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OWA operators in fuzzy querying

OWA operators in fuzzy querying. Mustafa Zali Spring 89. Introduction. Fuzzy Database has two important application in database systems: Representation of uncertain and imprecise information in a (relational) database ways to provide for more flexibility in the information retrieval process

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OWA operators in fuzzy querying

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  1. OWA operators in fuzzy querying Mustafa Zali Spring 89

  2. Introduction • Fuzzy Database has two important application in database systems: • Representation of uncertain and imprecise information in a (relational) database • ways to provide for more flexibility in the information retrieval process • Fuzzification of the relational algebra and calculus • Fuzzy queries and using aggregation Operator to combine the result of fuzzy queries.

  3. Agenda • Brief Introduction to Fuzzy Concepts • Historical Background • Fuzzy Data Model • Imprecise Queries • Linguistic Quantifiers and OWA Operators • Choosing weight for an OWA operator • Conclusion

  4. Brief Introduction to Fuzzy Concepts • Membership Definition(Membership Function A) For a set A, we define a membership function A such as A(x) =1 if and only if x  A 0if and only if x  A We can say that the function A maps the elements in the universal set X to the set {0,1}. A: X {0,1}

  5. Brief Introduction to Fuzzy Concepts Fuzzy Sets and Membership Functions: If U is a collection of objects denoted generically by x, then a fuzzy setA in U is defined as a set of ordered pairs: membership function

  6. Brief Introduction to Fuzzy Concepts • A= "young" , B="very young"

  7. Brief Introduction to Fuzzy Concepts • Union • Intersection

  8. Fuzzy Database • Fuzzy Logic has given numerous extension of the classical relational models. • More readable queries, human consistent and easier to use queries. • Extend SQL by some fuzzy constructs. • SELECT and WHERE clause fuzzified. • Fuzzy Queries use linguistic terms in conditions.

  9. Fuzzy Database • Fuzzy Queries construct from • Fuzzy values: “young” and • Fuzzy relations: “much greater than” • Linguistic Quantifiers: “most”, “all most” • Fuzzy aggregation operators used to unify some different fuzzy sets. • To aggregate the result of given by conditions of queries we use aggregation operators as an alternate for AND, OR

  10. Fuzzy Data Model • Two basic extended data models for fuzzy relational databases can be identified: • one is based on possibility distribution • Tuples associated with possibility degrees • Attribute values represented possibility distributions • one is based on similarity

  11. Fuzzy Data Model

  12. Imprecise Queries • An imprecise (fuzzy) query to a relational database is a query containing natural language expressions, as for example in “low salary”, • imprecise referred to as linguistic terms, to specify: • imprecise values, comparison operators, as for example in “salary much greater than USD 2,000”, • non-standard aggregation scheme of the fulfillment degrees of partial conditions, as for example in “most of the important conditions have to be satisfied”.

  13. Imprecise Queries • The semantics of these expressions is modeled using fuzzy logic that preserves their inherent imprecision • SELECT * • FROM employees • WHERE “Most of conditions among • ‘age IS young, salary IS high, • jan_sales IS MUCH GREATER THAN jun_sales, ...’ • are to be satisfied”

  14. Imprecise Queries • Equivalent • SELECT * • FROM employees • WHERE feb_sales > • most (jan_sales, mar_sales, . . ., dec_sales) • SELECT * • FROM employees • WHERE “Most of conditions among • ‘feb_sales > jan_sales, feb_sales > mar_sales, • ..., feb_sales > dec_sales’ • are to be satisfied”

  15. Advantages of Imprecise Queries • Better representation of the user’s requirements via a direct use of linguistic terms, notably those expressing a more complex aggregation of partial conditions, • Reduction of the risk of an empty answer due to the flexibility of the fuzzy logic based modeling of linguistic terms.

  16. Aggregation Operator • Aggregation Operator used to combine several fuzzy sets to one fuzzy. • Used to combine the result of conditions of a query.

  17. Representation vs. Retrieval • In this work we concentrate on fuzzy ways for more flexibility of data retrieval. • Data is not represented fuzzy. • The queries are in natural language.

  18. Linguistic Quantifiers and OWA Operators • Linguistic Quantifier: Most Asian are tall. • Formal form of it is: Q x P(x). • Q = Most, x = Asian, P(x): Asian are tall. • Q is a fuzzy set by this membership function: • For example: • Truth value of Q:

  19. Linguistic Quantifiers and OWA Operators • OWA (ordered weighting averaging) • where bi is i-th largest element among ai’s • Min: • Max: • Average:

  20. Choosing Weights for an OWA Operator • OWA may be used to model linguistic quantifiers. • One way to defining weights is: • Query most of them is young (1, 0.4, 0.5, 0.1) • 0.4 vs. 0.44

  21. Choosing Weights for an OWA Operator • Two measure for choosing weights • ORness • Dispersion • The ORness is, in a sense, a measure of similarity of a given OWA operator to the “max” operator • The closer the weights to one another (to 1/m): the higher the value of dispersion

  22. Linguistic Quantifiers in Imprecise Queries • The weight vector determined using: • experimental data • A linguistic quantifier in the sense of Zadeh: • Analytic Method: a fixed value of certain characteristic features of the OWA operator

  23. Analytic Method • Determine the weight vector W such that the OWA operator obtained has a fixed required value of ORness and at the same time has the maximum possible value of dispersion.

  24. Analytic Method • A simple approximate procedure for some class of the OWA operators, exponential OWA operators. The weights of the exponential WA operators are defined as:

  25. Analytic Method • Filev and Yager proposed a modified version of previous method

  26. Analytic Method • In the case when the linguistic quantifier “most” explicitly represented by an OWA, it is directly applicable for the interpretation of only for n = m.

  27. Analytic Method • User guided approach • Change weights • when an increase of the ORness is required • when a decrease of the ORness is required

  28. Analytic Method • Here we present a simple algorithm, which yields quite satisfactory results, and is implemented in FQUERY for Access

  29. Conclusion • Consider the role of fuzzy linguistic quantifiers in flexible database queries • New simple algorithms that may be relevant from a practical point of view

  30. References • SlawomirZadrozny, JanuszKacprzyk: Issues in the practical use of the OWA operators in fuzzy querying. J. Intell. Inf. Syst: 2009

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