Novel Characterizations of $LM$-Fuzzy Open Operators
محورهای موضوعی : Transactions on Fuzzy Sets and Systems
1 - School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China.
کلید واژه: $LM$-fuzzy topology, $LM$-fuzzy closure operator, $LM$-fuzzy semiopen operator, $LM$-fuzzy preopen operator, $LM$-fuzzy regular open operator,
چکیده مقاله :
In this paper, we present some characterizations of the $LM$-fuzzy interior operator, the $LM$-fuzzy closure operator, $LM$-fuzzy semiopen operator and $LM$-fuzzy preopen operator in an $LM$-fuzzy topological space. Based on them, we introcuced the notions of $LM$-fuzzy regularly open operators and $LM$-fuzzy regularly closed operators and show that these kinds of openness degrees are di erent from those de ned by level $L$-topology.
In this paper, we present some characterizations of the $LM$-fuzzy interior operator, the $LM$-fuzzy closure operator, $LM$-fuzzy semiopen operator and $LM$-fuzzy preopen operator in an $LM$-fuzzy topological space. Based on them, we introcuced the notions of $LM$-fuzzy regularly open operators and $LM$-fuzzy regularly closed operators and show that these kinds of openness degrees are di erent from those de ned by level $L$-topology.
[1] K. K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl., 82 (1981), 14-32.
[2] P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indag. Math., 85 (1982), 403-414.
[3] A. Ghareeb, A new form of F-compactness in L-fuzzy topological spaces, Math. Comput. Modelling, 54 (2011), 2544-2550.
[4] A. Ghareeb, Preconnectedness degree of L-fuzzy topological spaces, Int. J. Fuzzy Log. Intell. Syst., 11(1) (2011), 54-58.
[5] A. Ghareeb, L-fuzzy semi-preopen operator in L-fuzzy topological spaces, Neural Comput & Applic, 21 (2012), 87-92.
[6] A. Ghareeb and F.-G. Shi, SP-compactness and SP-connectedness degree in L-fuzzy pretopological spaces, J. Intell. Fuzzy Syst., 31 (2016), 1435-1445.
[7] A. Ghareeb, W.F. Al-Omeri, New degrees for functions in (L;M)-fuzzy topological spaces based on (L;M)-fuzzy semiopen and (L;M)-fuzzy preopen operators, J. Intell. Fuzzy Syst., 36 (2019), 787-803.
[8] M. H. Ghanim and O. A. Tantawy and F. M. Selin, Gradation of supra-openness, Fuzzy Sets Syst., 109 (2000), 245-250.
[9] U. Hohle and S. E. Rodabaugh (Eds), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Kluwer Academic Publishers, Boston/ Dordrecht/ London, (1999).
[10] H. L. Huang and F.-G. Shi, L-fuzzy numbers and their properties, Inform Sci, 178 (2008), 1141-1151.
[11] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, (1985).
[12] S. J. Lee and E. P. Lee, Fuzzy r-continuous and fuzzy r-semicontinuous maps, Int. J. Math. Math. Sci., 27 (2001), 53-63.
[13] S. J. Lee and E. P. Lee, Fuzzy r-preopen sets and fuzzy r-precontinuous maps, Bull. Korean Math. Soc., 36 (1999), 91-108.
[14] S. J. Lee and E. P. Lee, Fuzzy r-regular open sets and fuzzy almost r-continuous maps, Bull. Korean Math. Soc., 39 (2002), 441-453.
[15] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41.
[16] C. Y. Liang and F.-G. Shi, A new kind of measure of compactness in (L;M)-fuzzy supratopological spaces, J. Intell. Fuzzy Syst., 33(2017), 2109-2117.
[17] N. Nanda, Strongly compact fuzzy topological spaces, Fuzzy Sets and Syst., 42 (1991), 259-262.
[18] F.-G. Shi, Theory of L -nested sets and L -nested sets and its applications, Fuzzy Systems Math., 4 (1995), 65-72 (in Chinese).
19] F.-G. Shi, L-fuzzy relations and L-fuzzy subgroups, J Fuzzy Math., 8 (2000), 491-499.
[20] F.-G. Shi, L-fuzzy interiors and L-fuzzy closures, Fuzzy Sets Syst., 160 (2009), 1218-1232.
[21] F.-G. Shi and C. Y. Liang, Measures of compactness in L-fuzzy pretopological spaces, J. Intell. Fuzzy Syst., 26 (2014), 1557-1561.
[22] F.-G. Shi and B. Pang, Categories isomorphic to the category of L-fuzzy closure system spaces, Iran. J. Fuzzy Syst., 10 (2013), 129-148.
[23] M. K. Singal and N. Prakash, Fuzzy preopen sets and fuzzy preseparation axioms, Fuzzy Sets Syst., 44 (1991), 273-281.
[24] A. P. Sostak, On a fuzzy topological structure, Rendiconti Circolo Matematico Palermo Suppl. Ser. II, 11 (1985), 89-103.
[25] A. M. Zahran, Almost continuity and δ-continuity in fuzzifying topology, Fuzzy Sets Syst., 116 (2000), 339-352.
[26] F. M. Zeyada and A. K. Mousa, Regular open sets in fuzzifying topology rede ned, J. Egyptian Math. Soc., 22 (2014), 484-488.
[27] J. Zhang, F.-G. Shi and C.-Y. Zheng, On L-fuzzy topological spaces, Fuzzy Sets Syst., 149 (2005), 473-484.
