| Title of paper:
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Some algebraic properties of the matrix representation of intuitionistic fuzzy modal operators
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| Author(s):
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| Gökhan Çuvalcioğlu
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| Department of Mathematics, University of Mersin, Turkey
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| gcuvalcioglu@gmail.com
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| Esra Aykut
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| Department of Mathematics, University of Mersin, Turkey
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| esraxaykut@gmail.com
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| Presented at:
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19th International Conference on Intuitionistic Fuzzy Sets, 4–6 June 2015, Burgas, Bulgaria
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| Published in:
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"Notes on IFS", Volume 21, 2015, Number 2, pages 140—149
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| Download:
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 PDF (898 Kb, File info)
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| Abstract:
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Herewith proposed is an application of elements of the theory of intuitionistic fuzzy sets to a problem from the area of agriculture, namely application of different intuitionistic fuzzy operators to the problem of ensuring economic irrigation of farmland. We start from the assumption that the separation of an agricultural area can be done in the same way as the separation of image. Separating an area requires the use of certain variables, and the proposed application exhibits a variety of such variables like temperature, level of afforestation, type of trees, various characteristics of soil, including soil moisture, slope of the terrain, air humidity in agricultural area, etc. From all these variables, we have chosen to include in our model the type of soil, air humidity and soil humidity.For the purpose of the present research, we benefit from the definition of membership function implementing the enhancement algorithm as described with membership functions in [8] and [math]\displaystyle{ Z_{\alpha,\beta}^{\omega} }[/math], [math]\displaystyle{ F_{\alpha,\beta} }[/math], [math]\displaystyle{ B_{\alpha,\beta} }[/math] as described in [2,3]. These operators were used for optimal tuning the variables in the economic irrigation model.
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| Keywords:
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Intuitionistic fuzzy modal operators, Agricultural application, Intuitionistic fuzzy logic, Contrast enhancement.
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| AMS Classification:
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03E72
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| References:
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- Atanassov, K. T. (1983) Intuitionistic fuzzy sets, VII ITKR's Session, Sofia, June 1983 (deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci. No. 1697184 (in Bulgarian).
- Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Spinger Physica-Verlag, Heidelberg.
- Çuvalcioğlu, G., On the Diagram of One Type Modal Operatorss on Intuitionistic Fuzzy Sets: Last Expanding with [math]\displaystyle{ Z_{\alpha,\beta}^{\omega} }[/math], Iranian J. of Fuzzy Systems, 10(1), 2013, 89–106.
- Çuvalcıoğlu, G., S. Yılmaz and K. Atanassov. Matrix representation of the second type of intuitionistic fuzzy modal operators, Notes on Intuitionistic Fuzzy Sets, 20(5), 2014, 9–16.
- Çuvalcıoğlu, G., & Aykut, E. (2014) An application of the intuitionistic fuzzy modal operator Eα,β, Notes on Intuitionistic Fuzzy Sets, 20(5), 57-61.
- Marinov, E., Velizarova, E., & Atanassov, K. (2013) An intuitionistic fuzzy estimation of the area of 2D-figures, Notes on Intuitionistic Fuzzy Sets, 19(2), 57-70.
- Marinov, E., Velizarova, E., & Atanassov, K. (2014) An intuitionistic fuzzy estimation of the area of 2D-figures based on the Pick's formula. Modern Approaches in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Volume 1: Foundations. (Atanassov, K., M. Baczynski, J. Drewniak, J. Kacprzyk, M. Krawczak, E. Szmidt, M. Wygralak, S. Zadrozny, eds.), SRI-PAS, Warsaw, 145-157.
- Pal, S. K., & King, R. A. (1981) Image Enhancement Using Smoothing with Fuzzy Sets, IEEE Transactions on Systems, Man, and Cybernetics, SMC-1(7), 494-501.
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