Null values in fuzzy databases

Since in the real world, it often occurs that information is missing, database systems clearly need some facilities to deal with missing data. With respect to traditional database systems, the most commonly adopted approach to this problem is based on null values and three valued logic. This paper deals with the semantics and the use of null values in fuzzy databases. In dealing with missing information a distinction is made between incompleteness due to unavailability and incompleteness due to inapplicability. Both the database modelling and database querying aspects are described. With respect to attribute values, incompleteness due to unavailability is modelled by possibility distributions, which is a commonly used technique in the fuzzy databases. Domain specific null values, represented by a bottom symbol, are used to model incompleteness due to inapplicability. Extended possibilistic truth values are used to formalize the impact of data manipulation and (flexible) querying operations in the presence of these null values. The different cases of appearances of null values in the handling of selection conditions of flexible database queries are described in detail.

[1]  Patrick Bosc,et al.  About projection-selection-join queries addressed to possibilistic relational databases , 2005, IEEE Transactions on Fuzzy Systems.

[2]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[3]  N. Rescher.  Many Valued Logic , 1969 .

[4]  E. F. Codd,et al.  Missing information (applicable and inapplicable) in relational databases , 1986, SGMD.

[5]  Olga Pons,et al.  A Server for Fuzzy SQL Queries , 1998, FQAS.

[6]  Gert de Cooman,et al.  From Possibilistic Information to Kleene’s Strong Multi-Valued Logics , 1999 .

[7]  Didier Dubois.  Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification , 2001, Fuzzy Days.

[8]  E. F. Codd.  More commentary on missing information in relational databases (applicable and inapplicable information) , 1987, SGMD.

[9]  Joachim Biskup,et al.  A Formal Approach to Null Values in Database Relations , 1979, Advances in Data Base Theory.

[10]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[11]  Arthur M. Keller,et al.  Approaches for updating databases with incomplete information and nulls , 1984, 1984 IEEE First International Conference on Data Engineering.

[12]  Ronald R. Yager,et al.  Calculating attribute values using inheritance structures in fuzzy object-oriented data models , 1999, IEEE Trans. Syst. Man Cybern. Part C.

[13]  Slawomir Zadrozny,et al.  FQUERY for Access: towards human consistent querying user interface , 1996, SAC '96.

[14]  Zongmin Ma,et al.  Advances In Fuzzy Object-oriented Databases: Modeling And Applications , 2004 .

[15]  Adnan Yazici,et al.  Fuzzy Database Modeling , 1998, J. Database Manag..

[16]  E. F. Codd,et al.  Understanding relations , 1973, SGMD.

[17]  Guy De Tré,et al.  Conjunctive Aggregation of Extended Possibilistic Truth Values and Flexible Database Querying , 2002, FQAS.

[18]  John Grier Hibben,et al.  Symbolic Logic and Its Applications.@@@The Development of Symbolic Logic. , 1907 .

[19]  Curtis E. Dyreson,et al.  A Bibliography on Uncertainty Management in Information Systems , 1996, Uncertainty Management in Information Systems.

[20]  Patrick Bosc,et al.  Some approaches for relational databases flexible querying , 1992, Journal of Intelligent Information Systems.

[21]  C. J. Date.  Null Values in Database Management , 1982, BNCOD.

[22]  Bernard De Baets,et al.  Aggregating constraint satisfaction degrees expressed by possibilistic truth values , 2003, IEEE Trans. Fuzzy Syst..

[23]  Rita De Caluwe.  Fuzzy And Uncertain Object-Oriented Databases: Concepts And Models , 1997 .

[24]  Donald H. Kraft,et al.  Fuzzy sets in database and information systems: Status and opportunities , 2005, Fuzzy Sets Syst..

[25]  Frederick E. Petry,et al.  Principles and Applications , 1997 .

[26]  Guy De Tré,et al.  Modelling Uncertainty in Multimedia Database Systems: An Extended Possibilistic Approach , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[27]  Marc H. Scholl,et al.  A Formalization of ODMG Queries , 1997, DS-7.

[28]  Patrick Bosc,et al.  Fuzzy databases : principles and applications , 1996 .

[29]  Nancy A. Mathiowetz.  Respondent Expressions of Uncertainty: Data Source for Imputation , 1998 .

[30]  Jeffrey D. Ullman,et al.  Principles of Database Systems , 1980 .

[31]  Patrick Bosc,et al.  SQLf: a relational database language for fuzzy querying , 1995, IEEE Trans. Fuzzy Syst..

[32]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[33]  Carlo Zaniolo,et al.  Database relations with null values , 1982, J. Comput. Syst. Sci..

[34]  Tomasz Imielinski,et al.  Incomplete Information in Relational Databases , 1984, JACM.

[35]  E. F. Codd,et al.  Extending the database relational model to capture more meaning , 1979, ACM Trans. Database Syst..

[36]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[37]  Gloria Bordogna,et al.  Recent Issues on Fuzzy Databases , 2000 .

[38]  Yannis Vassiliou,et al.  Null values in data base management a denotational semantics approach , 1979, SIGMOD '79.

[39]  Guy De Tré,et al.  Extended possibilistic truth values , 2002, Int. J. Intell. Syst..

[40]  Yehoshua Sagiv,et al.  Can we use the universal instance assumption without using nulls? , 1981, SIGMOD '81.

[41]  E. F. CODD,et al.  A relational model of data for large shared data banks , 1970, CACM.

[42]  Arthur M. Keller.  Set-Theoretic Problems of Null Completion in Relational Databases , 1986, Inf. Process. Lett..

[43]  Henri Prade,et al.  Extrapolation of fuzzy values from incomplete data bases , 1989, Inf. Syst..

[44]  Roger Frost,et al.  International Organization for Standardization (ISO) , 2004 .

[45]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[46]  Motohide Umano,et al.  Fuzzy relational algebra for possibility-distribution-fuzzy-relational model of fuzzy data , 1994, Journal of Intelligent Information Systems.

[47]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[48]  Henri Prade,et al.  Generalizing Database Relational Algebra for the Treatment of Incomplete/Uncertain Information and Vague Queries , 1984, Inf. Sci..

[49]  Gert de Cooman,et al.  Towards a Possibilistic Logic , 1995 .

[50]  Ronald R. Yager,et al.  An approach to compute default attribute values in fuzzy object oriented data models , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[51]  Amihai Motro,et al.  Management of uncertainty in database systems , 1995 .

[52]  Thomas Lukasiewicz,et al.  Issues in uncertainty in AI: editorial , 2003 .