Representation of Fuzzy Knowledge in Relational Databases

Authors: José Galindo ; Angélica Urrutia ; Mario PiattiniPublic:Database and Expert Systems Applications (DEXA’04)

Adviser ： RC. ChenSpeaker: Chih-Hung Hsu

Date:2006/12/14

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Outline

• Abstract

• Introduction

• Fuzzy Attributes

• Representation of Fuzzy Attributes

• Representation of Fuzzy Metaknowldege Data： The FMB

• Conclusions and Future Lines

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Abstract

• Implement fuzzy databases based on the relational model

• Two aspects of fuzzy information– how to represent fuzzy data– how to represent fuzzy metaknowledge data

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Introduction

• Fuzzy relation database allow storing and/or treating vague and uncertain information

• FuzzyEER model is an extension of the EER model to create conceptual schemas with fuzzy semantics and notations

• fuzzy attributes, fuzzy entities, fuzzy relationships, fuzzy specializations

• incorporate the FuzzyEER concepts in a relational DBMS

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Fuzzy Attributes (1/6)

• Fuzzy Sets as Fuzzy Values

• Type 1– precise data– can be transformed or manipulated using

fuzzy conditions

• Type 2– imprecise data over an ordered referential– allow the storage of imprecise information

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Fuzzy Attributes (2/6)

• Type 3– data of discreet non-ordered dominion with

analogy

• Type 4– as Type 3– they are defined in the same way as Type 3

attributes

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Fuzzy Attributes (3/6)

• Fuzzy Degrees as Fuzzy Values– only use degrees in the interval [0,1]– most important possible meanings of the

degrees:• Fulfillment degree• Uncertainty degree• Possibility degree• Importance degree

– associated and non-associated degrees

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Fuzzy Attributes (4/6)

• Type 5– Degree in each value of an attribute– some attributes may have a fuzzy degree

associated to them– need to know the meaning of the degree and

the meaning of the associated attribute

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Fuzzy Attributes (5/6)

• Type 6– Degree in a set of values of different attributes– the degree is associated to some attributes and

this is an unusual case

• Type 7– Degree in the whole instance of the relation– can represent something like the “membership

degree” of this tuple to the relation of the database

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Fuzzy Attributes (6/6)

• Type 8– Non-associated degrees

– there are cases in which the imprecise information, which we wish to express, can be represented by using only the degree, without associating this degree to another specific value or values

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Representation of Fuzzy Attributes(1/5)

• Fuzzy attributes Type 1 doesn’t allow fuzzy values

• Fuzzy attributes Type 2 need five classic attributes:– One stores the kind of value (Table 1)

– the others four store the crisp values representing the fuzzy value

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Representation of Fuzzy Attributes(2/5)

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Representation of Fuzzy Attributes(3/5)

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• Fuzzy attributes Type 3 need a variable number of attributes:– one stores the kind of value (Table 2)

• number 3 needs only two values , but number 4 needs 2n values, where n is the maximum length for possibility distributions for each fuzzy attribute

• Fuzzy attributes Type 4 are represented just like Type 3

Representation of Fuzzy Attributes(4/5)

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Representation of Fuzzy Attributes(5/5)

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Representation of Fuzzy Metaknowledge Data: The FMB (1/2)

• Information in the FMB• Attributes with fuzzy capabilities: fuzzy attributes

and fuzzy degrees (Type 1 to 8)

• The metaknowledge of each attribute is different according to its type– Types 1 and 2: This last value is used in comp

arisons like “much greater than”– Types 3 and 4: Value n, name of linguistic lab

els and, only for Type 3, the similarity relationship between whatever two labels

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– Types 5 and 6: Meaning of the degree and attribute or attributes to which the degree is associated

– Types 7 and 8: Meaning of the degree

• Other objects:– fuzzy qualifiers (Give me employees who

belong to most of projects)– fuzzy quantifiers (An employee must work in

many projects)

Representation of Fuzzy Metaknowledge Data: The FMB (2/2)

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Conclusions and Future Lines

• Implement fuzzy databases modeled with the FuzzyEER model

• Represent fuzzy data and fuzzy metaknowledge data

• FSQL (Fuzzy SQL) language may be used in those databases