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Issue:A variety of functions concerning intuitionistic fuzzy M-clopen sets in intuitionistic fuzzy topological spaces: Difference between revisions

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  | issue          = [[Notes on Intuitionistic Fuzzy Sets/32/1|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 1]], pages 30–39
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/32/1|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 1]], pages 40–50
  | doi            = https://doi.org/10.7546/nifs.32.1.30-39
  | doi            = https://doi.org/10.7546/nifs.32.1.40-50
  | file            = NIFS-32-1-030-039.pdf
  | file            = NIFS-32-1-040-050.pdf
  | format          = PDF
  | format          = PDF
  | size            = 1319
  | size            = 199
  | abstract        = This paper introduces a novel class of mappings: slightly intuitionistic fuzzy ''M''-continuous functions, intuitionistic fuzzy totally ''M''-continuous functions, and intuitionistic fuzzy ''M''-totally continuous functions, utilizing intuitionistic fuzzy ''M'' clopen sets. We examine the topological properties and characterizations of these mappings, explore the relationships between these new sets and existing sets in intuitionistic fuzzy topological spaces, and provide examples to illustrate the concepts.
  | abstract        = This paper introduces a novel class of mappings: slightly intuitionistic fuzzy ''M''-continuous functions, intuitionistic fuzzy totally ''M''-continuous functions, and intuitionistic fuzzy ''M''-totally continuous functions, utilizing intuitionistic fuzzy ''M'' clopen sets. We examine the topological properties and characterizations of these mappings, explore the relationships between these new sets and existing sets in intuitionistic fuzzy topological spaces, and provide examples to illustrate the concepts.
  | keywords        = Intuitionistic fuzzy topological spaces, Slightly intuitionistic fuzzy ''M'' continuous functions, Intuitionistic fuzzy totally ''M''-continuous functions, Intuitionistic fuzzy ''M''-totally continuous functions.  
  | keywords        = Intuitionistic fuzzy topological spaces, Slightly intuitionistic fuzzy ''M'' continuous functions, Intuitionistic fuzzy totally ''M''-continuous functions, Intuitionistic fuzzy ''M''-totally continuous functions.  
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# Atanassov, K. (1983). Atanassov K. T. Intuitionistic Fuzzy Sets. VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal Bioautomation, 2016, 20(S1), S1–S6.
# Atanassov, K. (1983). Atanassov K. T. Intuitionistic Fuzzy Sets. VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal Bioautomation, 2016, 20(S1), S1–S6.
# Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
# Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
# Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications.
# Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag, Heidelberg, New York.
Springer-Verlag, Heidelberg, New York.
# Atanassov, K., & Stoeva, S. (1983). Intuitionistic fuzzy sets. Polish Symposium on Interval and Fuzzy Mathematics, Poznan, 23–26.
# Atanassov, K., & Stoeva, S. (1983). Intuitionistic fuzzy sets. Polish Symposium on Interval and Fuzzy Mathematics, Poznan, 23–26.
# Caldas, M., Jafari, S., & Kovar, M. M. (2004). Some properties of θ-open sets. Divulgaciones Matematicas ´ , 12(2), 161–169.
# Caldas, M., Jafari, S., & Kovar, M. M. (2004). Some properties of θ-open sets. Divulgaciones Matematicas ´ , 12(2), 161–169.
# C¸ oker, D. (1996). An introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces. Journal of Fuzzy Mathematics, 4, 749–764.
# Çoker, D. (1996). An introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces. Journal of Fuzzy Mathematics, 4, 749–764.
# C¸ oker, D. (1997). An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88(1), 81–89.
# Çoker, D. (1997). An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88(1), 81–89.
# C¸ oker, D., & Demirci, M. (1996). An introduction to intuitionistic fuzzy topological spaces in Sˆostaks sense. Busefal,67, 67–76.
# Çoker, D., & Demirci, M. (1996). An introduction to intuitionistic fuzzy topological spaces in Šostak's sense. BUSEFAL, 67, 67–76.
# Fora, A. A. A. (2017) The number of fuzzy clopen sets in fuzzy topological spaces. Journal of Mathematical Sciences and Applications, 5(1), 24–26.
# Fora, A. A. A. (2017) The number of fuzzy clopen sets in fuzzy topological spaces. Journal of Mathematical Sciences and Applications, 5(1), 24–26.
#  Gurcay, H., Haydar, A., & C¸ oker, D. (1997) On fuzzy continuity in intuitionistic fuzzy topological spaces. Journal of Fuzzy Mathematics, 5(2), 365–378.
#  Gurcay, H., Haydar, A., & Çoker, D. (1997) On fuzzy continuity in intuitionistic fuzzy topological spaces. Journal of Fuzzy Mathematics, 5(2), 365–378.
# Maghrabi, A. I. E., & Al-Johany, M. A. (2011). M-open set in topological spaces. Pioneer Journal of Mathematics and Mathematical Sciences, 4(2), 213–308.
# Maghrabi, A. I. E., & Al-Johany, M. A. (2011). M-open set in topological spaces. Pioneer Journal of Mathematics and Mathematical Sciences, 4(2), 213–308.
# Maghrabi, A. I. E., & Al-Johany, M. A. (2013). New types of functions by M-open sets. Journal of Taibah University for Science, 7(3), 137–145.
# Maghrabi, A. I. E., & Al-Johany, M. A. (2013). New types of functions by M-open sets. Journal of Taibah University for Science, 7(3), 137–145.
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# Manimaran, A., Prakash, K. A., & Thangaraj, P. (2011). Intuitionistic fuzzy totally continuous and totally semi-continuous mappings in intuitionistic fuzzy topological spaces. International journal of Advanced Scientific and Technical Research, 2(1), 505–509.
# Manimaran, A., Prakash, K. A., & Thangaraj, P. (2011). Intuitionistic fuzzy totally continuous and totally semi-continuous mappings in intuitionistic fuzzy topological spaces. International journal of Advanced Scientific and Technical Research, 2(1), 505–509.
# Mondal, T. K., & Samanta, S. K. (2002). On intuitionistic gradation of openness. Fuzzy Sets and Systems, 131(3), 323–336.
# Mondal, T. K., & Samanta, S. K. (2002). On intuitionistic gradation of openness. Fuzzy Sets and Systems, 131(3), 323–336.
# Samanta, S. K., & Mondal, T. K. (1997). Intuitionistic gradation of openness, intuitionistic fuzzy topology. Busefal, 73, 8–17.
# Samanta, S. K., & Mondal, T. K. (1997). Intuitionistic gradation of openness, intuitionistic fuzzy topology. BUSEFAL, 73, 8–17.
# Smets, P. (1981). The degree of belief in a fuzzy event. Information Sciences, 25(1), 1–19.
# Smets, P. (1981). The degree of belief in a fuzzy event. Information Sciences, 25(1), 1–19.
# Sobana, D., Chandrasekar, V., & Vadivel, A. (2018). On fuzzy e-open sets, fuzzy e-continuity and fuzzy e-compactness in intuitionistic fuzzy topological spaces. Sahand Communications in Mathematical Analysis, 12(1), 131–153.
# Sobana, D., Chandrasekar, V., & Vadivel, A. (2018). On fuzzy e-open sets, fuzzy e-continuity and fuzzy e-compactness in intuitionistic fuzzy topological spaces. Sahand Communications in Mathematical Analysis, 12(1), 131–153.

Latest revision as of 09:38, 13 March 2026

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http://ifigenia.org/wiki/issue:nifs/32/1/40-50
Title of paper: A variety of functions concerning intuitionistic fuzzy M-clopen sets in intuitionistic fuzzy topological spaces
Author(s):
G. Saravanakumar
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology (Deemed to be University), Avadi, Chennai-600062, India
saravananguru2612@gmail.com
K. A. Venkatesan
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology (Deemed to be University), Avadi, Chennai-600062, India
venkimaths1975@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 1, pages 40–50
DOI: https://doi.org/10.7546/nifs.32.1.40-50
Download:  PDF (199  Kb, File info)
Abstract: This paper introduces a novel class of mappings: slightly intuitionistic fuzzy M-continuous functions, intuitionistic fuzzy totally M-continuous functions, and intuitionistic fuzzy M-totally continuous functions, utilizing intuitionistic fuzzy M clopen sets. We examine the topological properties and characterizations of these mappings, explore the relationships between these new sets and existing sets in intuitionistic fuzzy topological spaces, and provide examples to illustrate the concepts.
Keywords: Intuitionistic fuzzy topological spaces, Slightly intuitionistic fuzzy M continuous functions, Intuitionistic fuzzy totally M-continuous functions, Intuitionistic fuzzy M-totally continuous functions.
AMS Classification: 54A40, 54A99, 03E72, 03E99.
References:
  1. Atanassov, K. (1983). Atanassov K. T. Intuitionistic Fuzzy Sets. VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal Bioautomation, 2016, 20(S1), S1–S6.
  2. Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
  3. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag, Heidelberg, New York.
  4. Atanassov, K., & Stoeva, S. (1983). Intuitionistic fuzzy sets. Polish Symposium on Interval and Fuzzy Mathematics, Poznan, 23–26.
  5. Caldas, M., Jafari, S., & Kovar, M. M. (2004). Some properties of θ-open sets. Divulgaciones Matematicas ´ , 12(2), 161–169.
  6. Çoker, D. (1996). An introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces. Journal of Fuzzy Mathematics, 4, 749–764.
  7. Çoker, D. (1997). An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88(1), 81–89.
  8. Çoker, D., & Demirci, M. (1996). An introduction to intuitionistic fuzzy topological spaces in Šostak's sense. BUSEFAL, 67, 67–76.
  9. Fora, A. A. A. (2017) The number of fuzzy clopen sets in fuzzy topological spaces. Journal of Mathematical Sciences and Applications, 5(1), 24–26.
  10. Gurcay, H., Haydar, A., & Çoker, D. (1997) On fuzzy continuity in intuitionistic fuzzy topological spaces. Journal of Fuzzy Mathematics, 5(2), 365–378.
  11. Maghrabi, A. I. E., & Al-Johany, M. A. (2011). M-open set in topological spaces. Pioneer Journal of Mathematics and Mathematical Sciences, 4(2), 213–308.
  12. Maghrabi, A. I. E., & Al-Johany, M. A. (2013). New types of functions by M-open sets. Journal of Taibah University for Science, 7(3), 137–145.
  13. Maghrabi, A. I. E., & Al-Johany, M. A. (2014). Further properties on M-continuity. Journal of Egyptian Mathematical Society, 22(1), 63–69.
  14. Maghrabi, A. I. E., & Al-Johany, M. A. (2014). Some applications of M-open set in topological spaces. Journal of King Saud University-Science, 26, 261–266.
  15. Manimaran, A., Prakash, K. A., & Thangaraj, P. (2011). Intuitionistic fuzzy totally continuous and totally semi-continuous mappings in intuitionistic fuzzy topological spaces. International journal of Advanced Scientific and Technical Research, 2(1), 505–509.
  16. Mondal, T. K., & Samanta, S. K. (2002). On intuitionistic gradation of openness. Fuzzy Sets and Systems, 131(3), 323–336.
  17. Samanta, S. K., & Mondal, T. K. (1997). Intuitionistic gradation of openness, intuitionistic fuzzy topology. BUSEFAL, 73, 8–17.
  18. Smets, P. (1981). The degree of belief in a fuzzy event. Information Sciences, 25(1), 1–19.
  19. Sobana, D., Chandrasekar, V., & Vadivel, A. (2018). On fuzzy e-open sets, fuzzy e-continuity and fuzzy e-compactness in intuitionistic fuzzy topological spaces. Sahand Communications in Mathematical Analysis, 12(1), 131–153.
  20. Suba, M., Shanmugapriya, R., Sakthivel, K., & Malini, T. N. M. (2022). Several types of functions of intuitionistic fuzzy M open sets in intuitionistic fuzzy topological spaces. International Journal of Mechanical Engineering, 7(4), 1639–1649.
  21. Suba, M., Shanmugapriya, R., Sakthivel, K., & Suresh, M. L. (2022). On intuitionistic fuzzy M closed sets in intuitionistic fuzzy topological spaces. International Journal of Mechanical Engineering, 7(4), 1633–1638.
  22. Sugeno, M. (1985). An introductory survey of fuzzy control. Information Sciences, 36(1–2), 59–83.
  23. Thakur, S. S., & Singh, S. (1998). On fuzzy semi-pre open sets and fuzzy semi-pre continuity. Fuzzy Sets and Systems, 98(3), 383–391.
  24. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353
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