In this paper, we introduce the notion of factorizations of fuzzy sets in complete residuated lattices. Moreover, we investigate fuzzy partially orders, the upper and lower approximation operators and Alexander (fuzzy) topologies on factorizations of fuzzy sets and give their examples.
BělohláR., Fuzzy Relational Systems, Kluwer Academic Publishers, New York. 2002.
2.
ĆirićM., IgnjatovićJ., DamljanovićN. and BašićM., Bisimiulations for fuzzy automata, Fuzzy Sets and Systems186 (2012), 100–139.
3.
HájekP., Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht. 1998.
4.
HöhleU. and KlementE.P., Non-classical Logic and Their Applications to Fuzzy Subsets, Kluwer Academic Publishers, Boston. 1995.
5.
HöhleU. and RodabaughS.E., Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series 3Kluwer Academic Publishers, Boston. 1999.
6.
IgnjatovićJ., ĆirićM. and BogdanovićS., Determinization of fuzzy automata with membership values in complete residuated lattices, Information Sciences178 (2008), 164–180.
7.
KimY.C., Alexandrov L-topologies, International Journal of Pure and Applied Mathematics93(2) (2014), 165–179.
8.
KimY.C., Join preserving maps, fuzzy preorders and Alexandrov fuzzy topologies, International Journal of Pure and Applied Mathematics92(5) (2014), 703–718.
9.
KimY.C. and KimY.S., L-approximation spaces and L-fuzzy quasi-uniform spaces, Information Sciences179 (2009), 2028–2048.
10.
LaiH. and ZhangD., Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems157 (2006), 1865–1885.
11.
LaiH. and ZhangD., Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory, Int J Approx Reasoning50 (2009), 695–707.
12.
LeiH.X. and LiY.M., Minimization of states in automata theory based on finite lattice-ordered monoid, Information Sciences177 (2007), 1413–1421.
13.
LiY.M., Finite automata theory with membership values in lattices, Information Sciences181 (2011), 1003–1017.
14.
LiY.M. and WangQ., The universal fuzzy automata, Fuzzy Sets and Systems249 (2014), 27–48.
15.
MordesonJ.N. and MalikD.S., Fuzzy Automata and Languages; Theory and Applications, Chapman&Hall/CRC, Boca Raton, London .
16.
PawlakZ., Rough sets, Int J Comput Inf Sci11 (1982), 341–356.
17.
PawlakZ., Rough probability, Bull Pol Acad Sci Math32 (1984), 607–615.
18.
QiuD.W., Automata theory bases on complete residuated lattice-valued logic, Science in China (Series F)44 (2001), 419–429.
19.
RadzikowskaA.M. and KerreE.E., A comparative study of fuzzy rough sets, Fuzzy Sets and Systems126 (2002), 137–155.
20.
SheY.H. and WangG.J., An axiomatic approach of fuzzy rough sets based on residuated lattices, Computers and Mathematics with Applications58 (2009), 189–201.
21.
SrivastavaA.K. and TiwariS.P., On relationships among fuzzy approximation operators, fuzzy topology, and fuzzy automata, Fuzzy Sets and Systems138 (2003), 197–204.
22.
StamenkovićA., ĆirićM. and IgnjatovićJ., Reduction of fuzzy automata by means of fuzzy quasi-orders, Information Sciences178 (2014), 168–198.
23.
TiwariS.P. and SrivastavaA.K., Fuzzy rough sets, fuzzy preorders and fuzzy topologies, Fuzzy Sets and Systems210 (2013), 63–68.
24.
WeeW.G. On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification, Ph.D. Thesis, Purdue University, 1967.
