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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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Information retrieval 14 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