AUTHORS: Dzenan Gusic, Sanela Nesimovic

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ABSTRACT: The needs of the modern world often require automatization of certain aspects of mankind activities. Science is no exception to this. In this paper we pay attention to vague functional dependencies as generalized functional dependencies. These dependencies are considered as fuzzy formulas. We give strict proof of the equivalence: any two-element vague relation instance on given scheme (which satisfies some set of vague functional dependencies) satisfies given vague functional dependency if and only if the attached fuzzy formula is a logical consequence of the corresponding set of fuzzy formulas. Thanks to this result, we put ourselves into position to automatically verify if some vague functional dependency follows from some set of vague functional dependencies. An appropriate example which supports this claim is also provided.

KEYWORDS: Automatization, vague functional dependencies, fuzzy formulas

REFERENCES:

[1] M. Baczynski and B. Jayaram, On the charac- ´ terizations of (S,N)-implications generated from continuous negations, in: Proceedings of the 11th Conf. Information Processing and Management of Uncertainity in Knowledge-based Systems, Paris 2006, pp. 436–443.

[2] M. Baczynski and B. Jayaram, On the charac- ´ terizations of (S,N)-implications, Fuzzy Sets and Systems 158, 2007, pp. 1713–1727.

[3] M. Baczynski and B. Jayaram, ´ Fuzzy Implications, Berlin–Heidelberg, Springer–Verlag, 2008

[4] J. F. Baldwin, Knowledge engineering using a fuzzy relational inference language, IFAC Proceedings Volumes 16, 1983, pp. 14–20.

[5] B. P. Buckles and F. E. Petry, A fuzzy representation of data for relational databases, Fuzzy Sets and Systems 7, 1982, pp. 213–216.

[6] B. P. Buckles and F. E. Petry, Fuzzy databases and their applications, Fuzzy Inform. Decision Processes 2, 1982, pp. 361–371.

[7] B. P. Buckles and F. E. Petry, Uncertainty models in information and database systems, J. Inform. Sci. 11, 1985, pp. 77–87.

[8] S. M. Chen, Similarity Measures Between Vague Sets and Between Elements, IEEE Transactions on Systems, Man and Cybernetics 27, 1997, pp. 153–159.

[9] S. M. Chen, Measures of Similarity Between Vague Sets, Fuzzy Sets and Systems 74, 1995, pp. 217–223.

[10] N. Dukic, D´ z. Gu ˇ siˇ c, A. Muratovi ´ c-Ribi ´ c, A. Al- ´ ihodziˇ c, E. Tabak, and H. Duki ´ c, From fuzzy ´ dependences to fuzzy formulas and vice versa, for Kleene-Dienes fuzzy implication operator, WSEAS Trans. on Systems and Control 13, 2018, pp. 285–297.

[11] N. Dukic, D ´ z. Gu ˇ siˇ c, and N. Kajmovi ´ c, Re- ´ ichenbach and f-generated implications in fuzzy database relations, Int. J. of Circuits, Systems and Signal Processing 12, 2018, pp. 285–297.

[12] C. Giardina, I. Sack, and D. Sinha, Fuzzy Field Relational Database Tech. Report 8332, Elect. Engng. and Computer Science Dept., Stevens Institute of Technology, Hoboken, NJ 1983

[13] P. Grzegorzewski, Distances Between Intuitionistic Fuzzy Sets and/or Interval-valued Fuzzy Sets Based on the Hausdorff Metric, Fuzzy Sets and Systems 148, 2004, pp. 319–328.

[14] Dz. Gu ˇ siˇ c, Continuous Maps in Fuzzy Relations, ´ WSEAS Trans. on Systems and Control 13, 2018, pp. 324–344.

[15] Dz. Gu ˇ siˇ c, On Fuzzy Dependencies and ´ g-generated Fuzzy Implications in Fuzzy Relations, WSEAS Trans. on Systems and Control 14, 2019, pp. 71–89.

[16] Dz. Gu ˇ siˇ c, Soundness and Completeness of In- ´ ference Rules for New Vague Functional Dependencies, in: N. Mastorakis, V. Mladenov and A. Bulucea (eds.) MATEC Web of Conferences, Vol. 292, 23rd International Conference on Circuits, Systems, Communications and Computers (CSCC 2019), Athens 2019, pp. 1–9.

[17] Dz. Gu ˇ siˇ c, Vague Functional Dependencies and ´ Resolution Principle, WSEAS Trans. on Mathematics 18, 2019, pp. 257–263.

[18] D. H. Hong and C. Kim, A note on Similarity Measures Between Vague Sets and Between Elements, Information Sciences 115, 1999, pp. 83– 96.

[19] M. Levene and G. Loizou, A Guided Tour of Relational Databases and Beyond, Springer– Verlag, London 1999

[20] F. Li and Z. Xu, Measures of Similarity Between Vague Sets, Journal of Software 12, 2001, pp. 922–927.

[21] A. Lu and W. Ng, Managing Merged Data by Vague Functional Dependencies, in: P. Atzeni, W. Chu, H. Lu, S. Zhou, T.-W. Ling (eds.) ER 2004 LNCS, vol. 3288, Springer-Verlag, Berlin Heidelberg 2004, pp. 259–272.

[22] M. Mas, M. Monserrat, and J. Torrens, QL-implications versus d-implications, Kybernetika 42, 2006, pp. 956–966.

[23] R. Mesiar and A. Mesiarova, Residual implications and left-continuous t-norms which are ordinal sums of semigroups, Fuzzy Sets and Systems 143, 2004, pp. 47–57.

[24] J. Mishra and S. Ghosh, A New Functional Dependency in a Vague Relational Database Model, International Journal of Computer Applications 39, 2012, pp. 29–36.

[25] D. Pei, R0 implication: characteristics and applications, Fuzzy Sets and Systems 131, 2002, pp. 297–302.

[26] Y. Shi, B. Van Gasse, D. Ruan, and E. Kerre, On the first place antitonicity in ql-implications, Fuzzy Sets and Systems 159, 2008, pp. 2988– 3013.

[27] Y. Shi, A Deep Study of Fuzzy Implications, Ph.D. dissertation, Faculty of Science, Ghent University, Ghent, 2009.

[28] M. Sozat and A. Yazici, A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations, Fuzzy Sets and Systems 117, 2001, pp. 161–181.

[29] E. Szmidt and J. Kacprzyk, Distances Between Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 114, 2000, pp. 505–518.

[30] E. Trillas, C. Del Campo, and S. Cubillo, When qm-operators are implication functions and conditional fuzzy relations, Int. J. Intelligent Systems 15, 2000, pp. 647–655.

[31] J. D. Ullman, Primciples of Database Systems, Computer Science Press, Rockville, MD 1982

[32] F. Zhao and Z. M. Ma, Functional Dependencies in Vague Relational Databases, in: IEEE International Conference on Systems, Man, and Cybernetics, vol. 5, Taipei, Taiwan 2006, pp. 4006– 4010.