Handling fuzzy information in 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 paper, we focus on such fuzzy relational databases. We classify two kinds of fuzzy data redundancies and define their removal. On this basis, we define fuzzy relational operations in relational algebra, which, being similar to the conventional relational databases, are complete and sound. In particular, we investigate fuzzy querying strategies and give the form of fuzzy querying with SQL. © 2002 Wiley Periodicals, Inc.     

Fuzzy relational algebra for possibility-distribution-fuzzy-relational model of fuzzy data

In the real world, there exist a lot of fuzzy data which cannot or need not be precisely defined. We distinguish two types of fuzziness: one in an attribute value itself and the other in an association of them. For such fuzzy data, we propose a possibility-distribution-fuzzy-relational model, in which fuzzy data are represented by fuzzy relations whose grades of membership and attribute values are possibility distributions. In this model, the former fuzziness is represented by a possibility distribution and the latter by a grade of membership. Relational algebra for the ordinary relational database as defined by Codd includes the traditional set operations and the special relational operations. These operations are classified into the primitive operations, namely, union, difference, extended Cartesian product, selection and projection, and the additional operations, namely, intersection, join, and division. We define the relational algebra for the possibility-distribution-fuzzy-relational model of fuzzy databases.     

Data dependencies in extended possibility‐based fuzzy relational databases

Based on the semantic equivalence degree the formal definitions of fuzzy functional dependencies (FFDs) and fuzzy multivalued dependencies (FMVDs) are first introduced to the fuzzy relational databases, where fuzziness of data appears in attribute values in the form of possibility attributions, as well as resemblance relations in attribute domain elements, called extended possibility‐based fuzzy relational databases. A set of inference rules for FFDs and FMVDs is then proposed. It is shown that FFDs and FMVDs are consistent and the inference rules are sound and complete, just as Armstrong's axioms for classic cases. © 2002 Wiley Periodicals, Inc.     

Semantic measure of fuzzy data in extended possibility‐based fuzzy relational databases

In this paper, we propose notions of equivalence and inclusion of fuzzy data in relational databases for measuring their semantic relationship. The fuzziness of data appears in attribute values in forms of possibility distribution as well as resemblance relations in attribute domain elements. An approach for evaluating semantic measures is presented. With the proposal, one can remove fuzzy data redundancy and define fuzzy functional dependency. © 2000 John Wiley & Sons, Inc.     

Generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries

This paper deals with relational databases which are extended in the sense that fuzzily known values are allowed for attributes. Precise as well as partial (imprecise, uncertain) knowledge concerning the value of the attributes are represented by means of [0,1]-valued possibility distributions in Zadeh's sense. Thus, we have to manipulate ordinary relations on Cartesian products of sets of fuzzy subsets rather than fuzzy relations. Besides, vague queries whose contents are also represented by possibility distributions can be taken into account. The basic operations of relational algebra, union, intersection, Cartesian product, projection, and selection are extended in order to deal with partial information and vague queries. Approximate equalities and inequalities modeled by fuzzy relations can also be taken into account in the selection operation. Then, the main features of a query language based on the extended relational algebra are presented. An illustrative example is provided. This approach, which enables a very general treatment of relational databases with fuzzy attribute values, makes an extensive use of dual possibility and necessity measures.     

Attribute-oriented fuzzy generalization in proximity- and similarity-based relational database systems

In this article we investigate an attribute-oriented induction approach for acquisition of abstract knowledge from data stored in a fuzzy database environment. We utilize a proximity-based fuzzy database schema as the medium carrying the original information, where lack of precise information about an entity can be reflected via multiple attribute values, and the classical equivalence relation is replaced with the broader fuzzy proximity relation. We analyze in detail the process of attribute-oriented induction by concept hierarchies, utilizing the original properties of fuzzy databases to support this established data mining technique. In our approach we take full advantage of the implicit knowledge about the similarity of original attribute values, included by default in the investigated fuzzy database schemas. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 763–779, 2007.     

Fuzzy database query languages and their relational completenesstheorem

Two fuzzy database query languages are proposed. They are used to query fuzzy databases that are enhanced from relational databases in such a way that fuzzy sets are allowed in both attribute values and truth values. A fuzzy calculus query language is constructed based on the relational calculus, and a fuzzy algebra query language is also constructed based on the relational algebra. In addition, a fuzzy relational completeness theorem such that the languages have equivalent expressive power is proved     

Managing fuzziness on conventional object-oriented platforms

During the last few years, many database researchers have aimed their efforts at extending the object-oriented model for dealing with different kinds of imperfect information. Some of these scholars have used the Fuzzy Set Theory to deal with imperfection because it has proved to be useful in problems where imprecision and uncertainty play important roles. This article describes an architecture that can be used to develop a fuzzy object-oriented system on top of an existing classical one. This article also introduces a general framework as the basis for managing fuzziness in conventional object-oriented systems. Foodbi, a fuzzy object-oriented database interface, is presented as a prototype that allows the creation of fuzzy object-oriented schemata that can be translated into sets of standard Java classes. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 781–803, 2007.     

基于模糊关系的数据模型分析

模糊性是现实世界事物的一个重要属性,不但描述事物的属性特征方面存在着模糊性,而且事物间的相互联系方面也存在着模糊性。本文基于模糊集合理论,实现一个简单模糊关系数据模型,包括模糊关系的定义、模糊关系运算及模糊关系的完整性。并简单介绍了模糊关系数据库技术的应用领域。     

A method for fuzzy clustering with ordinal attributes

Pattern vectors to be clustered may have attributes of various types including ordinal. The latter type of attribute with values such as “poor,” “very poor,” “good,” and “very good” is neither entirely numerical nor entirely qualitative. This leads to difficulties in clustering because it is meaningless to take differences of values of these ordinal attributes as is required for finding distance between pattern vectors. Representing ordinal values by numbers and then finding differences is incorrect. Rather, the ordinal values themselves may be considered as linguistic values of linguistic variables corresponding to fuzzy sets. This article discusses a method of fuzzy c-means clustering that uses fuzzy sets to represent ordinal values. Both the ratio-scaled and ordinal-scaled values can be treated in the same way by treating the ratio-scaled values as singletons. The same results are then obtained for the ratio-scaled attributes as in the traditional method. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 599–620, 2007.     

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.     

Resolving database incompatibility: an approach to performingrelational operations over mismatched domains

A solution to the problem of supporting relational database operations despite domain mismatch is presented. Mismatched domains occur when information must be obtained from databases that were developed independently. Domain differences are resolved by mapping conflicting attributes to common domains by means of a mechanism of virtual attributes and then applying a set of extended relational operations to the resulting values. When one-one mappings cannot be established between domains, the values that result from attribute mappings may be partial. A set of extended relational operators that formalize operations over partial values and thus manipulate the incomplete information that results from resolving domain mismatch is defined     

Null values in fuzzy databases

Since in the real world, it often occurs that information is missing, database systems clearly need some facilities to deal with missing data. With respect to traditional database systems, the most commonly adopted approach to this problem is based on null values and three valued logic. This paper deals with the semantics and the use of null values in fuzzy databases. In dealing with missing information a distinction is made between incompleteness due to unavailability and incompleteness due to inapplicability. Both the database modelling and database querying aspects are described. With respect to attribute values, incompleteness due to unavailability is modelled by possibility distributions, which is a commonly used technique in the fuzzy databases. Domain specific null values, represented by a bottom symbol, are used to model incompleteness due to inapplicability. Extended possibilistic truth values are used to formalize the impact of data manipulation and (flexible) querying operations in the presence of these null values. The different cases of appearances of null values in the handling of selection conditions of flexible database queries are described in detail.     

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.     

关系数据库中基于EPTV的模糊查询

关系数据库中空值存在不同的语义,并且会影响模糊查询结果。针对该问题,提出用标号来区分空值的语义,并且在EPTV逻辑的基础上,对关系运算和一些复杂的嵌套查询进行扩展,给出相关定义和计算方法。通过实例说明,与常规模糊查询相比,该方法能较好地反映空值对模糊查询结果的影响。     

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.     

关系数据库中的模糊知识发现

本文提出用部分量词和模糊谓词来表示模糊知识这一方法，在简要介绍数据抽象这一关系数据库中知识发现的方法后，详细描述了该方法中对模糊性问题的处理方法．     

Design and implementation of index structures for fuzzy spatial databases

Over the years database management systems have evolved to include spatially referenced data. Because spatial data are complex and have a number of unique constraints (i.e., spatial components and uncertain properties), spatial database systems can be effective only if the spatial data are properly handled at the physical level. Therefore, it is important to develop an effective spatial and aspatial indexing technique to facilitate flexible spatial and/or aspatial querying for such databases. For this purpose we introduce an indexing approach to use (fuzzy) spatial and (fuzzy) aspatial data. We use a number of spatial index structures, such as Multilevel Grid File (MLGF), G-tree, R-tree, and R^*-tree, for fuzzy spatial databases and compare the performances of these structures for various flexible queries. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 805–826, 2007.     

Evaluation of design requirements using fuzzy outranking methods

To increase customer satisfaction, quality function deployment is used to translate customer needs into technical design requirements (DRs). Determination of DRs for product development is very important because these requirements are the vital keys to successful products. The methods used to evaluate DRs in the literature can be categorized into multicriteria evaluation methods such as scoring methods, the analytic hierarchy method, analytic network process, and so forth. There are few papers using fuzzy multi‐attribute outranking methods to evaluate DRs. This article aims to compare the results of three different fuzzy outranking methods to evaluate the DRs in the PVC windows industry. A sensitivity analysis is also made by using the software, FOuR. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1229–1250, 2007.