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GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS

Year 2013, Volume: 62 Issue: 2, 67 - 74, 01.08.2013

Sevda Sağıroğlu Erdal Güner Eda Koçyiğit

https://doi.org/10.1501/Commua1_0000000699

Abstract

We define the generalized fuzzy neighbourhood systems onthe set of fuzzy points in a nonempty setXand investigate their properties by using a new interior operator. With the help of these conceptswe introduce generalized fuzzy continuity, which include many of thevariations of fuzzy continuity already in the literature, as special cases

Keywords

Generalized fuzzy topology generalized fuzzy neighbourhoodsystem fuzzy( 0)-continuity

References

  • M.E Abd El-Monsef, A.E. Ramadan, On fuzzy supra topological spaces, Indian J. Pure and Appl. Math. 18(4)(1987), 322–329.
  • N. Ajmal, S. K. Azad, Fuzzy almost continuity and its pointwise characterization by dual points and fuzzy sets, Fuzzy Sets and Systems, 34(1990), 81-101.
  • M. Alimohammady, M. Roohi, Fuzzy minimal structure and fuzzy minimal vector spaces, Chaos, Solutions and Fractals, 27(2006), 599-605.
  • K.K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82(1981) 14-32.
  • T. Back, Evolutionary Algorithm in Theory and Practice, Oxford University Press. 1996.
  • S.Z. Bai, W.W. Liang, Fuzzy non-continuous mapping and fuzzy pre-semi-seperation axioms, Fuzzy Sets and Systems, 94(1998), 261-268.
  • G. Balasubramanian, On fuzzy compact spaces and fuzzy-extremally disconnected spaces, Kybernetika, 33(3)(1997), 271-277.
  • G. Balasubramanian, On fuzzy preseperation axioms, Bull. Cal. Math. Soc., 90 (1998), 434.
  • C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24(1968) 182-190.
  • W.W. Chu, Neighbourhood and associative query answering, Journal of Intelligent Informa- tion Systems, 1(1992), 355-382.
  • Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (4)(2002), 357.
  • S. Dang, A. Behera, S. Nanda, On fuzzy weakly semi-continuous functions, Fuzzy Sets and Systems, 67(1994), 239-245.
  • C. De Mitri, E. Pascali, Characterization of fuzzy topologies from neighbourhoods of fuzzy points, J. Math. Anal. Appl. 93(1983), 1-14.
  • K. Essenger K. Some connections between topological and Modal Logic. Mathematical Logic Quarterly, 41(1995), 49-64.
  • R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56(1976), 633.
  • H. Maki, On generalizing semi-open and preopen sets, Report for Meeting on Topological Spaces Theory and its Applications, Yatsushiro College of Technology, (1996), 13-18.
  • S. Malakar, On fuzzy semi irresolute and strong irresolute functions, Fuzzy Sets and Systems, (1992), 239-244.
  • A.S. Mashhour, A.A. Allam, F.S. Mahmoud, F.H. Khedr, On supratopological spaces, Indian J. Pure and Appl. Math. 14(4)(1983), 502–510.
  • P.P. Ming, L.Y. Ming, Fuzzy topology. I. Neighbourhood structure of a fuzzy point and Moore Smith convergence, J. Math. Anal. Appl. 76(1980) 571-579.
  • A. Motro, Supporting goal queries in relational databases, Expert Database Systems, Pro- ceedings of the …rst International Conference, L. Kerchberg, Institute of Information Man- agement, Technology and Policy, University of S. Carolina., 1986.
  • M.N. Mukherjee, S.P. Sinha, Irresolute and almost open functions between fuzzy topological spaces, Fuzzy Sets and Systems, 29(1989), 381-388.
  • M.N. Mukherje, S.P. Sinha, On some weaker forms of fuzzy continuous and fuzzy open map- pings on fuzzy topological spaces, Fuzzy Sets ans Systems, 32 (1989), 103-114.
  • M.N. Mukherjee, S.P. Sinha, On some near-fuzzy continuous functions between fuzzy topo- logical spaces, Fuzzy Sets and Systems, 34(1990), 245-254.
  • A. Mukherjee, Fuzzy almost semi-continuous and almost semi-generalized continuous map- pings, Acta Cienc. Indica Math. 32(4)(2006), 1363–1368.
  • H.A. Othman, S. Latha, Some weaker forms of fuzzy almost continuous mappings, Bull. of Kerela Math. Assoc. 5(2)(2009), 109-113.
  • G. Palani Chetty, Generalized fuzzy topology, Ital. J. Pure and Appl. Mat. 24 (2008), 91-96.
  • Z. Pawlak, Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Pub- lishers, 1991.
  • R. Prasol, S.S. Thakur, R.K. Saraf, Fuzzy irresolute mappings, J. Fuzzy Math. 2(1994), 339.
  • R.K. Saraf, S. Mishra, G. Navalagi, On fuzzy strongly continuous functions, Bull. Greek Math. Soc. 47(2003), 153–159.
  • K.K. Saraf, M. Caldas, N. Navalagi, On strongly fuzzy preirresolute functions, Advances in Fuzzy Mathematics, 3(1)(2008), 19-25.
  • V. Seenivasan, G. Neyveli, G. Balasubramanian, Fuzzy semi irresolute functions, Mat. Bohemica, 132(2)(2007), 113-123.
  • A.B. Shahna, On fuzzy strong semi continuity and fuzzy precontinuity, Fuzzy Sets and Sys- tems, 44(2)(1991), 303-308.
  • S. Supriti, Fuzzy -continuous mappings, J. Math. Anal. Appl. 126(1987), 130-142.
  • S.S. Thakur, S. Singh, On fuzzy semi-preopen sets and fuzzy semi-precontinuity, Fuzzy Sets and Systems, 98(1998) 383-391.
  • L.A. Zadeh, Fuzzy sets, Information and Control, 8(1965), 338-353.
  • Current address : Ankara University, Faculty of Sciences, Dept. of Mathematics, Tando¼gan- Ankara, TURKEY E-mail address :ssagir@science.ankara.edu.tr, eyazar@science.ankara.edu.tr URL: http://communications.science.ankara.edu.tr/index.php?series=A1 guner@science.ankara.edu.tr

Year 2013, Volume: 62 Issue: 2, 67 - 74, 01.08.2013

Sevda Sağıroğlu Erdal Güner Eda Koçyiğit

https://doi.org/10.1501/Commua1_0000000699

Abstract

References

  • M.E Abd El-Monsef, A.E. Ramadan, On fuzzy supra topological spaces, Indian J. Pure and Appl. Math. 18(4)(1987), 322–329.
  • N. Ajmal, S. K. Azad, Fuzzy almost continuity and its pointwise characterization by dual points and fuzzy sets, Fuzzy Sets and Systems, 34(1990), 81-101.
  • M. Alimohammady, M. Roohi, Fuzzy minimal structure and fuzzy minimal vector spaces, Chaos, Solutions and Fractals, 27(2006), 599-605.
  • K.K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82(1981) 14-32.
  • T. Back, Evolutionary Algorithm in Theory and Practice, Oxford University Press. 1996.
  • S.Z. Bai, W.W. Liang, Fuzzy non-continuous mapping and fuzzy pre-semi-seperation axioms, Fuzzy Sets and Systems, 94(1998), 261-268.
  • G. Balasubramanian, On fuzzy compact spaces and fuzzy-extremally disconnected spaces, Kybernetika, 33(3)(1997), 271-277.
  • G. Balasubramanian, On fuzzy preseperation axioms, Bull. Cal. Math. Soc., 90 (1998), 434.
  • C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24(1968) 182-190.
  • W.W. Chu, Neighbourhood and associative query answering, Journal of Intelligent Informa- tion Systems, 1(1992), 355-382.
  • Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (4)(2002), 357.
  • S. Dang, A. Behera, S. Nanda, On fuzzy weakly semi-continuous functions, Fuzzy Sets and Systems, 67(1994), 239-245.
  • C. De Mitri, E. Pascali, Characterization of fuzzy topologies from neighbourhoods of fuzzy points, J. Math. Anal. Appl. 93(1983), 1-14.
  • K. Essenger K. Some connections between topological and Modal Logic. Mathematical Logic Quarterly, 41(1995), 49-64.
  • R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56(1976), 633.
  • H. Maki, On generalizing semi-open and preopen sets, Report for Meeting on Topological Spaces Theory and its Applications, Yatsushiro College of Technology, (1996), 13-18.
  • S. Malakar, On fuzzy semi irresolute and strong irresolute functions, Fuzzy Sets and Systems, (1992), 239-244.
  • A.S. Mashhour, A.A. Allam, F.S. Mahmoud, F.H. Khedr, On supratopological spaces, Indian J. Pure and Appl. Math. 14(4)(1983), 502–510.
  • P.P. Ming, L.Y. Ming, Fuzzy topology. I. Neighbourhood structure of a fuzzy point and Moore Smith convergence, J. Math. Anal. Appl. 76(1980) 571-579.
  • A. Motro, Supporting goal queries in relational databases, Expert Database Systems, Pro- ceedings of the …rst International Conference, L. Kerchberg, Institute of Information Man- agement, Technology and Policy, University of S. Carolina., 1986.
  • M.N. Mukherjee, S.P. Sinha, Irresolute and almost open functions between fuzzy topological spaces, Fuzzy Sets and Systems, 29(1989), 381-388.
  • M.N. Mukherje, S.P. Sinha, On some weaker forms of fuzzy continuous and fuzzy open map- pings on fuzzy topological spaces, Fuzzy Sets ans Systems, 32 (1989), 103-114.
  • M.N. Mukherjee, S.P. Sinha, On some near-fuzzy continuous functions between fuzzy topo- logical spaces, Fuzzy Sets and Systems, 34(1990), 245-254.
  • A. Mukherjee, Fuzzy almost semi-continuous and almost semi-generalized continuous map- pings, Acta Cienc. Indica Math. 32(4)(2006), 1363–1368.
  • H.A. Othman, S. Latha, Some weaker forms of fuzzy almost continuous mappings, Bull. of Kerela Math. Assoc. 5(2)(2009), 109-113.
  • G. Palani Chetty, Generalized fuzzy topology, Ital. J. Pure and Appl. Mat. 24 (2008), 91-96.
  • Z. Pawlak, Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Pub- lishers, 1991.
  • R. Prasol, S.S. Thakur, R.K. Saraf, Fuzzy irresolute mappings, J. Fuzzy Math. 2(1994), 339.
  • R.K. Saraf, S. Mishra, G. Navalagi, On fuzzy strongly continuous functions, Bull. Greek Math. Soc. 47(2003), 153–159.
  • K.K. Saraf, M. Caldas, N. Navalagi, On strongly fuzzy preirresolute functions, Advances in Fuzzy Mathematics, 3(1)(2008), 19-25.
  • V. Seenivasan, G. Neyveli, G. Balasubramanian, Fuzzy semi irresolute functions, Mat. Bohemica, 132(2)(2007), 113-123.
  • A.B. Shahna, On fuzzy strong semi continuity and fuzzy precontinuity, Fuzzy Sets and Sys- tems, 44(2)(1991), 303-308.
  • S. Supriti, Fuzzy -continuous mappings, J. Math. Anal. Appl. 126(1987), 130-142.
  • S.S. Thakur, S. Singh, On fuzzy semi-preopen sets and fuzzy semi-precontinuity, Fuzzy Sets and Systems, 98(1998) 383-391.
  • L.A. Zadeh, Fuzzy sets, Information and Control, 8(1965), 338-353.
  • Current address : Ankara University, Faculty of Sciences, Dept. of Mathematics, Tando¼gan- Ankara, TURKEY E-mail address :ssagir@science.ankara.edu.tr, eyazar@science.ankara.edu.tr URL: http://communications.science.ankara.edu.tr/index.php?series=A1 guner@science.ankara.edu.tr
There are 36 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Sevda Sağıroğlu This is me

Erdal Güner This is me

Eda Koçyiğit This is me

Publication Date August 1, 2013
Published in Issue Year 2013 Volume: 62 Issue: 2

Cite

APA Sağıroğlu, S., Güner, E., & Koçyiğit, E. (2013). GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 62(2), 67-74. https://doi.org/10.1501/Commua1_0000000699
AMA Sağıroğlu S, Güner E, Koçyiğit E. GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2013;62(2):67-74. doi:10.1501/Commua1_0000000699
Chicago Sağıroğlu, Sevda, Erdal Güner, and Eda Koçyiğit. “GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62, no. 2 (August 2013): 67-74. https://doi.org/10.1501/Commua1_0000000699.
EndNote Sağıroğlu S, Güner E, Koçyiğit E (August 1, 2013) GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62 2 67–74.
IEEE S. Sağıroğlu, E. Güner, and E. Koçyiğit, “GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 62, no. 2, pp. 67–74, 2013, doi: 10.1501/Commua1_0000000699.
ISNAD Sağıroğlu, Sevda et al. “GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62/2 (August 2013), 67-74. https://doi.org/10.1501/Commua1_0000000699.
JAMA Sağıroğlu S, Güner E, Koçyiğit E. GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62:67–74.
MLA Sağıroğlu, Sevda et al. “GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 62, no. 2, 2013, pp. 67-74, doi:10.1501/Commua1_0000000699.
Vancouver Sağıroğlu S, Güner E, Koçyiğit E. GENERALIZED NEIGHBOURHOOD SYSTEMS OF FUZZY POINTS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62(2):67-74.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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