\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. B\v{e}lohl\'avek, {\it Fuzzy relational systems: foundations
and principles}, Kluwer Academic Publishers, Norwell, MA, USA, 2002.
\bibitem{rb04} R. B\v{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. Hala\v{s}, {\it Congruences on posets}, Contributions to
General Algebra, {\bf 12} (2000), 195--210.
\bibitem{hd03} R. Hala\v{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.
)