Valerie V. Cross

Fuzzy objects for geographical information systems

Abstract Modeling, storing and retrieving geographical information has become an important part of our information society. Geographical information is typically specified in terms of collections of entities and phenomena that are structured aggregations of spatial entities. GIS features tend to form natural class hierarchies. Another characteristic of geographical information is that often it may be inexact or vague. With respect to these characteristics, the confluence of the two technologies fuzzy set theory and object-oriented databases could provide a powerful tool for knowledge representation underlying geographical information systems. The fuzzy object data model is currently being developed and prototype implementations have been undertaken using an integrative approach with existing software including an expert system shell and a commercial object-oriented database system. In this paper, the benefits of a fuzzy object data model for geographical information systems are examined, an overview of the model is presented, and the current prototype implementations are described.

Fuzzy semantic distance measures between ontological concepts

An emphasis has been placed on the use of ontologies for representing application domain knowledge. Determining a degree or measure of semantic similarity, semantic distance, or semantic relatedness between concepts from different systems or domains, is becoming an increasingly important task. This paper presents a brief overview of such measures between concepts within ontological representations and provides several examples of such measures found in the research literature. These measures are then examined within the framework of fuzzy set similarity measures. The use of a semantic similarity measure between elements that are part of a domain for which an ontological structure exists is explored in order to extend standard fuzzy set compatibility measures.

Fuzzy information retrieval

Over the past decade, information retrieval has emerged as an active research area in the application of fuzzy set theory. Fuzzy information retrieval utilizes fuzzy sets to represent documents, membership degrees for query term relevance, fuzzy logical operators to define queries, and fuzzy compatibility measures to assess the retrieval status value of a document. This paper presents an overview of fuzzy relational databases and fuzzy information retrieval. A general description of the main components of fuzzy information retrieval are given: document representation, query representation, computer-aided query formulation, document retrieval status, and performance measures. Examples of areas currently being researched are provided. The relation between fuzzy information retrieval and fuzzy relational databases is examined.Over the past decade, information retrieval has emerged as an active research area in the application of fuzzy set theory. Fuzzy information retrieval utilizes fuzzy sets to represent documents, membership degrees for query term relevance, fuzzy logical operators to define queries, and fuzzy compatibility measures to assess the retrieval status value of a document. This paper presents an overview of fuzzy relational databases and fuzzy information retrieval. A general description of the main components of fuzzy information retrieval are given: document representation, query representation, computer-aided query formulation, document retrieval status, and performance measures. Examples of areas currently being researched are provided. The relation between fuzzy information retrieval and fuzzy relational databases is examined.

A perspective from the Fuzzy Object Data Management Group (FODMG)

The Fuzzy Object Data Management Group has been formed as a joint international collaborative research effort among fuzzy database researchers in order to establish common terminology and concepts, to formalize and integrate the current body of fuzzy object model research, to provide a basis for future extensions, and to contribute to the commercial success of a fuzzy object data model. This paper presents the initial research efforts to use ODMG-93 object data model standard as the basis for defining a fuzzy object data model since it is becoming a defacto standard and several object-oriented database vendors are currently releasing commercial products in compliance with this standard. The syntactic extensions to the ODMG object model and the semantic issues related to these extensions in order to provide fuzzy set objects and fuzzy objects are presented. These extensions are an initial effort in accomplishing the challenging task of defining a fuzzy type and fuzzy hierarchy and their related semantics.

Patterns of fuzzy rule-based inference

Abstract Processing information in fuzzy rule-based systems generally employs one of two patterns of inference: composition or compatibility modification. Composition originated as a generalization of binary logical deduction to fuzzy logic, while compatibility modification was developed to facilitate the evaluation of rules by separating the evaluation of the input from the generation of the output. The first step in compatibility modification inference is to assess the degree to which the input matches the antecedent of a rule. The result of this assessment is then combined with the consequent of the rule to produce the output. This paper examines the relationships between these two patterns of inference and establishes conditions under which they produce equivalent results. The separation of the evaluation of input from the generation of output permits a flexibility in the methods used to compare the input with the antecedent of a rule with multiple clauses. In this case, the degree to which the input and the rule antecedent match is determined by the application of a compatibility measure and an aggregation operator. The order in which these operations are applied may affect the assessment of the degree of matching, which in turn may cause the production of different results. Separability properties are introduced to define conditions under which compatibility modification inference is independent of the input evaluation strategy.

Compatibility-based ranking of fuzzy numbers

A general approach to the ranking of n fuzzy numbers by applying fuzzy compatibility measures and the fuzzy minimum and fuzzy maximum operators is described. In an n/spl times/n binary fuzzy ranking relation the ranking of the fuzzy numbers A and B is based on the combined evidence that A is smaller than B and B is larger than A. From the fuzzy ranking a total ordering can be obtained for the n fuzzy numbers. The ranking method with two different compatibility measures; one from the set-theoretic class and another from the distance-based class, is applied to a case study from the literature and the results analyzed.

Unifying ontological similarity measures: A theoretical and empirical investigation

Abstract This paper theoretically and empirically investigates ontological similarity. Tversky’s parameterized ratio model of similarity [3] is shown as a unifying basis for many of the well-known ontological similarity measures. A new family of ontological similarity measures is proposed that allows parameterizing the characteristic set used to represent an ontological concept. The three subontologies of the prominent Gene Ontology (GO) are used in an empirical investigation of several ontological similarity measures. Another study using well known semantic similarity within two different anatomy ontologies, the NCIT anatomy and the mouse anatomy, is also presented for comparison to several of the GO results. A discussion of the correlation among the measures is presented as well as a comparison of the effects of two different methods of determining a concept’s information content, corpus-based and ontology-based.

Semantic Relatedness Measures in Ontologies Using Information Content and Fuzzy Set Theory

The success of the semantic Web is linked with the use of ontologies on the semantic Web. Ontologies help systems understand the meaning of information and can serve as the interface to the inferencing layer of the semantic Web. An increasingly important task is to determine a degree or measure of semantic relatedness between concepts within and across ontologies. This paper presents an overview of such measures using several examples found in the research literature. The relationship between a distance-based network semantic relatedness measure and an information theoretic measure is shown for the first time by using Tverskys set-theoretic measures and a new information content measure. New measures of semantic relatedness between ontological concepts are proposed by viewing each concept as a set of its descendent leaf concepts

Fuzzy ontologies for multilingual document exploitation

Multilingual document exploitation (MDE) involves assessing the relevance of individual foreign language documents to the course of a military mission. The current approach to relevance assessment (RA) in FALCon, an MDE system, runs a machine translation (MT) program to convert the documents into English and then provides a simple keyword search with a frequency count of the matched keywords. This paper explores the potential that fuzzy mathematics and ontologies have for improving performance in MDE. Research on information retrieval and filtering is examined and fuzzy extensions to these applications are presented for inclusion in RAVEN, an alternate MDE system design to FALCon.

Geometric compatibility modification

Abstract Compatibility modification is a rule-based inference strategy that uses the similarity of the input with the antecedent of a rule to modify the consequent. Existing compatibility modification inference techniques have employed a set theoretic assessment of compatibility. In this paper, a distance-based compatibility measure is derived from a generalization of the dissemblance index for fuzzy sets. This measure is then used to develop an inference technique based on geometric compatibility. This geometric approach is compared with two other distance-based inference techniques: linear rule interpolation and bound dependent linear revision.