SOME CHARACTERIZATIONS OF SLIGHTLY Σα – COMPACT FUZZY SETS

Authors:

Md. Abdul Mottalib Talukder,B. M. Khalid Hossain,

DOI NO:

https://doi.org/10.26782/jmcms.2025.03.00014

Keywords:

fuzzy sets,fuzzy topological spaces,sΣα-shelter,sΣα-compact,

Abstract

Within this paper, we create the ideas of slightly Σα-shelter, shortly sΣα - shelter, and slightly Σα-compact, shortly Σα-compact fuzzy sets. In addition, we have established certain theorems concerning our vision in fuzzy topological spaces, fuzzy subspaces, fuzzy continuity mapping, fuzzy open mapping, fuzzy T2-spaces (Hausdorff spaces), and their different characterizations. Finally, we have discussed our vision about the “good extension” characteristics

Refference:

I. Abbas, S. E. “On intuitionistic fuzzy compactness.” Information Sciences 173.1-3 (2005): 75-91. https://doi.org/10.1016/j.ins.2004.07.004
II. Aygün, Halis. “α-compactness in L-fuzzy topological spaces.” Fuzzy Sets and Systems 116.3 (2000): 317-324. 10.1016/S0165-0114(98)00345-5
III. Benchalli, S. S., and G. P. Siddapur. “On the level spaces of fuzzy topological spaces.” Bulletin of Mathematical Analysis and Applications 1.2 (2009): 57-65. https://eudml.org/doc/229234
IV. Chadwick, J. J. “A generalised form of compactness in fuzzy topological spaces.” Journal of Mathematical Analysis and Applications 162.1 (1991): 92-110. 10.1016/0022-247X(91)90180-8
V. Chang, Chin-Liang. “Fuzzy topological spaces.” Journal of mathematical Analysis and Applications 24.1 (1968): 182-190. 10.1016/0022-247X(68)90057-7
VI. Chen, Yixiang. “On compactness of induced I (L)-fuzzy topological spaces.” Fuzzy Sets and Systems 88.3 (1997): 373-378. 10.1016/S0165-0114(96)00074-7
VII. Dongsheng, Zhao. “The N-compactness in L-fuzzy topological spaces.” Journal of Mathematical Analysis and Applications 128.1 (1987): 64-79. 10.1016/0022-247x(87)90214-9
VIII. EL-Shafei, M. E., I. M. Hanafy, and A. I. Aggour. “RS-Compactness in L-fuzzy topological spaces.” Kyungpook Mathematical Journal 42.2 (2002): 417-428.
IX. Gantner, T. E., R. C. Steinlage, and R. H. Warren. “Compactness in fuzzy topological spaces.” Journal of Mathematical Analysis and Applications 62.3 (1978): 547-562. 10.1016/0022-247X(78)90148-8
X. Georgiou, D. N., and B. K. Papadopoulos. “On fuzzy compactness.” Journal of Mathematical Analysis and Applications 233.1 (1999): 86-101. 10.1006/jmaa.1999.6268
XI. Guojun, Wang. “A new fuzzy compactness defined by fuzzy nets.” Journal of Mathematical Analysis and Applications 94.1 (1983): 1-23. 10.1016/0022-247X(83)90002-1
XII. Hong, Woo Chorl. “RS-compact spaces.” Journal of the Korean Mathematical Society 17.1 (1980): 39-43.
XIII. Katsaras, A. K. “Ordered fuzzy topological spaces.” Journal of Mathematical Analysis and Applications 84.1 (1981): 44-58. 10.1016/0022-247X(81)90150-5
XIV. Kim, J. K. “α-compact fuzzy topological spaces.” Korean Journal of Computational and Applied Mathematics 1 (1994): 79-84. https://doi.org/10.1007/BF02943052
XV. Kudri, S. R. T. “Compactness in L-fuzzy topological spaces.” Fuzzy Sets and Systems 67.3 (1994): 329-336. 10.1016/0165-0114(94)90260-7
XVI. Kudri, S. R. T., and M. W. Warner. “RS-compactness in L-fuzzy topological spaces.” Fuzzy Sets and Systems 86.3 (1997): 369-376. 10.1016/S0165-0114(95)00405-X
XVII. Li, Hong-Yan, and Fu-Gui Shi. “Degrees of fuzzy compactness in L-fuzzy topological spaces.” Fuzzy sets and systems 161.7 (2010): 988-1001. 10.1016/j.fss.2009.10.012
XVIII. Lipschutz, Seymour. “General Topology, Schaum’s Outline Series.” (1965).
XIX. Lowen, R. “Fuzzy topological spaces and fuzzy compactness.” Journal of Mathematical analysis and applications 56.3 (1976): 621-633. 10.1016/0022-247X(76)90029-9
XX. Lowen, Robert. “Initial and final fuzzy topologies and the fuzzy Tychonoff theorem.” Journal of Mathematical Analysis and Applications 58.1 (1977): 11-21. 10.1016/0022-247X(77)90223-2
XXI. Lowen, Robert. “A comparison of different compactness notions in fuzzy topological spaces.” Journal of Mathematical Analysis and Applications 64.2 (1978): 446-454. 10.1016/0022-247X(78)90052-5
XXII. Lowen, R. “Compactness properties in the fuzzy real line.” Fuzzy Sets and Systems 13.2 (1984): 193-200. 10.1016/0165-0114(84)90019-8
XXIII. Mahbub, Aman, Sahadat Hossain, and M. Altab Hossain. “Some properties of compactness in intuitionistic fuzzy topological spaces.” International Journal of Fuzzy Mathematical Archive 16.2 (2018): 39-48. DOI: 10.22457/ijfma.v16n1a6
XXIV. Mashhour, A. S., M. H. Ghanim, and MA Fath Alla. ” -separation axioms and -compactness in fuzzy topological spaces.” Rocky Mountain Journal of Mathematics 16.3(1986): 591-600. https://www.jstor.org/stable/44237017
XXV. Meenakshi, Arunachalam R., and Muniasamy Kaliraja. “g-inverses of interval valued fuzzy matrices.” Journal of Mathematical & Fundamental Sciences 45.1 (2013): 83-92. 10.5614/j.math.fund.sci.2013.45.1.7
XXVI. Murdeshwar, Mangesh G. “General topology, Wiley” (1983).
XXVII. Noiri, Takashi. “On RS-compact spaces.” Journal of the Korean Mathematical Society 22.1 (1985): 19-34.
XXVIII. Pao-Ming, Pu, and Liu Ying-Ming. “Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence.” Journal of Mathematical Analysis and Applications 76.2 (1980): 571-599. 10.1016/0022-247X(80)90048-7
XXIX. Saha, Apu Kumar, and Debasish Bhattacharya. “Countable fuzzy topological space and countable fuzzy topological vector space.” Journal of Mathematical & Fundamental Sciences 47.2 (2015): 154-166. 10.5614/j.math.fund.sci.2015.47.2.4
XXX. Shi, Fu-Gui. “A new form of fuzzy -compactness.” Mathematica Bohemica 131.1 (2006): 15-28.
XXXI. Shi, Fu-Gui. “A new definition of fuzzy compactness.” Fuzzy sets and systems 158.13 (2007): 1486-1495. 10.1016/j.fss.2007.02.006
XXXII. Talukder, M. A. M., and D. M. Ali. “Certain features of partially -compact fuzzy sets.” Journal of Mechanics of Continua and Mathematical Sciences 9.1 (2014):1322-1340. 10.26782/jmcms.2014.07.00005
XXXIII. Warner, M. W., and R. G. McLean. “On compact Hausdofff L-fuzzy spaces.” Fuzzy Sets and Systems 56.1 (1993): 103-110. 10.1016/0165-0114(93)90190-S
XXXIV. Warner, M. W. “On fuzzy compactness.” Fuzzy Sets and Systems 80.1 (1996): 15-22. 10.1016/0165-0114(95)00132-8
XXXV. Wong, C. K. “Fuzzy topology: product and quotient theorems.” Journal of Mathematical Analysis and Applications 45.2 (1974): 512-521. 10.1016/0022-247X(74)90090-0
XXXVI. Ying, Mingsheng. “A new approach for fuzzy topology (I).” Fuzzy Sets and Systems 39.3 (1991): 303-321. 10.1016/0165-0114(91)90100-5
XXXVII. Ying, Mingsheng. “Compactness in fuzzifying topology.” Fuzzy Sets and Systems 55.1 (1993): 79-92. 10.1016/0165-0114(93)90303-Y.
XXXVIII. Zadeh, L. A. “Fuzzy Sets.” Information and Control 8.3 (1965):338-353. 10.1016/S0019-9958(65)90241-X

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