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.     

Knowledge acquisition in incomplete fuzzy information systems via the rough set approach

Abstract: Machine learning can extract desired knowledge from training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete and incomplete data sets. If attribute values are known as possibility distributions on the domain of the attributes, the system is called an incomplete fuzzy information system. Learning from incomplete fuzzy data sets is usually more difficult than learning from complete data sets and incomplete data sets. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete fuzzy data sets based on rough sets. The notions of lower and upper generalized fuzzy rough approximations are introduced. By using the fuzzy rough upper approximation operator, we transform each fuzzy subset of the domain of every attribute in an incomplete fuzzy information system into a fuzzy subset of the universe, from which fuzzy similarity neighbourhoods of objects in the system are derived. The fuzzy lower and upper approximations for any subset of the universe are then calculated and the knowledge hidden in the information system is unravelled and expressed in the form of decision rules.     

Fuzzy Conditional Probability Relations and their Applications in Fuzzy Information Systems

In our real-world applications, data may be imprecise in which levels or degrees of preciseness of data are intuitively different. In this case, fuzzy set expressions are considered as an alternative to represent the imprecise data. In general, the degree of similarity relationship between two fuzzy (imprecise) data in real-world applications may not necessarily be symmetric or transitive. In order to provide such a degree of similarity between two fuzzy data, we introduced the fuzzy conditional probability relation. The concept of a fuzzy conditional probability relation may be considered as a concrete example of weak similarity relation which in turn is a special type of fuzzy binary relation generalizing similarity relation. Two important applications concerning the application of Knowledge Discovery and Data Mining (KDD) in the presence of a fuzzy data table (usually called fuzzy information system), namely removing redundant objects and recognizing partial or total dependency of (domain) attributes, are considered induced by the fuzzy conditional probability relation. Here, the fuzzy information system contains precise as well as imprecise data (fuzzy values) about objects of interest characterized by some attributes. Related to the dependency of attributes, we introduce the fuzzy functional dependency that satisfies Armstrongs Axioms. In addition, we also discuss some interesting applications such as approximate data reduction and projection, approximate data querying and approximate joining in order to extend the query system.     

Fuzzy analysis of statistical evidence

Bayesian classifiers are effective methods for pattern classification, although their assumptions on the belief structure among attributes are not always justified. In this paper, we introduce a new classification method based on the possibility measure, which does not require a precise belief model and, in a sense, it includes the Bayesian classifiers as special cases. This new classification method uses the fuzzy operators to aggregate attributes information (evidence) and it is referred to as fuzzy analysis of statistical evidence (FASE). FASE has several nice properties. It is noise tolerant, it can handle missing values with ease, and it can extract statistical patterns from the data and represent them by knowledge of beliefs, which, in turn, are propositions for an expert system. Thus, from pattern classification to expert systems, FASE provides a linkage from inductive reasoning to deductive reasoning     

领域相关多媒体对象的基于内容查询

该文通过对多媒体对象领域知识特点的分析，指出了领域属性与多媒体对象分离的必要性，对多媒体对象的领域属性进行了分类，采用框架（frame）结构作为领域知识的表示模式，利用语义网表示领域概念之 分类关系以及同义关系，并用上下文（context）记录了特定用户更细的辅助知识，包括多媒体相似阈值刻画、模糊值的描述以及用户查询反馈等参数。该文还给出了多媒体对象相似的计算公式，分析了多媒体基于内容查询的各种类型，研究了多媒体查询处理过程。     

因素空间的属性圆定义及其在对象分类中的应用

为使汪培庄先生提出的因素空间理论便于应用,和基于该理论对多域值属性影响对象集合进行聚类分析,提出了以研究对象为中心的图形化域值属性表示方法,即属性圆。属性圆可以表示无穷多个域属性对对象的影响。先基于属性圆概念进行对象的相似性分析,后为计算方便将图形定义转化为数值相似性定义,进而研究了对象集合的聚类分析方法。实施的聚类原则为:严格遵照相似与不相似划分,参考模糊相似划分。列举了一个实际电气系统的系统可靠性表述群作为研究对象集合,对表述群进行聚类分析。结果表明:决策集D与对象集U的对应关系说明对对象集的划分就其决策属性而言是非奇异的、准确的。这说明尽管在不同环境下对系统进行了可靠性评价,但是这些评价语义是相对客观的,评价的语义可以相互佐证。     

A method for ranking fuzzy numbers and its application todecision-making

Since fuzzy numbers represent uncertain numeric values, it is difficult to rank them according to their magnitude. In the paper, a method for ranking fuzzy numbers is proposed. The method considers the overall possibility distributions of fuzzy numbers in their evaluations for ranking and provides users with a method of changing viewpoints for evaluations. Users represent their viewpoints with fuzzy sets. The method evaluates fuzzy numbers with a satisfaction function and the viewpoint given by users and then ranks the numbers according to their evaluation values. The satisfaction function is a measure of comparisons between fuzzy numbers. In order to illustrate the ranking method, two numeric examples are shown, and for the comparative study, our method is compared with four existing ranking methods through eight examples. As an example of potential applications, the proposed method is applied to a decision-making problem: a two-person game with fuzzy profit and loss. The ranking method is used to analyze player choices     

Management of uncertainty in LIFE FEShell fuzzy frame system

LIFE FEShell is a fuzzy expert system shell that handles several kinds of uncertainty. LIFE FEShell is based on fuzzy logic, possibility theory, fuzzy measures and the fuzzy integral and is constructed in four parts: Fuzzy Production System (FPS), Fuzzy Frame System (FFS), FPS Object Editor (FPOE), and Fuzzy Frame Editor (FFE). We are now developing a few expert systems on LIFE FEShell to study and solve problems that are likely to arise during the implementation of these systems.

In this paper, we present an analysis of uncertainty in the frame system and show details of the LIFE FEShell Fuzzy Frame System and its handling of uncertainty. LIFE FEShell FFS allows linguistic representations in data and evaluation functions and handles its hierarchical definitions to accommodate their linguistic polysemy. Data may be set not only with crisp values, but also using possibility distributions as slot values, data grades, and link grades.     

Mining fuzzy association rules from uncertain data

Association rule mining is an important data analysis method that can discover associations within data. There are numerous previous studies that focus on finding fuzzy association rules from precise and certain data. Unfortunately, real-world data tends to be uncertain due to human errors, instrument errors, recording errors, and so on. Therefore, a question arising immediately is how we can mine fuzzy association rules from uncertain data. To this end, this paper proposes a representation scheme to represent uncertain data. This representation is based on possibility distributions because the possibility theory establishes a close connection between the concepts of similarity and uncertainty, providing an excellent framework for handling uncertain data. Then, we develop an algorithm to mine fuzzy association rules from uncertain data represented by possibility distributions. Experimental results from the survey data show that the proposed approach can discover interesting and valuable patterns with high certainty.     

Fuzzy semantic tagging and flexible querying of XML documents extracted from the Web

The relational database model is widely used in real applications. We propose a way of complementing such a database with an XML data warehouse. The approach we propose is generic, and driven by a domain ontology. The XML data warehouse is built from data extracted from the Web, which are semantically tagged using terms belonging to the domain ontology. The semantic tagging is fuzzy, since, instead of tagging the values of the Web document with one value of the domain ontology, we propose to use tags expressed in terms of a possibility distribution representing a set of possible terms, each term being weighted by a possibility degree. The querying of the XML data warehouse is also fuzzy: the end-users can express their preferences by means of fuzzy selection criteria. We present our approach on a first application domain: predictive microbiology.     

Refining imprecise data by integrity constraints

Uncertain data in databases were originally denoted as null values, which represent the meaning of ‘values unknown at present.” Null values were generalized into partial values, which correspond to a set of possible values, to provide a more powerful notion. In this paper, we derive some properties to refine partial values into more informative ones. In some cases, they can even be refined into definite values. Such a refinement is possible when there exist range constraint on attribute domains, or referential integrities, functional dependencies, or multivalued dependencies among attributes.

Our work actually eliminates redundant elements in a partial value. By this process, we not only provide a more concise and informative answer to users, but also speedup the computation of queries issued afterward. Besides, it reduces the communication cost when imprecise data are requested to be transmitted from one site to another site in a distributed environment.     

Fuzzy quality function deployment: determining the distributions of effort dedicated to technical change

A model is presented that develops the Quality Function Deployment (QFD) House of Quality tool into a fuzzy‐set based multi‐criteria decision‐making process to determine the distributions of effort directed toward technical changes. When customers are polled for desired product‐specific attributes, the responses are typically defined by linguistic variables that represent a fuzzy set distribution. Fuzzy sets also define customer perceptions of the product attributes and technical expert opinions about product design criteria relative to marketplace competitors. Therefore, for each technical criterion, the following factors have an effect on the decision to implement change(s): (1) fuzzy sets providing evidence of customer need for attributes; (2) motivation to change to satisfy desired customer attributes; (3) motivation for technical criterion change; and (4) the strength of the relationships between the attributes and the technical criterion. Priority rankings are linked to the distributions of effort to apply in fulfilling continuous product improvement.     

Domains and active domains: what this distinction implies for theestimation of projection sizes in relational databases

Database optimizers require statistical information about data distributions in order to evaluate result sizes and access plan costs for processing user queries. In this context, we consider the problem of estimating the size of the projections of a database relation, when measures on attribute domain cardinalities are maintained in the system. Our main theoretical contribution is a new formal model, the AD (active domain) model, which is valid under the hypotheses of attribute independence and uniform distribution of attribute values, derived considering the difference between the time-invariant domain (the set of values that an attribute can assume) and the time-dependent (“active”) domain (the set of values that are actually assumed, at a certain time). Early models developed under the same assumptions are shown to be formally incorrect. Since the AD model is computationally highly demanding, we also introduce an approximate, easy-to-compute model, the A²D (approximate active domain) model that, unlike previous approximations, yields low errors on all the parameter space of the active domain cardinalities. Finally, we extend the A²D model to the case of nonuniform distributions and present experimental results confirming the good behavior of the model     

挖掘语言值关联规则

讨论了大型数据库上数量属性的关联规则问题.为了软化论域的划分边界,应用相关的模糊c-方法(relationalfuzzyc-means,简称RFCM)算法确定正态模糊数的两个参数,并借助正态模糊数模型来划分数量属性的论域,由此生成一系列的语言值关联规则.另外,给出了语言值关联规则的挖掘方法.由于语言值能很好地表示抽象的概念,从而使得挖掘出的关联规则更抽象、更容易被人理解.     

Self-organizing fuzzy aggregation models to rank the objects withmultiple attributes

In this paper, a kind of ranking system, called agent-clients evaluation system, is proposed and investigated where there is no such authority with the right to predetermine weights of attributes of the entities evaluated by multiple evaluators for obtaining an aggregated evaluation result from the given fuzzy multiattribute values of these entities. Three models are proposed to evaluate the entities in such a system based on fuzzy inequality relation, possibility, and necessity measures, respectively. In these models, firstly the weights of attributes are automatically sought by fuzzy linear programming (FLP) problems based on the concept of data envelopment analysis (DEA) to make a summing-up assessment from each evaluator. Secondly, the weights for representing each evaluator's credibility are obtained by FLP to make an integrated evaluation of entities from the viewpoints of all evaluators. Lastly, a partially ordered set on a one-dimensional space is obtained so that all entities can be ranked easily. Because the weights of attributes and evaluators are obtained by DEA-based FLP problems, the proposed ranking models can be regarded as fair-competition and self-organizing ones so that the inherent feature of evaluation data can be reflected objectively     

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.     

Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information

In the classical Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), the decision maker (DM) gives the pair-wise comparisons of alternatives with crisp truth degree 0 or 1. However, in the real world, DM is not sure enough in all comparisons and can express his/her opinion with some fuzzy truth degree. Thus, DM's preferences are given through pair-wise comparisons of alternatives with fuzzy truth degrees, which may be represented as trapezoidal fuzzy numbers (TrFNs). Considered such fuzzy truth degrees, the aim of this paper is to develop a new fuzzy linear programming technique for solving multiattribute decision making (MADM) problems with multiple types of attribute values and incomplete weight information. In this method, TrFNs, real numbers, and intervals are used to represent the multiple types of decision information. The fuzzy consistency and inconsistency indices are defined as TrFNs due to the alternatives’ comparisons with fuzzy truth degrees. Hereby a new fuzzy linear programming model is constructed and solved by the possibility linear programming method with TrFNs developed in this paper. The fuzzy ideal solution (IS) and the attribute weights are then obtained. The distances of alternatives from the fuzzy IS can be calculated to determine their ranking order. The implementation process of the method proposed in this paper is illustrated with a strategy partner selection example. The comparison analyzes show that the method proposed in this paper generalizes the classical LINMAP, fuzzy LINMAP and possibility LINMAP.     

Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets

In this paper, we present a new method to handle fuzzy multiple attributes group decision-making problems based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. First, we present the arithmetic operations between interval type-2 fuzzy sets. Then, we present a fuzzy ranking method to calculate the ranking values of interval type-2 fuzzy sets. We also make a comparison of the ranking values of the proposed method with the existing methods. Based on the proposed fuzzy ranking method and the proposed arithmetic operations between interval type-2 fuzzy sets, we present a new method to handle fuzzy multiple attributes group decision-making problems. The proposed method provides us with a useful way to handle fuzzy multiple attributes group decision-making problems in a more flexible and more intelligent manner due to the fact that it uses interval type-2 fuzzy sets rather than traditional type-1 fuzzy sets to represent the evaluating values and the weights of attributes.