اخبار و اعلانات
آمار
| تعداد نشریات | 32 |
| تعداد شماره‌ها | 739 |
| تعداد مقالات | 7,168 |
| تعداد مشاهده مقاله | 11,710,288 |
| تعداد دریافت فایل اصل مقاله | 8,035,999 |
New intuitionistic fuzzy operations, operators and topological structures | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 20، شماره 7، بهمن و اسفند 2023، صفحه 37-53 اصل مقاله (178.27 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7629 | ||
| نویسندگان | ||
| K. T. Atanassov* 1؛ R. Tsvetkov2 | ||
| 1Bulgarian Academy of Sciences Centre of Biomedical Engineering 1113 Sofia, Bulgeria | ||
| 2Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1000 Sofia, Bulgaria | ||
| چکیده | ||
| Two new intuitionistic fuzzy operations (union and intersection) are defined. Based on them, two new topological operators (of a closure and of an interior types) are introduced. Some properties of these obects are studied. Based on them, four new intuitionistic fuzzy topological structures are introduced and some of their properties are discussed. Integral forms of both new intuitionistic fuzzy operations and of both intuitionistic fuzzy operators are given. | ||
| کلیدواژه‌ها | ||
| Intuitionistic fuzzy operation؛ intuitionistic fuzzy operator؛ intuitionistic fuzzy set؛ intuitionistic fuzzy topological structure | ||
| مراجع | ||
|
[1] K. Atanassov, Intuitionistic fuzzy sets, Springer, Heidelberg, 1999.
[2] K. Atanassov, On intuitionistic fuzzy sets theory, Springer, Berlin, 2012.
[3] K. Atanassov, Intuitionistic fuzzy modal topological structure, Mathematics, 10 (2022), 3313. DOI: 10.3390/ math10183313.
[4] K. Atanassov, On the intuitionistic fuzzy modal feeble topological structures, Notes on Intuitionistic Fuzzy Sets, 28(3) (2022), 211-222.
[5] K. Atanassov, On four intuitionistic fuzzy feeble topological structures, 2022 IEEE 11th International Conference on Intelligent Systems (IS), Warsaw, 12-14 Oct. 2022. DOI: 10.1109/IS57118.2022.10019726.
[6] K. Atanassov, On intuitionistic fuzzy temporal topological structures, Axioms, 12 (2023), 182. DOI: 10.3390/axioms12020182.
[7] K. Atanassov, N. Angelova, T. Pencheva, On two intuitionistic fuzzy modal topological structures, Axioms, (submitted).
[8] K. Atanassov, P. Vassilev, R. Tsvetkov, Intuitionistic fuzzy sets, Measures and Integrals, “Prof. M. Drinov” Academic Publishing House, Sofia, 2013.
[9] P. Blackburn, J. van Bentham, F. Wolter, Modal logic, North Holland, Amsterdam, 2006.
[10] N. Bourbaki, Eléments de mathématique, livre III: Topologie généralé , Chapitre 1: Structures Topologiques, Chapitre 2: Structures Uniformes. Herman, Paris, 1960 (Third Edition, in French).
[11] C. L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24 (1968), 182-190.
[12] D. Çoker, On topological structures using intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 3(5) (1997), 138-142.
[13] D. Çoker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88(1) (1997), 181-189.
[14] A. El-Latif, M. Khalaf, Connectedness in intuitionistic fuzzy topological spaces in Sostaks sense, Italian Journal of Pure and Applied Mathematics, 35 (2015), 649-668.
[15] R. Feys, Modal logics, Gauthier, Paris, 1965.
[16] A. Haydar E¸s, D. Çoker, More on fuzzy compactness in intuitionistic fuzzy topological spaces, Notes Intuitionistic Fuzzy Sets, 2(1) (1996), 4-10.
[17] Y. C. Kim, S. E. Abbas, Connectedness in intuitionistic fuzzy topological spaces, Communications of the Korean Mathematical Society, 20 (2005), 117-134.
[18] G. Klir, B. Yuan, Fuzzy sets and fuzzy logic, Prentice Hall, New Jersey, 1995.
[19] K. Kuratowski, Topology, Vol. 1, New York, Acad. Press, 1966.
[20] S. J. Lee, E. P. Lee, The category of intuitionistic fuzzy topological spaces, Bulletin of the Korean Mathematical Society, 37 (2000), 63-76.
[21] F. G. Lupiañez, Separation in intuitionistic fuzzy topological spaces, International Journal of Pure and Applied Mathematics, 17(1) (2004), 29-34.
[22] F. G. Lupiañez, On intuitionistic fuzzy topological spaces, Kybernetes, 35(5-6) (2006), 743-747.
[23] E. Mendelson, Introduction to mathematical logic, Princeton, New Jersey, D. Van Nostrand, 1964.
[24] S. Milles, The lattice of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations, Applications and Applied Mathematics, 15(2) (2020), 942-956.
[25] G. A. Mints, Short introduction to modal logic, University of Chicago Press, Chicago, 1992.
[26] K. Mondal, S. K. Samanta, A study on intuitionistic fuzzy topological spaces, Notes Intuitionistic Fuzzy Sets, 9(1) (2003), 1-32.
[27] J. Munkres, Topology, Prentice Hall Inc., New Jersey, Second Ed. 2014.
[28] O. Özbakir, D. Çoker, Fuzzy multifunctions in intuitionistic fuzzy topological spaces, Notes Intuitionistic Fuzzy Sets, 5(3) (1999), 1-5.
[29] P. Rajarajeswari, R. Krishna Moorthy, Intuitionistic fuzzy completely weakly generalized continuous mappings, Notes Intuitionistic Fuzzy Sets, 18(1) (2012), 25-36.
[30] S. E. Rodabaugh, E. P. Klement, U. Höhle, Applications of category theory to fuzzy subsets, Kluwer Academic Publishers, Dordrecht, 1992.
[31] R. Roopkumar, C. Kalaivani, Continuity of intuitionistic fuzzy proper functions on intuitionistic smooth fuzzy topological spaces, Notes Intuitionistic Fuzzy Sets, 16(3) (2010), 1-21.
[32] W. Rudin, Functional analysis, New York, McGraw-Hill, 1991.
[33] R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27 (2006), 331-334.
[34] S. Thakur, R. Chaturvedi, Generalized continuity in intuitionistic fuzzy topological spaces, Notes Intuitionistic Fuzzy Sets, 12(1) (2006), 38-44.
[35] S. Tiwari, On relationships among intuitionistic fuzzy approximation operators, intuitionistic fuzzy topology and intuitionistic fuzzy automata, Notes Intuitionistic Fuzzy Sets, 16(1) (2010), 1-9.
[36] S. Yılmaz, G. Cuvalcoglu, On level operators for temporal intuitionistic fuzzy sets, Notes Intuitionistic Fuzzy Sets, 20(2) (2014), 6-15.
[37] L. Ying Ming, L. Mao Kang, Fuzzy topology, World Science, Singapore, 1997.
[38] H. Yongfa, J. Changjun, Some properties of intuitionistic fuzzy metric spaces, Notes Intuitionistic Fuzzy Sets, 10(1) (2004), 18-26.
[39] L. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. | ||
|
آمار تعداد مشاهده مقاله: 472 تعداد دریافت فایل اصل مقاله: 829 |
||