article, we focus on such fuzzy relational databases and investigate three update operations for the fuzzy relational databases, which are Insertion, Deletion, and Modification, respectively. We develop the strategies and implementation algorithms of these operations. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 237–258, 2007.     

Reduction of the decision table: A rough approach

In this article, we generalize Pawlak's rough approach for simplifying the decision table in an information system. We consider an information system where attribute values are not always quantitative, but are rather subjective, having vague or imprecise meanings. Some objects may have attribute values that are almost identical; that is, they cannot be distinguished clearly by the attributes. This observation is analyzed here being based on fuzzy proximity relations on different domain of attributes. Finally we find out the minimal solution of the table. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1143–1150, 2004.     

Correlation coefficient for type‐2 fuzzy sets

Type‐2 fuzzy sets are a generalization of the ordinary fuzzy sets in which each fuzzy set is characterized by a fuzzy membership function. In this article we consider how to define the correlation coefficient between two type‐2 fuzzy sets. We have adopted the embedded function model and interpret each type‐2 fuzzy set as a weighted ensemble of ordinary fuzzy sets. Using this interpretation enables us to define a correlation coefficient between two type‐2 fuzzy sets. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 143–153, 2006.     

On the consistency of rule bases based on lattice‐valued first‐order logic LF(X)

The consistency of a rule base is an essential issue for rule‐based intelligent information processing. Due to the uncertainty inevitably included in the rule base, it is necessary to verify the consistency of the rule base while investigating, designing, and applying a rule‐based intelligent system. In the framework of the lattice‐valued first‐order logic system LF(X), which attempts to handle fuzziness and incomparability, this article focuses on how to verify and increase the consistency degree of the rule base in the intelligent information processing system. First, the representations of eight kinds of rule bases in LF(X) as the generalized clause set forms based on these rule bases' nonredundant generalized Skolem standard forms are presented. Then an α‐automated reasoning algorithm in LF(X), also used as an automated simplification algorithm, is proposed. Furthermore, the α‐consistency and the α‐simplification theories of the rule base in LF(X) are formulated, and especially the coherence between these two theories is proved. Therefore, the verification of the α‐consistency of the rule base, often an infinity problem that is difficult to solve, can be transformed into a finite and achievable α‐simplification problem. Finally, an α‐simplification stepwise search algorithm for verifying the consistency of the rule base as well as a kind of filtering algorithm for increasing the consistency level of the rule base are proposed. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 399–424, 2006.     

Clustering web search results using fuzzy ants

Algorithms for clustering Web search results have to be efficient and robust. Furthermore they must be able to cluster a data set without using any kind of a priori information, such as the required number of clusters. Clustering algorithms inspired by the behavior of real ants generally meet these requirements. In this article we propose a novel approach to ant‐based clustering, based on fuzzy logic. We show that it improves existing approaches and illustrates how our algorithm can be applied to the problem of Web search results clustering. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 455–474, 2007.     

Ordered incremental training with genetic algorithms

Incremental training has been used for genetic algorithm (GA)‐based classifiers in a dynamic environment where training samples or new attributes/classes become available over time. In this article, ordered incremental genetic algorithms (OIGAs) are proposed to address the incremental training of input attributes for classifiers. Rather than learning input attributes in batch as with normal GAs, OIGAs learn input attributes one after another. The resulting classification rule sets are also evolved incrementally to accommodate the new attributes. Furthermore, attributes are arranged in different orders by evaluating their individual discriminating ability. By experimenting with different attribute orders, different approaches of OIGAs are evaluated using four benchmark classification data sets. Their performance is also compared with normal GAs. The simulation results show that OIGAs can achieve generally better performance than normal GAs. The order of attributes does have an effect on the final classifier performance where OIGA training with a descending order of attributes performs the best. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1239–1256, 2004.     

Cost‐sensitive learning and decision making for massachusetts pip claim fraud data

In this article, we investigate the issue of cost‐sensitive classification for a data set of Massachusetts closed personal injury protection (PIP) automobile insurance claims that were previously investigated for suspicion of fraud by domain experts and for which we obtained cost information. After a theoretical exposition on cost‐sensitive learning and decision‐making methods, we then apply these methods to the claims data at hand to contrast the predictive performance of the documented methods for a selection of decision tree and rule learners. We use standard logistic regression and (smoothed) naive Bayes as benchmarks. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1197–1215, 2004.     

Fuzzy logic‐based networks: A study in logic data interpretation

Fuzzy neurons may have outstanding learning abilities and are endowed with significant interpretation capabilities. In this study, we are concerned with the development of logic networks composed of fuzzy neurons. The main phase of the design includes the granulation of the output space (via triangular fuzzy sets) being realized with the use of fuzzy equalization. In the sequel these fuzzy sets are used to guide the construction of a family of fuzzy sets in the input space. Further processing of the resulting fuzzy sets deals with some additional aggregation of those that are not sufficiently distinct. This helps reduce the size of the logic network. We include comprehensive experimentation and offer a thorough interpretation of the networks. Experiments concerning real‐world continuous data help evaluate the network's appealing properties: transparent interpretability and practical feasibility. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 1249–1267, 2006.     

Fuzzy classifier system architectures for mobile robotics: An experimental comparison

We present an experimental comparison between two approaches to optimization of the rules for a fuzzy controller. More specifically, the problem is autonomous acquisition of an “investigative” obstacle avoidance competency for a mobile robot. We report on results from investigating two alternative approaches to the use of a Learning Classifier System (LCS) to optimize the fuzzy rule base. One approach operates at the level of whole rule bases, the “Pittsburgh” LCS. The other approach operates at the level of individual rules, the “Michigan” LCS. In this work, both of these Fuzzy Classifier Systems were designed to operate only on the rules of fuzzy controllers, with predefined fuzzy membership functions. There are two main results from this work. First, both approaches were capable of producing fuzzy controllers with subtle interactions between rules leading to competencies exceeding that of the hand‐coded fuzzy controller presented in this article. Second, the Michigan approach suffered more seriously than the Pittsburgh approach from the well‐known LCS “cooperation/competition” problem, which is accentuated here by the structural combination of Evolutionary Computation and a fuzzy system. This problem was alleviated a little by the combination of a clustered subpopulation niche system and a fitness‐sharing scheme applied to the Michigan approach, but still remains. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 993–1019, 2007.     

Forecasting enrollments using high‐order fuzzy time series and genetic algorithms

In recent years, many researchers have presented different forecasting methods to deal with forecasting problems based on fuzzy time series. When we deal with forecasting problems using fuzzy time series, it is important to decide the length of each interval in the universe of discourse due to the fact that it will affect the forecasting accuracy rate. In this article, we present a new method to deal with the forecasting problems based on high‐order fuzzy time series and genetic algorithms, where the length of each interval in the universe of discourse is tuned by using genetic algorithms, and the historical enrollments of the University of Alabama are used to illustrate the forecasting process of the proposed method. The proposed method can achieve a higher forecasting accuracy rate than the existing methods. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 485–501, 2006.     

A fuzzy logic approach to experience‐based reasoning

Experience‐based reasoning (EBR) is a reasoning paradigm that has been used in almost every human activity such as business, military missions, and teaching activities since early human history. However, EBR has not been seriously studied from either a logical or mathematical viewpoint, although case‐based reasoning (CBR) researchers have paid attention to EBR to some extent. This article will attempt to fill this gap by providing a unified fuzzy logic‐based treatment of EBR. More specifically, this article first reviews the logical approach to EBR, in which eight different rules of inference for EBR are discussed. Then the article proposes fuzzy logic‐based models to these eight different rules of inference that constitute the fundamentals for all EBR paradigms from a fuzzy logic viewpoint, and therefore will form a theoretical foundation for EBR. The proposed approach will facilitate research and development of EBR, fuzzy systems, intelligent systems, knowledge management, and experience management. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 867–889, 2007.     

New results on static output feedback H ∞ control for fuzzy singularly perturbed systems: a linear matrix inequality approach

This paper presents the novel approaches of designing robust fuzzy static output feedback H _∞ controller for a class of nonlinear singularly perturbed systems. Specifically, the considered system is approximated by a fuzzy singularly perturbed model. With the use of linear matrix inequality (LMI) methods, two methods are provided to design fuzzy static output feedback H _∞ controllers. The resulted controllers can guarantee that the closed‐loop systems are asymptotically stable and satisfy H _∞ performances for sufficiently small ?. In contrast to the existing results, the proposed approaches have two advantages: (i) the gains of controller are solved directly by a set of ?‐independent LMIs, and therefore, the problem of selecting the initial values in iterative LMIs algorithm can be avoided, and (ii) the smaller control input efforts are needed. The given methods are easy to implement and can be applied to both standard and nonstandard nonlinear singularly perturbed systems. Two numerical examples are provided to illustrate the effectiveness of the developed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Inclusion measures,similarity measures,and the fuzziness of fuzzy sets and their relations

The inclusion measure, the similarity measure, and the fuzziness of fuzzy sets are three important measures in fuzzy set theory. In this article, we investigate the relations among inclusion measures, similarity measures, and the fuzziness of fuzzy sets, prove eight theorems that inclusion measures, similarity measures, and the fuzziness of fuzzy sets can be transformed by each other based on their axiomatic definitions, and propose some new formulas to calculate inclusion measures, similarity measures, and the fuzziness of fuzzy sets. These results can be applied in many fields, such as pattern recognition, image processing, fuzzy neural networks, fuzzy reasoning, and fuzzy control. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 639–653, 2006.