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Fuzzy Set Models of IR

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Vaibhav Khanna

Fuzzy Model is a set theoretic model of document retrieval based on fuzzy theory. An opposite to this is the Exact match mechanism by which only the objects satisfying some well specified criteria, against object attributes, are returned to the user as a query answer.

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Information Retrieval : 14 Fuzzy Set Models of IR Prof Neeraj Bhargava Vaibhav Khanna Department of Computer Science School of Engineering and Systems Sciences Maharshi Dayanand Saraswati University Ajmer
Fuzzy Set Model • Matching of a document to a query terms is approximate or vague • This vagueness can be modeled using a fuzzy framework, as follows: – each query term defines a fuzzy set – each doc has a degree of membership in this set • This interpretation provides the foundation for many IR models based on fuzzy theory • In here, we discuss the model proposed by Ogawa, Morita, and Kobayashi
Fuzzy Set Model • Fuzzy set theory deals with the representation of classes whose boundaries are not well defined • Key idea is to introduce the notion of a degree of membership associated with the elements of the class • This degree of membership varies from 0 to 1 and allows modelling the notion of marginal membership • Thus, membership is now a gradual notion, contrary to the crispy notion enforced by classic Boolean logic
Fuzzy Set Model • A fuzzy subset A of a universe of discourse U is characterized by a membership function • This function associates with each element u of U a number μA(u) in the interval [0, 1] • The three most commonly used operations on fuzzy sets are: – the complement of a fuzzy set – the union of two or more fuzzy sets – the intersection of two or more fuzzy sets
Fuzzy Set Model • Let, U be the universe of discourse • A and B be two fuzzy subsets of U • A be the complement of A relative to U • u be an element of U • Then,
Fuzzy Information Retrieval • Fuzzy sets are modeled based on a thesaurus, which defines term relationships • A thesaurus can be constructed by defining a term- term correlation matrix C
Fuzzy IR: An Example
Fuzzy IR: An Example
Fuzzy IR: An Example
Assignment • Explain the concept of Fuzzy Set models and Fuzzy Information Retrieval

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Fuzzy Set Models of IR

  • 1. Information Retrieval : 14 Fuzzy Set Models of IR Prof Neeraj Bhargava Vaibhav Khanna Department of Computer Science School of Engineering and Systems Sciences Maharshi Dayanand Saraswati University Ajmer
  • 2. Fuzzy Set Model • Matching of a document to a query terms is approximate or vague • This vagueness can be modeled using a fuzzy framework, as follows: – each query term defines a fuzzy set – each doc has a degree of membership in this set • This interpretation provides the foundation for many IR models based on fuzzy theory • In here, we discuss the model proposed by Ogawa, Morita, and Kobayashi
  • 3. Fuzzy Set Model • Fuzzy set theory deals with the representation of classes whose boundaries are not well defined • Key idea is to introduce the notion of a degree of membership associated with the elements of the class • This degree of membership varies from 0 to 1 and allows modelling the notion of marginal membership • Thus, membership is now a gradual notion, contrary to the crispy notion enforced by classic Boolean logic
  • 4. Fuzzy Set Model • A fuzzy subset A of a universe of discourse U is characterized by a membership function • This function associates with each element u of U a number μA(u) in the interval [0, 1] • The three most commonly used operations on fuzzy sets are: – the complement of a fuzzy set – the union of two or more fuzzy sets – the intersection of two or more fuzzy sets
  • 5. Fuzzy Set Model • Let, U be the universe of discourse • A and B be two fuzzy subsets of U • A be the complement of A relative to U • u be an element of U • Then,
  • 6. Fuzzy Information Retrieval • Fuzzy sets are modeled based on a thesaurus, which defines term relationships • A thesaurus can be constructed by defining a term- term correlation matrix C
  • 7. Fuzzy IR: An Example
  • 8. Fuzzy IR: An Example
  • 9. Fuzzy IR: An Example
  • 10. Assignment • Explain the concept of Fuzzy Set models and Fuzzy Information Retrieval