JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (02): 47-54.doi: 10.6040/j.issn.1671-9352.0.2014.207

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The projective objects in the category of fuzzy quantales

LU Jing, ZHAO Bin   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2014-05-08 Revised:2014-11-03 Online:2015-02-20 Published:2015-01-27

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Abstract: The concept of fuzzy weakly ⊗-stable completely distributive lattices is introduced. It is proved that the family of all down sets of a fuzzy ordered semigroup with a appropriate operation ⊗ is a fuzzy weakly ⊗-stable completely distributive lattice. A necessary and sufficient condition for a fuzzy completely distributive lattice to be a fuzzy weakly ⊗-stable completely distributive lattice is given. Finally, projective objects in the category of fuzzy quantales are studied. It is also proved that the E-projective objects in the category of fuzzy quantales are exactly the fuzzy weakly ⊗-stable completely distributive lattices.

Key words: -stable completely distributive lattice, fuzzy completely distributive lattice, projective object, fuzzy weakly ⊗

CLC Number: 

  • O153.1
[1] MULVEY C J. &[J]. Rendiconti del Circolo Matematico diPalermo II, 1986, 12(2):99-104.
[2] MULVEY C J, PELLETIER J W. On the quantisation of points[J]. Journal of Pure and Applied Algebra, 2001, 159(2-3):231-295.
[3] ROSENTHAL K I. Quantale and their applications[M]. New York: Longman Scientific & Technical, 1990.
[4] ZADEH L A. Similarity relations and fuzzy orderings[J]. Information Sciences, 1971, 3(2):177-200.
[5] BěLOHLÁVEK R. Fuzzy ralational systems: foundations and principles[M]. New York: Kluwer Academic Publishers, Plenum Publishers, 2002.
[6] BODENHOFER U. Similarity-based generalization of fuzzy orderings preserving the classical axioms[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2000, 8(5):593-610.
[7] BODENHOFERr U. Representations and constructions of similarity-based fuzzy orderings[J]. Fuzzy Sets and Systems, 2003, 137(1):113-136.
[8] FAN Lei. A new approach to quantitative domain theory[J]. Electronic Notes in Theoretical Computer Science, 2001, 45(1):77-87.
[9] ZHANG Qiye, FAN Lei. Continuity in quantitative domains[J]. Fuzzy Sets and Systems, 2005, 154(1):118-131.
[10] YAO Wei, LU Lingxia. Fuzzy Galois connections on fuzzy posets[J]. Mathatical Logic Quarterly, 2009, 55(1):84-91.
[11] ADÁMEK J, HERRLICH H, STRECKER G E. Abstract and concrete catagories[M]. New York: Wiley Interscience, 1990.
[12] GRÄTER G. Universal Algebras[M]. 2nd. New York: Springer-Verlag, 1979.
[13] 汪开云. 模糊Domain与Quantale中若干问题的研究[D]. 西安: 陕西师范大学, 2012. WANG Kaiyun. Some researches on fuzzy domains and fuzzy quantales[D]. Xi'an: Shaanxi Normal University, 2012.
[14] 赖洪亮. Ω-范畴序结构性质的研究[D]. 成都: 四川大学, 2007. LAI Hongliang. On the order structure properties of Ω-categories[D]. Chengdu: Sichuan University, 2007.
[15] LI Yongming, ZHOU Meng, LI Zhihui. Projective and injective objects in the category of quantales[J]. Journal of Pure and Applied Algebra, 2002, 176(2-3):249-258.
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