Hao, J., Li, Q., Guo, L. (2014). Fuzzy order congruences on fuzzy posets. Iranian Journal of Fuzzy Systems, 11(6), 89-109. doi: 10.22111/ijfs.2014.1750
Jing Hao; Qingguo Li; Lankun Guo. "Fuzzy order congruences on fuzzy posets". Iranian Journal of Fuzzy Systems, 11, 6, 2014, 89-109. doi: 10.22111/ijfs.2014.1750
Hao, J., Li, Q., Guo, L. (2014). 'Fuzzy order congruences on fuzzy posets', Iranian Journal of Fuzzy Systems, 11(6), pp. 89-109. doi: 10.22111/ijfs.2014.1750
Hao, J., Li, Q., Guo, L. Fuzzy order congruences on fuzzy posets. Iranian Journal of Fuzzy Systems, 2014; 11(6): 89-109. doi: 10.22111/ijfs.2014.1750
1College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450000, China
2College of Mathematics and Econometrics, Hunan University, Chang- sha, 410082, China
3College of Information Science and Engineering, Hunan University, Changsha, 410082, China
Abstract
Fuzzy order congruences play an important role in studying the categorical properties of fuzzy posets. In this paper, the correspondence between the fuzzy order congruences and the fuzzy order-preserving maps is discussed. We focus on the characterization of fuzzy order congruences on the fuzzy poset in terms of the fuzzy preorders containing the fuzzy partial order. At last, fuzzy complete congruences on fuzzy complete lattices are discussed.
bibitem{ahs90} J. Adamek, H. Herrlich and G. Strecker, {it Abstract and concrete categories: the joy of cats}, John Wiley and Sons, New York, 1990.
bibitem{rb02} R. Bv{e}lohl'avek, {it Fuzzy relational systems: foundations and principles}, Kluwer Academic Publishers, Norwell, MA, USA, 2002.
bibitem{rb04} R. Bv{e}lohl'{a}vek, {it Concept lattices and order in fuzzy logic}, Ann. Pure Appl. Logic, {bf 128} (2004), 277--298.
bibitem{bt03} K. Blount and C. Tsinakis, {it The structure of residuated lattices}, Int. J. Algebr. Comput., {bf 13}textbf{(4)} (2003), 437--461.
bibitem{ub04} U. Bodenhofer, {it Applications of fuzzy orderings: an overview}, In: K. T. Atanasov, O. Hryniewicz, J. Kacprycz, eds., Soft Computing. Foundations and Theoretical Aspects, EXIT, Warsaw, (2004), 81--95.
bibitem{ub07} U. Bodenhofer, B. De Baets and J. Fodor, {it A compendium of fuzzy weak orders}, Fuzzy Sets and Systems, {bf 158} (2007), 811--829.
bibitem{csn98} I. Chajda and V. Sn'{a}v{s}el, {it Congruences in ordered sets}, Math. Bohem., {bf 123}textbf{(1)} (1998), 95--100.
bibitem{cib07} M. '{C}iri'{c}, J. Ignjatovi'{c} and S. Bogdanovi'{c}, {it Fuzzy equivalence relations and their equivalence classes}, Fuzzy Sets and Systems, {bf 158} (2007), 1295--1313.
bibitem{dp02} B. A. Davey and H. A. Priestley, {it Introduction to lattices and order}, Cambridge University Press, Cambridge, 2002.
bibitem{debm98} B. De Baets and R. Mesiar, {it T-partitions}, Fuzzy Sets and Systems, {bf 97} (1998), 211--223.
bibitem{debm02} B. De Baets and R. Mesiar, {it Metrics and T-equalities}, J. Math. Anal. Appl., {bf 267} (2002) 531--547.
bibitem{mde03I} M. Demirci, {it Indistinguishability operators in measurement theory, Part I: Conversions of indistinguishability operators with respect to scales}, Internat. J. General Systems, {bf 32} (2003), 415--430.
bibitem{mde03II} M. Demirci, {it Indistinguishability operators in measurement theory, Part II: Construction of indistinguishability operators based on probability distributions}, Internat. J. General Systems, {bf 32} (2003), 431--458.
bibitem{mde04} M. Demirci and J. Recasens, {it Fuzzy groups, fuzzy functions and fuzzy equivalence relations}, Fuzzy Sets and Systems, {bf 144} (2004), 441--458.
bibitem{lf01} L. Fan, {it A new approach to quantitative domain theory}, Electronic Notes in Theoretical Computer Science, {bf 45} (2001), 77--87.
bibitem{fsw96} R. C. Flagg, Ph. S"{u}nderhauf and K. R. Wagner, {it A logical approach to quantitative domain theory}, Topology Atlas Preprint, {bf 23} (1996), 10--29.
bibitem{gsw99} B. Ganter, G. Stumme and R. Wille, {it Formal concept analysis: Mathematical Foundations}, Springer, Berlin, 1999.
bibitem{jag67} J. A. Goguen, {it $L$-fuzzy sets}, J. Math. Anal. Appl., {bf 18} (1967), 145--174.
bibitem{fuzzy10} R. Gonz'{a}lez-del-Campo, L. Garmendia and B. De Baets, {it Transitive closure of $L$-fuzzy relations and interval-valued fuzzy relations}, Fuzzy Systems (FUZZ), 2010 IEEE International Conference on, July (2010), 1--8.
bibitem{rh00} R. Halav{s}, {it Congruences on posets}, Contributions to General Algebra, {bf 12} (2000), 195--210.
bibitem{hd03} R. Halav{s} and D. Hort, {it A characterization of 1-,2-,3-,4-homomorphisms of ordered sets}, Czechoslovak Math. J., {bf 53}textbf{(128)} (2003), 213--221.
bibitem{hol85} U. H"{o}hle and N. Blanchard, {it Partial ordering in $L$-under determinate sets}, Information Science, {bf 35} (1985), 133--144.
bibitem{pk05} P. K"{o}rtesi, {it Congruences and isotone maps on partially ordered sets}, Mathematica Pannonica, {bf 16}textbf{(1)} (2005), 39--55.
bibitem{lzh07} H. Lai and D. Zhang, {it Complete and directed complete $Omega$-categories}, Theor. Comput. Sci., {bf 388} (2007), 1--25.
bibitem{mar11} P. Martinek, {it Completely lattice $L$-ordered sets with and without $L$-equality}, Fuzzy Sets and Systems, {bf 166} (2011), 44--55.
bibitem{szk08} K. P. Shum, P. Zhu and N. Kehayopulu, {it III-Homomorphisms and III-congruences on posets}, Discrete Math., {bf 308} (2008), 5006--5013.
bibitem{et99} E. Turunen, {it Mathematics behind fuzzy logic}, Physica--Verlag, 1999.
bibitem{ven92} P. Venugopalan, {it Fuzzy ordered sets}, Fuzzy Sets and Systems, {bf46} (1992), 221--226.
bibitem{wag94} K. R. Wagner, {it Solving recursive domain equations with enriched categories}, Ph.D. Thesis, School of Computer Science, Carnegie Mellon University, Technical Report CMU-CS-94-159, July 1994.
bibitem{wag97} K. R. Wagner, {it Liminf convergence in $Omega$-categories}, Theor. Comput. Sci., {bf 184} (1997), 61--104.
bibitem{wd39} M. Ward and R. P. Dilworth, {it Residuated lattices}, T. Am. Math. Soc., {bf 45} (1939), 335--354.
bibitem{xzhf09} W. Xie, Q. Zhang and L. Fan, {it The Dedekind-MacNeille completions for fuzzy posets}, Fuzzy Sets and Systems, {bf 160} (2009), 2292--2316.
bibitem{xs05} X. Xie and X. Shi, {it Order-congruences on S-posets}, Commun. Korean Math. Soc., {bf 20}textbf{(1)} (2005), 1--14.
bibitem{yao10} W. Yao, {it Quantitative domains via fuzzy sets: part I: continuity of fuzzy directed complete posets}, Fuzzy Sets and Systems, {bf 161} (2010), 973--987.
bibitem{zad71} L. A. Zadeh, {it Similarity relations and fuzzy orderings}, Information Science, {bf 3} (1971), 177--200.
bibitem{zf05} Q. Zhang and L. Fan, {it Continuity in quantitative domains}, Fuzzy Sets and Systems, {bf 154} (2005), 118--131.
bibitem{zxf09} Q. Zhang, W. Xie and L. Fan, {it Fuzzy complete lattices}, Fuzzy Sets and Systems, {bf 160} (2009), 2275--2291.