Optimization of the normalization of fuzzy relational databases by using alternative methods of calculation for the Fuzzy Functional Dependency

Although, in comparison to standard databases, a tremendous benefit is often derived by using fuzzy databases, their distribution is very low. A reason for the relatively poor acceptance of fuzzy relational databases is to be seen in the difficulty to carry out an adequate normalization. The various procedures discussed in the literature possess miscellaneous weaknesses. In this work a normalization method is regarded whose most significant deficit lies in the fuzzy functional dependency (FFD) because thereby comprehensible results are not produced. Therefore, it is registered which alternatives for the determination of the degree of FFD exist. Furthermore, it is examined with which of these methods the just addressed disadvantage can be eliminated. For this purpose, the presented methods are applied to several examples in order to identify their characteristics.

[1]  L. Zadeh Calculus of fuzzy restrictions , 1996 .

[2]  Wenyi Zeng,et al.  Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations , 2006, Int. J. Intell. Syst..

[3]  Yannis A. Tolias,et al.  Generalized fuzzy indices for similarity matching , 2001, Fuzzy Sets Syst..

[4]  Sujeet Shenoi,et al.  An equivalence classes model of fuzzy relational databases , 1990 .

[5]  Adnan Yazici,et al.  A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations , 2001, Fuzzy Sets Syst..

[6]  Liu Xuecheng,et al.  Entropy, distance measure and similarity measure of fuzzy sets and their relations , 1992 .

[7]  Weimin Ma,et al.  Functional dependencies in extended possibility-based fuzzy relational databases , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[8]  YaziciAdnan,et al.  A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations , 2001 .

[9]  Rami Zwick,et al.  Measures of similarity among fuzzy concepts: A comparative analysis , 1987, Int. J. Approx. Reason..

[10]  A. Tversky Features of Similarity , 1977 .

[11]  Stephen Shaoyi Liao,et al.  Functional dependencies with null values, fuzzy values, and crisp values , 1999, IEEE Trans. Fuzzy Syst..

[12]  Juan C. Cubero,et al.  A new definition of fuzzy functional dependency in fuzzy relational databases , 1994, Int. J. Intell. Syst..

[13]  H. Damasio,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence: Special Issue on Perceptual Organization in Computer Vision , 1998 .

[14]  A. Kaufman,et al.  Introduction to the Theory of Fuzzy Subsets. , 1977 .

[15]  A. Bonaert Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[16]  M. Nakata,et al.  Functional dependencies in fuzzy databases , 1997, Proceedings of 1st International Conference on Conventional and Knowledge Based Intelligent Electronic Systems. KES '97.

[17]  Ingo Schmitt Ähnlichkeitssuche in Multimedia-Datenbanken - Retrieval, Suchalgorithmen und Anfragebehandlung , 2005 .

[18]  C.J.H. Mann Similarity and Compatibility in Fuzzy Set Theory – Assessment and Applications , 2002 .

[19]  Sujeet Shenoi,et al.  Functional dependencies and normal forms in the fuzzy relational database model , 1992, Inf. Sci..

[20]  B. Tyagi,et al.  Fuzzy functional dependencies and independencies in extended fuzzy relational database models , 1995 .

[21]  M. Les,et al.  A knowledge server for reasoning about temporal constraints between classes and instances of events , 2004 .

[22]  V. Cross,et al.  Similarity and Compatibility in Fuzzy Set Theory: Assessment And Applications , 2010 .

[23]  Etienne E. Kerre,et al.  Normalization Based on Fuzzy Functional Dependency in a Fuzzy Relational Data Model , 1996, Inf. Syst..

[24]  Shi-Jay Chen,et al.  A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-mean Averaging Operator , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[25]  Miin-Shen Yang,et al.  On a similarity measure between LR‐type fuzzy numbers and its application to database acquisition , 2005, Int. J. Intell. Syst..

[26]  Ranjit Biswas,et al.  Fuzzy Functional Dependencies in Relational Databases , 2006 .

[27]  C. Pappis,et al.  A comparative assessment of measures of similarity of fuzzy values , 1993 .

[28]  A. P. Bonaert,et al.  Introduction to the Theory of Fuzzy Subsets-vol. 1: Fundamental Theoretical Elements , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[29]  Devendra K. Tayal,et al.  A complete axiomatization of fuzzy functional dependencies using fuzzy function , 2005, Fuzzy Sets Syst..

[30]  Simone Santini,et al.  Similarity Measures , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

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

[32]  Ronald R. Yager Fuzzy set and possibility theory : recent developments , 1982 .

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

[34]  Wen-June Wang,et al.  New similarity measures on fuzzy sets and on elements , 1997, Fuzzy Sets Syst..