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Dzenan Gusic



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Dzenan Gusic


WSEAS Transactions on Systems and Control


Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 14, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 14, 2019



On Completeness of Inference Rules for Vague Functional and Vague Multivalued Dependencies in Two-Element Vague Relation

AUTHORS: Dzenan Gusic

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ABSTRACT: In this paper we pay attention to completeness of the inference rules for vague functional and vague multivalued dependencies in two-element, vague relation instances. Motivated by the fact that the set of the inference rules is a complete set, that is, these exists a vague relation instance on given relation scheme which satisfies all vague functional and vague multivalued dependencies in the closure of the union of some set of vague functional and some set of vague multivalued dependencies, and violates a vague functional, respectively, a vague multivalued dependency outside of the closure, we prove that the vague relation instance may be chosen to contain only two elements.

KEYWORDS: Vague functional dependencies, vague multivalued dependencies, interpretations, inference rules, completeness

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, Springer–Verlag, Berlin–Heidelberg 2008

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

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

[6] 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.

[7] 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.

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

[9] 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.

[10] Dz. Gu ˇ siˇ c, Soundness and Completeness of In- ´ ference Rules for New Vague Functional Dependencies, MATEC Web of Conferences, to appear.

[11] Dz. Gu ˇ siˇ c, Soundness of Inference Rules for ´ New Vague Multivalued Dependencies, MATEC Web of Conferences, to appear.

[12] Dz. Gu ˇ siˇ c, Completeness of Inference Rules for ´ New Vague Multivalued Dependencies, WSEAS Trans. on Math., to appear.

[13] Dz. Gu ˇ siˇ c, Vague Functional Dependencies and ´ Resolution Principle, WSEAS Trans. on Math., to appear.

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

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

[16] A. Lu and W. Ng, Managing Merged Data by Vague Functional Dependencies, in: ER 2004 LNCS, Berlin 2004, pp. 259–272.

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

[18] 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.

[19] 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.

[20] J. Mishra and S. Ghosh, A Vague Multivalued Data Dependency, Fuzzy Inf. Eng. 4, 2013, pp. 459–473.

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

[22] 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.

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

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

[25] 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.

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

WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 14, 2019, Art. #30, pp. 232-238


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