FUZZY GAMMA SEMI-PREOPEN AND FUZZY GAMMA SEMI PRECLOSED SETS IN FUZZY BITOPOLOGICAL SPACES
DOI:
https://doi.org/10.48165/Keywords:
Fuzzy bitopological spaces, (δi, δj) F-γ-open, (δi, δj) F-γ-semi-preopen, (δi, δj) F-γ- semi-preclosed, (δi, δj) F-γ-semi-pre neighbourhood, (δi, δj) F-γ-semi-pre q- neighbourhood, (δi,δj) F-γ-semi-preinterior, (δi,δj) F-γ-semi-preclosureAbstract
This article proposes the concept of fuzzy gamma semi-preopen (respectively, fuzzy gamma semi-preclosed) sets in fuzzy bitopological spaces, which is weaker than the concept of fuzzy strongly semiopen (respectively, fuzzy strongly semiclosed) set, fuzzy semi-preopen (respectively, fuzzy semi-preclosed) set, fuzzy semiopen (respectively, fuzzy semiclosed) set, fuzzy preopen (respectively, fuzzy preclosed) set, fuzzy gamma open (respectively, fuzzy gamma closed) set, fuzzy gamma semiopen (respectively, fuzzy gamma semiclosed) set and fuzzy gamma preopen (respectively, fuzzy gamma preclosed) set in fuzzy bitopological spaces. This paper examines the aspects and attributes of fuzzy gamma semi-preopen (respectively, fuzzy gamma semi preclosed) sets with examples and investigates the relationship between these concepts and relevant concepts in fuzzy bitopological spaces. This article introduces the definition of fuzzy gamma semi-pre neighbourhood and fuzzy gamma semi-pre q- neighbourhood. Further, it characterizes fuzzy gamma semi-preinterior and fuzzy gamma semi-preclosure and establishes their fundamental properties.
References
Andrijevic, D. (1986). Semi preopen sets, Mat. Vesnik, 38, 24-32.
Azad, A.K. (1981). On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, Journal of Mathematical Analysis and Applications,82 , 14−32.
Zong, Bai Shi (1992). Fuzzy strongly semiopen sets and fuzzy strongly semicontinuity, Fuzzy Sets Syst., 52 , 345−351.
Chandrasekhara Rao, K. and Nagoor Gani, A. (2003). Pairwise preconnected spaces, Bulletin of Pure and Applied Sciences, Vol. 22E, No. 1, 159-163.
Chandrasekhara Rao, K. and Nagoor Gani, A. (2003). Second ℑ1ℑ2- semiopen sets, Bulletin of Pure and Applied Sciences, Vol. 22E, No. 1, 245-250.
Chandrasekhara Rao, K. and Nagoor Gani, A. (2004). On ℑ1ℑ2- semi pre open sets and ℑ1ℑ2-quasi open sets, National Academy of Science Letters, Vol.27, No.7&8 , 279-283.
Chang, C.L. (1968). Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24, 182−190.
Hanafy, I.M. (1999). Fuzzy γ-open sets and fuzzy γ-continuity,J. Fuzzy Math., 7 (2), 419-430. [9] Kandil, A. and El-Shafee, M.E. (1989). Biproximities and fuzzy bitopological spaces, Simon Stevin, 63 (1), 45–66.
Khedr, F.H., Al-Areefi, S.M. and Noiri, T. (1992). Precontinuity and semi-precontinuity in bitopological spaces, Indian Journal of Pure and Applied Mathematics,23, 625–633. [11] Maki, H., Umehara, J. and Noiri, T. (1996). Every topological space is pre T1/2, Mem Fac. Sci. Kochi Univ. Ser. A. Math., 17, 33-42.
Maki, H., Rao, K.C. and Nagoor Gani, A. (1999). On generalizing semi-open and preopen sets, Pure Appl. Math. Sci., Vol. XLIX, No.1-2, 17-29.
Mashour, A.S., Abd El-Monsef, M.E. and El-Deeb, S.N. (1982). On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53, 47-53.
Mashour, A.S., Ghanim, M.H. and Fath Alla, M.A. (1986). On fuzzy non-continuous mappings, Bull Calcutta Math. Soc., 78, 57−69.
Mahmoud, F.S., Fath Alla, M.A. and Khalaf, M.M. (2004). Fuzzy-γ-open sets and fuzzy-γ-continuity in fuzzy bitopological spaces, Applied Mathematics and Computation, 153, 117−126. [16] Nagoorgani, A., Rameeza Bhanu, J. (2017). (δi,δj) F-γ-semiopen and (δi,δj) F-γ-semiclosed sets in fuzzy bitopological spaces, Annals of Pure and Applied Mathematics, Vol. 15, No. 2, 173-184. [17] Nagoorgani, A. and Rameeza Bhanu, J. (2019). Fuzzy gamma preopen and Fuzzy gamma preclosed sets in fuzzy bitopological spaces,American International Journal of Science, Technology, Engineering and Mathematics, Special issue of 2nd ICCSPAM (2019), 125 −130.
Park, J.H. and Lee, B.Y. (1994). Fuzzy semi-preopen sets and fuzzy semi-precontinuous mappings,Fuzzy Sets Syst., 67, 359−364.
Park, J.H. (1998). On fuzzy pairwise semi-precontinuity, Fuzzy Sets Syst., 93, 375−379. [20] Pu, P.M. and Liu, Y.M. (1980). Fuzzy topology.I. Neighbourhood structure of a fuzzy point and Moore Smith convergence, Journal of Mathematical Analysis and Applications, 76, 571−599. [21] Sampath Kumar, S. (1997). On decomposition of pairwise continuity, Bull. Cal. Math. Soc., 89, 441- 446.
Sampath Kumar, S. (1994). On fuzzy pairwise α-continuity and fuzzy pre-continuity, Fuzzy Sets Syst., 62, 231−238.
Sampath Kumar, S. (1994). Semi-open sets, semi-continuity and semi-open mapping in fuzzy bitopological spaces, Fuzzy Sets Syst., 64, 421−426.
Singal, M.K. and Prakash, Niti (1991). Fuzzy preopen sets and fuzzy preseparation axioms, Fuzzy Sets Syst., 44, 273−281.
Thakur, S.S. and Singh, Surendra (1998). On fuzzy semi-preopen sets and fuzzy semi-precontinuity, Fuzzy Sets Syst., 98, 383-391.
Wong, C.K. (1974). Fuzzy point and local properties of fuzzy topology, Journal of Mathematical Analysis and Applications, 46, 328−361.
Zadeh, L.A. (1965). Fuzzy sets, Information and Control, 8, 338–353.
Published
Issue
Section
How to Cite
