Intuitionistic Fuzzy Multivalued Dependency and Intuitionistic Fuzzy Fourth Normal Form

Intuitionistic fuzzy databases are used to handle imprecise and uncertain data as they represent the membership, nonmembership, and hesitancy associated with a certain element in a set. This paper presents the Intuitionistic Fuzzy Fourth Normal Form to decompose the multivalued dependent data. A technique to determine Intuitionistic Fuzzy multivalued dependencies by working on the closure of dependencies has been proposed. We derive the closure by obtaining all the logically implied dependencies by a set of Intuitionistic Fuzzy multivalued dependencies, i.e., Inference Rules. A complete set of inference rules for the Intuitionistic Fuzzy multivalued dependencies has been given along with the derivation of each rule. These rules help us to compute the dependency closure and we further use the same for defining the Intuitionistic Fuzzy Fourth Normal Form.

[1]  Olga Pons,et al.  Dealing with Disjunctive and missing Information in Logic fuzzy Databases , 1996, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[2]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[3]  K. Atanassov.  More on intuitionistic fuzzy sets , 1989 .

[4]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[5]  Yannis Vassiliou.  Functional Dependencies and Incomplete Information , 1980, VLDB.

[6]  Witold Lipski,et al.  On semantic issues connected with incomplete information databases , 1979, ACM Trans. Database Syst..

[7]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[8]  S. Jyothi,et al.  Multivalued dependencies in fuzzy relational databases and lossless join decomposition , 1997, Fuzzy Sets Syst..

[9]  Asma R. Shora,et al.  Data Dependencies and Normalization of Intuitionistic Fuzzy Databases , 2014 .

[10]  Etienne E. Kerre,et al.  On the composition of intuitionistic fuzzy relations , 2003, Fuzzy Sets Syst..

[11]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[12]  Olga Pons,et al.  Computing Fuzzy Dependencies with Linguistic Labels , 1999 .

[13]  R. Sunderraman,et al.  A Generalized Relational Model for Indefinite and Maybe Information , 1991, IEEE Trans. Knowl. Data Eng..

[14]  Arun K. Majumdar,et al.  Fuzzy Functional Dependencies and Lossless Join Decomposition of Fuzzy Relational Database Systems , 1988, ACM Trans. Database Syst..

[15]  Nicolas Spyratos,et al.  Partition semantics for incomplete information in relational databases , 1988, SIGMOD '88.

[16]  Gultekin Özsoyoglu,et al.  Incomplete Relational Database Models Based on Intervals , 1993, IEEE Trans. Knowl. Data Eng..

[17]  Janusz Kacprzyk,et al.  Intuitionistic Fuzzy Sets in some Medical Applications , 2001, Fuzzy Days.

[18]  Janusz Kacprzyk,et al.  Intuitionistic Fuzzy Sets in Intelligent Data Analysis for Medical Diagnosis , 2001, International Conference on Computational Science.

[19]  Panagiotis Chountas,et al.  On Intuitionistic Fuzzy Expert Systems With Temporal Parameters , 2006 .

[21]  Y. Jun.  Intuitionistic fuzzy finite state machines , 2005 .

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

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

[24]  Ranjit Biswas,et al.  On Intuitionistic Fuzzy Databases , 2002, JCIS.