Measuring the quality of queries in the fuzzy relational databases

In this paper, we develop a new method to measure the quality of each tuple as an answer with respect to Select‐Project‐Join (SPJ) queries so that we can determine which answers are better answers to the given query in a fuzzy relational database. The quality of an answer is viewed as how much sure information is provided, and how much extra information is needed so that it will be a sure answer to the query. The less extra information that is required and the more sure information that is provided by an answer, the higher the quality of that answer is, and in consequence, it will be more reliable. © 2001 John Wiley & Sons, Inc.     

Tuning the matching function for a threshold weighting semantics in a linguistic information retrieval system

Information retrieval is an activity that attempts to produce documents that better fulfill user information needs. To achieve this activity an information retrieval system uses matching functions that specify the degree of relevance of a document with respect to a user query. Assuming linguistic‐weighted queries we present a new linguistic matching function for a threshold weighting semantics that is defined using a 2‐tuple fuzzy linguistic approach (Herrera F, Martínez L. IEEE Trans Fuzzy Syst 2000;8:746–752). This new 2‐tuple linguistic matching function can be interpreted as a tuning of that defined in “Modelling the Retrieval Process for an Information Retrieval System Using an Ordinal Fuzzy Linguistic Approach” (Herrera‐Viedma E. J Am Soc Inform Sci Technol 2001;52:460–475). We show that it simplifies the processes of computing in the retrieval activity, avoids the loss of precision in final results, and, consequently, can help to improve the users' satisfaction. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 921–937, 2005.     

A Comparative Study for Crisp and Fuzzy Query by a Software Tool

In this paper, through a developed software, crisp and fuzzy query were compared on a classical database. By means of this fuzzy query software tool, some fields (attribute) of a database table can be fuzzified and a supplementary database, which includes fuzzy values, is formed. Developed software tool is applied on a sample database including some fields about the students for the evaluation of scholarship application. It is concluded that, the fuzzy query method is more flexible and the results of such query are more predictive and satisfactory.This paper is an extended version of the paper which has been accepted at KES 2005 9th international conference on knowledge-based intelligent information and engineering systems.     

Object-stack: An object-oriented approach for top-k keyword querying over fuzzy XML

Keyword search is the most popular technique of searching information from XML (eXtensible markup language) document. It enables users to easily access XML data without learning the structure query language or studying the complex data schemas. Existing traditional keyword query methods are mainly based on LCA (lowest common ancestor) semantics, in which the returned results match all keywords at the granularity of elements. In many practical applications, information is often uncertain and vague. As a result, how to identify useful information from fuzzy data is becoming an important research topic. In this paper, we focus on the issue of keyword querying on fuzzy XML data at the granularity of objects. By introducing the concept of “object tree”, we propose the query semantics for keyword query at object-level. We find the minimum whole matching result object trees which contain all keywords and the partial matching result object trees which contain partial keywords, and return the root nodes of these result object trees as query results. For effectively and accurately identifying the top-K answers with the highest scores, we propose a score mechanism with the consideration of tf*idf document relevance, users’ preference and possibilities of results. We propose a stack-based algorithm named object-stack to obtain the top-K answers with the highest scores. Experimental results show that the object-stack algorithm outperforms the traditional XML keyword query algorithms significantly, and it can get high quality of query results with high search efficiency on the fuzzy XML document.     

European option pricing under fuzzy environments

The application of fuzzy sets theory to the Black–Scholes formula is proposed in this article. Owing to the vague fluctuation of financial markets from time to time, the risk‐free interest rate, volatility, and the price of underlying assets may occur imprecisely. In this case, it is natural to consider the fuzzy interest rate, fuzzy volatility, and fuzzy stock price. The form of “Resolution Identity” in fuzzy sets theory will be invoked to propose the fuzzy price of European options. Under these assumptions, the European option price at time t will turn into a fuzzy number. This will allow a financial analyst to choose the European price at his (her) acceptable degree of belief. To obtain the belief degree, the optimization problems have to be solved. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 89–102, 2005.     

Flexible querying via if-sets

The traditional query languages used in database management systems require precise and unambiguous queries only. Fuzzy querying was introduced to relax this rigidity and allow the user more natural information retrieval. In this article we suggest how to enrich fuzzy querying by the use of IF-sets. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 587–597, 2007.     

An Imprecision-based Language for the Web

In this paper, we introduce a fuzzy language to extract information from the web extending the web query language WebSQL [1]. These extensions are based on two observations: the inadequacy of traditional Boolean query languages for web documents, and the need to move beyond the notion of query providing just a set of answers in order to provide a better data presentation through answers' restructuring. In order to address the first issue, we consider fuzzy sets to express imprecision in data, queries and answers. In our case, data imprecision comes from the data classification provided by several search engines. Query imprecision occurs in weighting values provided at query definition time. Answer imprecision allows to filter and rank the answers. To address the second point, we provide an answer restructuring language to model the restructuring phase that follows the query phase. The restructuring language allows creation/deletion of links and page creation. Thus several answer organizations are possible as a result to the same query. The resulting language extends in a uniform framework WebSQL. Then we provide a mapping for the language constructs into an extended relational algebra called SAME^W[2] expressing similarity-based queries over imprecisely classified data, queries involving navigation among web pages and answer restructurings. Finally, we study the optimization of similarity-based queries using equivalence and containment rules holding for SAME^Wand presenting several algorithms for query evaluation.     

Evidential reasoning using extended fuzzy Dempster–Shafer theory for handling various facets of information deficiency

This work investigates the problem of combining deficient evidence for the purpose of quality assessment. The main focus of the work is modeling vagueness, ambiguity, and local nonspecificity in information within a unified approach. We introduce an extended fuzzy Dempster–Shafer scheme based on the simultaneous use of fuzzy interval‐grade and interval‐valued belief degree (IGIB). The latter facilitates modeling of uncertainties in terms of local ignorance associated with expert knowledge, whereas the former allows for handling the lack of information on belief degree assignments. Also, generalized fuzzy sets can be readily transformed into the proposed fuzzy IGIB structure. The reasoning for quality assessment is performed by solving nonlinear optimization problems on fuzzy Dempster–Shafer paradigm for the fuzzy IGIB structure. The application of the proposed inference method is investigated by designing a reasoning scheme for water quality monitoring and validated through the experimental data available for different sampling points in a water distribution network. © 2011 Wiley Periodicals, Inc.     

Reliability of answers to queries in relational databases

The author studies the problem of determining the reliability of answers to queries in a relational database system, where the information in the database comes from various sources with varying degrees of reliability. An extended relational model is proposed in which each tuple in a relation is associated with an information source vector which identifies the information source(s) that contributed to that tuple. The author shows how relational algebra operations can be extended, and implemented using information source vectors, to calculate the vector corresponding to each tuple in the answer to a query, and hence, to identify information source(s) contributing to each tuple in the answer. This also enables the database system to calculate the reliability of each tuple in the answer to a query as a function of the reliability of information sources     

On a similarity measure between LR‐type fuzzy numbers and its application to database acquisition

This article presents a new similarity measure for LR‐type fuzzy numbers. The proposed similarity measure is based on a defined metric between LR‐type fuzzy numbers. It is known that an exponential operation is highly useful in dealing with the classical Shannon entropy and cluster analysis. We adopted, therefore, the exponential operation on this metric. Furthermore, we analyze its properties and make numerical comparisons to several similarity measures. The results show that the proposed similarity measure can overcome the drawbacks of the existing similarity measures. We then apply it to compound attributes for handling null queries to database systems. These applications can also be widely used in fuzzy queries to databases. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 1001–1016, 2005.     

Structure and stability analysis of general Mamdani fuzzy dynamic models

Mamdani fuzzy models have always been used as black‐box models. Their structures in relation to the conventional model structures are unknown. Moreover, there exist no theoretical methods for rigorously judging model stability and validity. I attempt to provide solutions to these issues for a general class of fuzzy models. They use arbitrary continuous input fuzzy sets, arbitrary fuzzy rules, arbitrary inference methods, Zadeh or product fuzzy logic AND operator, singleton output fuzzy sets, and the centroid defuzzifier. I first show that the fuzzy models belong to the NARX (nonlinear autoregressive with the extra input) model structure, which is one of the most important and widely used structures in classical modeling. I then divide the NARX model structure into three nonlinear types and investigate how the settings of the fuzzy model components, especially input fuzzy sets, dictate the relations between the fuzzy models and these types. I have found that the fuzzy models become type‐2 models if and only if the input fuzzy sets are linear or piecewise linear (e.g., trapezoidal or triangular), becoming type 3 if and only if at least one input fuzzy set is nonlinear. I have also developed an algorithm to transfer type‐2 fuzzy models into type‐1 models as far as their input–output relationships are concerned, which have some important properties not shared by the type‐2 models. Furthermore, a necessary and sufficient condition has been derived for a part of the general fuzzy models to be linear ARX models. I have established a necessary and sufficient condition for judging local stability of type‐1 and type‐2 fuzzy models. It can be used for model validation and control system design. Three numeric examples are provided. Our new findings provide a theoretical foundation for Mamdani fuzzy modeling and make it more consistent with the conventional modeling theory. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 103–125, 2005.     

Ant colony optimization of clustering models

The original ant system algorithm is simplified leading to a generalized ant colony optimization algorithm that can be used to solve a wide variety of discrete optimization problems. It is shown how objective function based clustering models such as hard and fuzzy c‐means can be optimized using particular extensions of this simplified ant optimization algorithm. Experiments with artificial and real datasets show that ant clustering produces better results than alternating optimization because it is less sensitive to local extrema. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 1233–1251, 2005.     

Intelligent fuzzy queries for multimedia databases

Multimedia databases have emerged to cope up with the huge amount of multimedia data, which comes up as a result of technological advancement. However, more intelligent techniques are required to satisfy different query requirements of multimedia users. This study extends the query capability of a multimedia database through the integration of a fuzzy rule‐based system. In addition to fuzzy semantic rules, which deduce new information from the data stored in the database, fuzzy spatial and temporal relations, which are inherent to multimedia applications, are defined in the rule‐based system. Users can formulate fuzzy semantic, spatial, temporal, and spatiotemporal queries, resulting in the deduction of new information using the rules defined in the rule‐based system. With some practical examples, the paper presents how a fuzzy rule‐based system integrated to a fuzzy multimedia database improves the query capabilities of the database system intelligently. © 2011 Wiley Periodicals, Inc.     

Project risk evaluation using a fuzzy analytic hierarchy process: An application to information technology projects

Projects are critical to the realization of performing organization's strategies. Each project contains some degree of risk and it is required to be aware of these risks and to develop the necessary responses to get the desired level of project success. Because projects' risks are multidimensional, they must be evaluated by using multi‐attribute decision‐making methods. The aim of this article is to provide an analytic tool to evaluate the project risks under incomplete and vague information. The fuzzy analytic hierarchy process (AHP) as a suitable and practical way of evaluating project risks based on the heuristic knowledge of experts is used to evaluate the riskiness of an information technology (IT) project of a Turkish firm. The means of the triangular fuzzy numbers produced by the IT experts for each comparison are successfully used in the pairwise comparison matrices. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 559–584, 2006.     

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.     

Dominance relation and rules in an incomplete ordered information system

Rough sets theory has proved to be a useful mathematical tool for classification and prediction. However, as many real‐world problems deal with ordering objects instead of classifying objects, one of the extensions of the classical rough sets approach is the dominance‐based rough sets approach, which is mainly based on substitution of the indiscernibility relation by a dominance relation. In this article, we present a dominance‐based rough sets approach to reasoning in incomplete ordered information systems. The approach shows how to find decision rules directly from an incomplete ordered decision table. We propose a reduction of knowledge that eliminates only that information that is not essential from the point of view of the ordering of objects or decision rules. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 13–27, 2005.     

Fuzzy independence and extended conditional probability

In many applications, the use of Bayesian probability theory is problematical. Information needed to feasibility calculate is unavailable. There are different methodologies for dealing with this problem, e.g., maximal entropy and Dempster-Shafer Theory. If one can make independence assumptions, many of the problems disappear, and in fact, this is often the method of choice even when it is obviously incorrect. The notion of independence is a 0–1 concept, which implies that human guesses about its validity will not lead to robust systems. In this paper, we propose a fuzzy formulation of this concept. It should lend itself to probabilistic updating formulas by allowing heuristic estimation of the “degree of independence.” We show how this can be applied to compute a new notion of conditional probability (we call this “extended conditional probability”). Given information, one typically has the choice of full conditioning (standard dependence) or ignoring the information (standard independence). We list some desiderata for the extension of this to allowing degree of conditioning. We then show how our formulation of degree of independence leads to a formula fulfilling these desiderata. After describing this formula, we show how this compares with other possible formulations of parameterized independence. In particular, we compare it to a linear interpolant, a higher power of a linear interpolant, and to a notion originally presented by Hummel and Manevitz [Tenth Int. Joint Conf. on Artificial Intelligence, 1987]. Interestingly, it turns out that a transformation of the Hummel-Manevitz method and our “fuzzy” method are close approximations of each other. Two examples illustrate how fuzzy independence and extended conditional probability might be applied. The first shows how linguistic probabilities result from treating fuzzy independence as a linguistic variable. The second is an industrial example of troubleshooting on the shop floor.     

Hierarchical spatial relation based on a contiguity graph

Autonomous agents traversing a natural space need to be knowledgeable of its space configuration. The existing space models in geographic information systems and robotics, however, deal with only the topological relations among numerous types of spatial relations. We aim to develop an enhanced space model that elaborates the spatial relations with respect to their relevant physical relations. Specifically, the spatial relations in a space configuration are further characterized with the gravitation as a potential factor to affect the space configuration. The resulting space model is capable of capturing an extended set of spatial relations over existing models such as a four‐intersection model. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 867–892, 2005.     

Learning cooperative linguistic fuzzy rules using the best–worst ant system algorithm

Within the field of linguistic fuzzy modeling with fuzzy rule‐based systems, the automatic derivation of the linguistic fuzzy rules from numerical data is an important task. In the last few years, a large number of contributions based on techniques such as neural networks and genetic algorithms have been proposed to face this problem. In this article, we introduce a novel approach to the fuzzy rule learning problem with ant colony optimization (ACO) algorithms. To do so, this learning task is formulated as a combinatorial optimization problem. Our learning process is based on the COR methodology proposed in previous works, which provides a search space that allows us to obtain fuzzy models with a good interpretability–accuracy trade‐off. A specific ACO‐based algorithm, the Best–Worst Ant System, is used for this purpose due to the good performance shown when solving other optimization problems. We analyze the behavior of the proposed method and compare it to other learning methods and search techniques when solving two real‐world applications. The obtained results lead us to remark the good performance of our proposal in terms of interpretability, accuracy, and efficiency. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 433–452, 2005.     

A neuro‐fuzzy computing technique for modeling laser‐diode nonlinearity in a radio‐over‐fibre link

Neuro‐fuzzy (NF) models are well‐known robust learning systems that combine the advantages of fuzzy sets and neurocomputation theory. This article presents the application of the NF approach to the computation of 3^rd‐order intermodulation power levels in microwave‐intensity‐modulated GaAlAs laser diodes for radio‐over‐fibre communications. The excellent agreement between the computed results and experimental measurements validates the presented NF approach. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005