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Issue:Norms over intuitionistic fuzzy subrings and ideals of a ring: Difference between revisions

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[[Category:Publications in 2016 year|{{PAGENAME}}]]
[[Category:Publications in 2016 year|{{PAGENAME}}]]
{{issue/title
{{issue/title
  | title          = Regular weakly generalized locally closed sets in intuitionistic fuzzy topological spaces
  | title          = Norms over intuitionistic fuzzy subrings and ideals of a ring
  | shortcut        = nifs/22/5/63-71
  | shortcut        = nifs/22/5/72-83
}}
}}
{{issue/author
{{issue/author
  | author          = L. Senthil Kumar
  | author          = Rasul Rasuli
  | institution    = Department of Mathematics SVS College of Engineering
  | institution    = Mathematics Department, Faculty of Science
  | address        = Coimbatore-642 109, Tamilnadu, India
  | address        = Payame Noor University (PNU), Tehran, Iran
  | email-before-at = senthilmaths29
  | email-before-at = rasulirasul
  | email-after-at  = gmail.com
  | email-after-at  = yahoo.com
}}
}}
{{issue/data
{{issue/data
| issue          = [[Notes on Intuitionistic Fuzzy Sets/22/5|"Notes on IFS", Volume 22, 2016, Number 5]], pages 63—71
| issue          = [[Notes on Intuitionistic Fuzzy Sets/22/5|"Notes on IFS", Volume 22, 2016, Number 5]], pages 72—83
| file            = NIFS-22-5-63-71.pdf
| file            = NIFS-22-5-72-83.pdf
| format          = PDF
| format          = PDF
| size            = 123
| size            = 123
| abstract        = The purpose of this paper is to introduce and study the concepts of regular weakly generalized locally closed sets,  regular weakly generalized locally continuous mappings in intuitionistic fuzzy topological spaces. Some of their properties are explored.
| abstract        = In this paper, we apply norms over intuitionistic fuzzy subrings and ideals of a ring. We introduce the notions of intuitionistic  
| keywords        = Intuitionistic fuzzy topology, Intuitionistic fuzzy regular weakly generalized closed set, Intuitionistic fuzzy regular weakly generalized continuous mapping, Intuitionistic fuzzy regular weakly generalized locally closed sets, Intuitionistic fuzzy regular weakly generalized locally continuous mappings
 
| ams            = 54A40, 03E72
fuzzy subrings and ideals of a ring with respect a ''t''-norm ''T'' and a ''t''-conorm ''C'' and investigate some related properties under homomorphism.
| keywords        = Ring theory, Norms, Fuzzy set theory, Intuitionistic fuzzy subrings, Intuitionistic fuzzy ideals, Homomorphisms, Direct products.
| ams            = 13Axx, 03B45, 03E72, 20K30, 20K25
| references      =  
| references      =  
# Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96.
# Abu Osman, M. T. (1987) On some products of fuzzy subgroups, Fuzzy Sets and Systems, 24, 79–86.
# Chang, C. L. (1968). Fuzzy topological spaces, J. Math. Anal. Appl, 24, 182–190.
# Ajmal, N. & Thomas, K. V. (1995) The lattice of fuzzy ideals of a ring, Fuzzy Sets and Systems, 74, 371–379.
# Coker, D. (1997) An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88, 81–89.
# Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.
# Jeon, J. K., Jun, Y. B., & Park, J. H. (2005), Intuitionistic fuzzy alpha continuity and intuitionistic fuzzy pre continuity, International journal of Mathematics and Mathematical Sciences, 3091–3101.
# Atanassov, K. T. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
# Padmapriya, S., Uma M.K & Roja, E. (2012) On some applications of intuitionistic π-β-locally closed sets, Int. Jr. of Mathematics Sciences & Applications, 2, 573–580.
# Banejee, B. & Basnet, D. Kr. (2003) Intuitionistic fuzzy subrings and ideals, J. Fuzzy Math., 11(1), 139–155.
# Rajarajeswari, P. & Kumar, L. S. (2012) Regular Weakly Generalized Closed Sets in Intuitionistic Fuzzy Topological Spaces, International journal of Computer Applications, 43, 14–17.
# Biswas, R. (1989) Intuitionistic fuzzy subrings, Mathematical Forum, 10, 37–46.
# Rajarajeswari, P. & Kumar, L. S. (2013) Intuitionistic Fuzzy Regular Weakly Generalized Irresolute Mappings, Far East Journal of Mathematical Sciences, 72, 117–130.
# Buckley, J. J. & Eslami, E. (2002) An introduction to fuzzy logic and fuzzy sets, Springer-Verlag, Berlin Heidelberg GmbH.
# Rajarajeswari, P. & Kumar, L. Senthil (2012) Regular Weakly Generalized Continuous Mappings in Intuitionistic Fuzzy Topological Spaces, International Journal of Mathematical Archive, 3(5), 1957–1962.
# Coker, D. (1997) An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88, 81–99.
# Sakthivel, K. (2012) Intuitionistic Fuzzy Alpha Generalized Closed Sets and Intuitionistic Fuzzy alpha generalized Open Sets, The Mathematical Education, 4
# Coker, D. & Es, A. H. (1995) On fuzzy compactness in intuitionistic fuzzy topological spaces, J. Fuzzy Math., 3(4), 899–909.
# Sakthivel, K. (2010) Intuitionistic Fuzzy Alpha Generalized Continuous Mappings and Intuitionistic Alpha Generalized Irresolute Mappings, Applied Mathematical Sciences, 4, 1831–1842.
# Gurcay, H., Coker, D. & Es, A. H. (1997) On fuzzy continuity in intuitionistic fuzzy topological spaces, J. Fuzzy Math., 5(2), 355–378.
# Seok, J. L. & Eun, P. L. (2000) The category of intuitionistic fuzzy topological spaces, Bull. Korean Math. Soc, 63–76.
# Hur, K. , Jang, S. Y. & Kang, H. W. (2003) Intuitionistic fuzzy subgroupoids, International Journal of Fuzzy Logic and Intelligent Systems, 3(1), 72–77.
# Thakur, S. S. & Chaturvedi, R (2006) Generalized continuity in intuitionistic fuzzy topological spaces, Notes on Intuitionistic Fuzzy Sets, 12, 38–44.
# Hur, K., Kang, H. W. & Song, H. K. (2003) Intuitionistic fuzzy subgroups and subrings, Honam Math. J. , 25(1), 19–41.
# Zadeh, L. A (1965) Fuzzy sets, Information and Control, 8, 338–353.
# Lee, S. J. & Lee, E. P. (2000) The category of intuitionistic fuzzy topological spaces, Bull. Korean Math. Soc., 37(1), 63–76.
# Majumdar, S.& Sultana, Q. S. (1996) The lattice of fuzzy ideals of a ring, Fuzzy Sets and Systems, 81, 271–273.
# Malik, D. S., Mordeson, J. N. & Sen, M. K. (1997) Fundamentals of Abstract Algebra, McGraw Hill.
# Zadeh, L. A. (1965) Fuzzy sets, Inform. and Control, 8, 338–353.
# Zhang, Q. & Meng, G. (2000) On the lattice of fuzzy ideals of a ring, Fuzzy Sets and Systems, 112, 349–353.
  | citations      =  
  | citations      =  
  | see-also        =  
  | see-also        =  
}}
}}

Revision as of 13:24, 17 January 2017

shortcut
http://ifigenia.org/wiki/issue:nifs/22/5/72-83
Title of paper: Norms over intuitionistic fuzzy subrings and ideals of a ring
Author(s):
Rasul Rasuli
Mathematics Department, Faculty of Science, Payame Noor University (PNU), Tehran, Iran
rasulirasul@yahoo.com
Published in: "Notes on IFS", Volume 22, 2016, Number 5, pages 72—83
Download:  PDF (123  Kb, Info)
Abstract: In this paper, we apply norms over intuitionistic fuzzy subrings and ideals of a ring. We introduce the notions of intuitionistic

fuzzy subrings and ideals of a ring with respect a t-norm T and a t-conorm C and investigate some related properties under homomorphism.

Keywords: Ring theory, Norms, Fuzzy set theory, Intuitionistic fuzzy subrings, Intuitionistic fuzzy ideals, Homomorphisms, Direct products.
AMS Classification: 13Axx, 03B45, 03E72, 20K30, 20K25
References:
  1. Abu Osman, M. T. (1987) On some products of fuzzy subgroups, Fuzzy Sets and Systems, 24, 79–86.
  2. Ajmal, N. & Thomas, K. V. (1995) The lattice of fuzzy ideals of a ring, Fuzzy Sets and Systems, 74, 371–379.
  3. Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.
  4. Atanassov, K. T. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
  5. Banejee, B. & Basnet, D. Kr. (2003) Intuitionistic fuzzy subrings and ideals, J. Fuzzy Math., 11(1), 139–155.
  6. Biswas, R. (1989) Intuitionistic fuzzy subrings, Mathematical Forum, 10, 37–46.
  7. Buckley, J. J. & Eslami, E. (2002) An introduction to fuzzy logic and fuzzy sets, Springer-Verlag, Berlin Heidelberg GmbH.
  8. Coker, D. (1997) An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88, 81–99.
  9. Coker, D. & Es, A. H. (1995) On fuzzy compactness in intuitionistic fuzzy topological spaces, J. Fuzzy Math., 3(4), 899–909.
  10. Gurcay, H., Coker, D. & Es, A. H. (1997) On fuzzy continuity in intuitionistic fuzzy topological spaces, J. Fuzzy Math., 5(2), 355–378.
  11. Hur, K. , Jang, S. Y. & Kang, H. W. (2003) Intuitionistic fuzzy subgroupoids, International Journal of Fuzzy Logic and Intelligent Systems, 3(1), 72–77.
  12. Hur, K., Kang, H. W. & Song, H. K. (2003) Intuitionistic fuzzy subgroups and subrings, Honam Math. J. , 25(1), 19–41.
  13. Lee, S. J. & Lee, E. P. (2000) The category of intuitionistic fuzzy topological spaces, Bull. Korean Math. Soc., 37(1), 63–76.
  14. Majumdar, S.& Sultana, Q. S. (1996) The lattice of fuzzy ideals of a ring, Fuzzy Sets and Systems, 81, 271–273.
  15. Malik, D. S., Mordeson, J. N. & Sen, M. K. (1997) Fundamentals of Abstract Algebra, McGraw Hill.
  16. Zadeh, L. A. (1965) Fuzzy sets, Inform. and Control, 8, 338–353.
  17. Zhang, Q. & Meng, G. (2000) On the lattice of fuzzy ideals of a ring, Fuzzy Sets and Systems, 112, 349–353.
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