Research Article
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(r,s)-Convergent Nets

Year 2012, Volume: 41 Issue: 2, 175 - 190, 01.02.2012

H. Aygün S.e. Abbas

Abstract

We introduce the notions of (r, s)-adherent point, (r, s)-accumulation point, (r, s)-cluster point, (r, s)-limit point and (r, s)-derived set in an intuitionistic fuzzy topological spaces and investigate some of their properties. Also, we define (r, s)-convergent nets and investigate some of their properties.

Keywords

Intuitionistic fuzzy set Intuitionistic fuzzy topology 2000 AMS Classification: 54 A 20

References

  • Abbas, S. E. and Ayg¨un, H. Intuitionistic fuzzy semiregularization spaces, Information Sci- ences 176, 745–757,2006.
  • Atanassov, K. Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1), 87–96, 1986.
  • Chang, C. L. Fuzzy topological spaces, J. Math. Anal. Appl. 24, 182–190, 1968.
  • Chattopadhyay, K. C., Hazra, R. N. and Samanta, S. K. Gradation of openness: fuzzy topol- ogy, Fuzzy Sets and Systems 49, 237–242, 1992.
  • Chen, S. L. and Cheng, J. S. On convergence of nets of L-fuzzy sets, J. Fuzzy Math. 2, 517– 524, 1994.
  • Chen, S. L. and Cheng, J. S. Semi-continuous and irresolute order-homeomorphisms on fuzzes, Fuzzy Sets and Systems 64, 105–112, 1994.
  • Chen, S. L. and Cheng, J. S. θ-convergence of nets of L-fuzzy sets and its applications, Fuzzy Sets and Systems 86, 235–240, 1997.
  • C¸ oker, D. An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88, 81–89, 1997.
  • C¸ oker, D. and Demirci, M. An introduction to intuitionistic fuzzy topological spaces in ˇSostak sense, Busefal 67, 67–76, 1996.
  • Demirci, M. Neighbourhood structures in smooth topological spaces, Fuzzy Sets and Systems 92, 123–128, 1997.
  • Georgiou, D. N. and Papadopoulos, B. K. Convergences in fuzzy topological spaces, Fuzzy Sets and Systems 101, 495–504, 1999.
  • H¨ohle, U. Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl. 78, 659– 673, 1980.
  • H¨ohle, U. and ˇSostak, A. P. A general theory of fuzzy topological spaces, Fuzzy Sets and Systems 73, 131–149, 1995.
  • H¨ohle, U. and ˇSostak, A. P. Axiomatic Foundations of Fixed-Basis Fuzzy Topology, The Handbooks of Fuzzy Sets Series, 3 (Chapter 3), (Kluwer Academic Publishers, Dordrecht, 1999).
  • Kubiak, T. On fuzzy topologies (Ph.D. Thesis, A. Mickiewicz, Poznan, 1985).
  • Kubiak, T. and ˇSostak, A. P. Lower set-valued fuzzy topologies, Quaestiones Math. 20 (3), 423–429, 1997.
  • Lee, E. P. and Im, Y. B. Mated fuzzy topological spaces, J. Korea Fuzzy Logic Intell. Sys. Soc. 11 (2), 161–165, 2001.
  • Liu, Y. M. and Luo, M. K. Fuzzy Topology (Scientific Publishing Co., Singapore, 1997).
  • Pao-Ming, P. and Ying-Ming, L. Fuzzy topology I: Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76, 571–599, 1980.
  • Samanta, S. K. and Mondal, T. K. On intuitionistic gradation of openness, Fuzzy Sets and Systems 131, 323–336, 2002.
  • ˇSostak, A. P. On a fuzzy topological structure, Suppl. Rend. Circ. Matem. Palerms ser II 11, 89–103, 1985.
  • ˇSostak, A. P. Two decades of fuzzy topology: basic ideas, notions and results, Russian Math. Surveys 44 (6), 125–186, 1989.
  • ˇSostak, A. P. Basic structures of fuzzy topology, J. Math. Sci. 78 (6), 662–701, 1996.
  • Wang, G.- J. Pointwise topology on completely distributive lattice, Fuzzy Sets and Systems 30, 53–62, 1989.

(r,s)-Convergent Nets

Year 2012, Volume: 41 Issue: 2, 175 - 190, 01.02.2012

H. Aygün S.e. Abbas

Abstract

References

  • Abbas, S. E. and Ayg¨un, H. Intuitionistic fuzzy semiregularization spaces, Information Sci- ences 176, 745–757,2006.
  • Atanassov, K. Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1), 87–96, 1986.
  • Chang, C. L. Fuzzy topological spaces, J. Math. Anal. Appl. 24, 182–190, 1968.
  • Chattopadhyay, K. C., Hazra, R. N. and Samanta, S. K. Gradation of openness: fuzzy topol- ogy, Fuzzy Sets and Systems 49, 237–242, 1992.
  • Chen, S. L. and Cheng, J. S. On convergence of nets of L-fuzzy sets, J. Fuzzy Math. 2, 517– 524, 1994.
  • Chen, S. L. and Cheng, J. S. Semi-continuous and irresolute order-homeomorphisms on fuzzes, Fuzzy Sets and Systems 64, 105–112, 1994.
  • Chen, S. L. and Cheng, J. S. θ-convergence of nets of L-fuzzy sets and its applications, Fuzzy Sets and Systems 86, 235–240, 1997.
  • C¸ oker, D. An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88, 81–89, 1997.
  • C¸ oker, D. and Demirci, M. An introduction to intuitionistic fuzzy topological spaces in ˇSostak sense, Busefal 67, 67–76, 1996.
  • Demirci, M. Neighbourhood structures in smooth topological spaces, Fuzzy Sets and Systems 92, 123–128, 1997.
  • Georgiou, D. N. and Papadopoulos, B. K. Convergences in fuzzy topological spaces, Fuzzy Sets and Systems 101, 495–504, 1999.
  • H¨ohle, U. Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl. 78, 659– 673, 1980.
  • H¨ohle, U. and ˇSostak, A. P. A general theory of fuzzy topological spaces, Fuzzy Sets and Systems 73, 131–149, 1995.
  • H¨ohle, U. and ˇSostak, A. P. Axiomatic Foundations of Fixed-Basis Fuzzy Topology, The Handbooks of Fuzzy Sets Series, 3 (Chapter 3), (Kluwer Academic Publishers, Dordrecht, 1999).
  • Kubiak, T. On fuzzy topologies (Ph.D. Thesis, A. Mickiewicz, Poznan, 1985).
  • Kubiak, T. and ˇSostak, A. P. Lower set-valued fuzzy topologies, Quaestiones Math. 20 (3), 423–429, 1997.
  • Lee, E. P. and Im, Y. B. Mated fuzzy topological spaces, J. Korea Fuzzy Logic Intell. Sys. Soc. 11 (2), 161–165, 2001.
  • Liu, Y. M. and Luo, M. K. Fuzzy Topology (Scientific Publishing Co., Singapore, 1997).
  • Pao-Ming, P. and Ying-Ming, L. Fuzzy topology I: Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76, 571–599, 1980.
  • Samanta, S. K. and Mondal, T. K. On intuitionistic gradation of openness, Fuzzy Sets and Systems 131, 323–336, 2002.
  • ˇSostak, A. P. On a fuzzy topological structure, Suppl. Rend. Circ. Matem. Palerms ser II 11, 89–103, 1985.
  • ˇSostak, A. P. Two decades of fuzzy topology: basic ideas, notions and results, Russian Math. Surveys 44 (6), 125–186, 1989.
  • ˇSostak, A. P. Basic structures of fuzzy topology, J. Math. Sci. 78 (6), 662–701, 1996.
  • Wang, G.- J. Pointwise topology on completely distributive lattice, Fuzzy Sets and Systems 30, 53–62, 1989.
There are 24 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Research Article
Authors

H. Aygün This is me

S.e. Abbas This is me

Publication Date February 1, 2012
Published in Issue Year 2012 Volume: 41 Issue: 2

Cite

APA Aygün, H., & Abbas, S. (2012). (r,s)-Convergent Nets. Hacettepe Journal of Mathematics and Statistics, 41(2), 175-190.
AMA Aygün H, Abbas S. (r,s)-Convergent Nets. Hacettepe Journal of Mathematics and Statistics. February 2012;41(2):175-190.
Chicago Aygün, H., and S.e. Abbas. “(r,s)-Convergent Nets”. Hacettepe Journal of Mathematics and Statistics 41, no. 2 (February 2012): 175-90.
EndNote Aygün H, Abbas S (February 1, 2012) (r,s)-Convergent Nets. Hacettepe Journal of Mathematics and Statistics 41 2 175–190.
IEEE H. Aygün and S. Abbas, “(r,s)-Convergent Nets”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, pp. 175–190, 2012.
ISNAD Aygün, H. - Abbas, S.e. “(r,s)-Convergent Nets”. Hacettepe Journal of Mathematics and Statistics 41/2 (February2012), 175-190.
JAMA Aygün H, Abbas S. (r,s)-Convergent Nets. Hacettepe Journal of Mathematics and Statistics. 2012;41:175–190.
MLA Aygün, H. and S.e. Abbas. “(r,s)-Convergent Nets”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, 2012, pp. 175-90.
Vancouver Aygün H, Abbas S. (r,s)-Convergent Nets. Hacettepe Journal of Mathematics and Statistics. 2012;41(2):175-90.

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