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K-FLAT PROJECTIVE FUZZY QUANTALES | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 6، دوره 14، شماره 5، دی 2017، صفحه 65-81 اصل مقاله (429.93 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3433 | ||
نویسندگان | ||
Jing Lu1؛ Kaiyun Wang2؛ Bin Zhao ![]() | ||
1College of Mathematics and Information Science, Shaanxi Normal Univer- sity, Xi'an 710119, P.R. China | ||
2College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, P.R. China | ||
چکیده | ||
In this paper, we introduce the notion of {\bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we prove that {\bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {\bf K} as examples. | ||
کلیدواژهها | ||
Fuzzy quantale؛ Fuzzy binary relation؛ {bf K}-flat projective fuzzy quantale؛ Comonad | ||
مراجع | ||
[1] J. Adamek and H. Herrlich and G. E. Strecker, Abstract and Concrete Categories: The Joy of Cats, John Wiley & Sons, New York, (1990), 1-507. [2] B. Banaschewski, Projective frames: a general view, Cahiers Topologie Geom. Dierentielle Cat., XLVI (2005), 301-312. [3] R. Belohlavek, Fuzzy Relational Systems: Foundations and Principles, Kluwer Aca- demic/Plenum Publishers, New York, 20 (2002), 1-369. [4] R. P. Dilworth, Non-commutative residuated lattices, Trans. Amer. Math. Soc., 46 (1939), 426-444. [5] L. Fan, A new approach to quantitative domain theory, Electron. Notes Theor. Comput. Sci., 45(1) (2001), 77-87. [6] G. Gierz, et al., Continuous Lattices and Domains, Encyclopedia of Mathematics and its Applications, vol. 93, Cambridge University Press, Cambridge, 93 (2003), 1-591. [7] H. Herrlich and G. E. Strecker, Category Theory, An introduction, Second edition, Sigma Series in Pure Mathematics, vol. 1, Heldermann Verlag, Berlin, 1 (1979), 1-400. [8] P. T. Johnstone, Stone Spaces, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 3 (1982), 1-370. [9] D. Kruml and J. Paseka, Algebraic and categorical ascepts of quantales, Handb. Algebra, 5 (2008), 323-362. [10] H. L. Lai and D. X. Zhang, Complete and directed complete -categories, Theor. Comput. Sci., 388 (2007), 1-25. [11] Y. M. Li, M. Zhou and Z. H. Li, Projective and injective objects in the category of quantales, J. Pure Appl. Algebra, 176 (2002), 249-258. [12] J. Lu and B. Zhao, The projective objects in the category of fuzzy quantales, J. Shandong Univ. (Nat. Sci.), (in Chinese), 50(2) (2015), 47-54 . [13] C. J. Mulvey, &, Supplemento ai Rendiconti del Circolo Matematico di Palermo, II(12) (19 86), 99-104. [14] C. J. Mulvey and J. W. Pelletier, On the quantisation of points, J. Pure Appl. Algebra, 159 (2001), 231-295. [15] J. Paseka, Projective quantale: A general view, Int. J. Theor. Phys., 47(1) (2008), 291-296. [16] K. I. Rosenthal, Quantales and their Applications, Pitman Research Notes in Mathematics Series, vol. 234, Longman Scientic & Technical, Essex, 234 (1990), 1-165. [17] S. A. Solovyov, A representation theorem for quantale algebras, Contrib. Gen. Algebra, 18 (2008), 189-198. [18] K. Y. Wang and B. Zhao, Some properties of the category of fuzzy quantales, J. Shaanxi Norm. Univ. (Nat. Sci. Ed.), (in Chinese), 41(3) (2013), 1-6 . [19] K. Y. Wang, Some researches on fuzzy domains and fuzzy quantales, Ph. D. Thesis, College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, (2012), 1-115. [20] M. Ward, Structure residuation, Ann. Math., 39 (1938), 558-568. [21] R. Wang and B. Zhao, Quantale algebra and its algebraic ideal, Fuzzy Syst. Math., (in Chinese), 24 (2010), 44-49. [22] M. Ward and R. P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc., 45 (1939), 335- 354. [23] W. Yao and L. X. Lu, Fuzzy Galois connections on fuzzy posets, Math. Log. Quart., 55(1) (2009), 105-112. [24] W. Yao, Quantitative domains via fuzzy sets: Part I: Continuity of fuzzy directed complete posets, Fuzzy Sets Syst., 161(7) (2010), 973-987. [25] W. Yao, An approach to fuzzy frames via fuzzy posets, Fuzzy Sets Syst., 166 (2011), 75-89. [26] W. Yao, A survey of fuzzications of frames, the Papert-Papert-Isbell adjunction and sobri- ety, Fuzzy Sets Syst., 190 (2012), 63-81. [27] L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3) (1965), 338-353. [28] Q. Y. Zhang and L. Fan, Continuity in quantitative domains, Fuzzy Sets Syst., 154(1) (2005), 118-131. | ||
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