As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: September/October 2024.
Open Call for Papers: International Workshop on Intuitionistic Fuzzy Sets • 13 December 2024 • Banska Bystrica, Slovakia/ online (hybrid mode).
Deadline for submissions: 16 November 2024.

Issue:Non-linear arithmetic operation on generalized triangular intuitionistic fuzzy numbers

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/20/1/9-19
Title of paper: Non-linear arithmetic operation on generalized triangular intuitionistic fuzzy numbers
Author(s):
Sankar Prasad Mondal
Department of Mathematics, Bengal Engineering and Science University, Shibpur, P.O.-Botanic Garden, Howrah, West Bengal 711103, India
Tapan Kumar Roy
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O.-Botanic Garden, Howrah, West Bengal 711103, India
roy_t_k@yahoo.co.in
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 20, 2014, Number 1, pages 9-19
Download:  PDF (191  Kb, File info)
Abstract: In this paper we discussed some nonlinear operation on generalized triangular intuitionistic fuzzy number. Some examples and an application are given.
Keywords: Fuzzy set, Intuitionistic fuzzy number.
AMS Classification: 03E72, 03E75, 26E50.
References:
  1. Zadeh, L. A., Fuzzy sets, Information and Control, Vol. 8, 1965, 338–353.
  2. Dubois, D., H. Parade, Operation on Fuzzy Number. International Journal of Fuzzy Systems, Vol. 9, 1978, 613–626.
  3. Atanassov, K. T., Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, 1983 (in Bulgarian).
  4. Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, 1986, 87–96.
  5. Deng-Feng-Li, A note on “Using intuitionistic fuzzy sets for fault tree analysis on printed circuit board assembly”, Micro Electronics Reliability, Vol. 48, 2008, 1741.
  6. Mahapatra, G. S., T. K. Roy, Reliability Evaluation using Triangular Intuitionistic Fuzzy numbers Arithmetic operations, World Academy of Science, Engineering and Technology Vol. 50, 2009, 574–581.
  7. Nagoorgani, A., K. Ponnalagu, A new approach on solving intuitionistic fuzzy linear programming problem, Applied Mathematical Sciences, Vol. 6, 2012, No. 70, 3467–3474.
  8. Atanassov, K. T., G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 31, 1989, No. 3, 343–349.
  9. Atanassov, K. T., More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 33, 1989, No. 1, 37–46.
  10. Atanassov, K. T., Intuitionistic Fuzzy Sets, Physica–Verlag, Heidelberg, 1999.
  11. Atanassov, K. T., Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 110, 2000, 267–269.
  12. Atanassov, K. T., G. Gargov, Elements of intuitionistic fuzzy logic, Part I, Fuzzy Sets and Systems, Vol. 95, 1998, No. 1, 39–52.
  13. Szmidt, E., J. Kacprzyk, Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 114, 2000, No. 3, 505–518.
  14. Buhaescu, T., Some observations on intuitionistic fuzzy relations, Itinerant Seminar of Functional Equations, Approximation and Convexity, Cluj-Napoca, 1989, 111–118.
  15. Ban, A. I., Nearest interval approximation of an intuitionistic fuzzy number, Computational Intelligence, Theory and Applications, Springer–Verlag, Berlin, Heidelberg, 2006, 229–240.
  16. Deschrijver, G., E. E. Kerre, On the relationship between intuitionistic fuzzy sets and some other extensions of fuzzy set theory, Journal of Fuzzy Mathematics, Vol. 10, 2002, No. 3, 711–724.
  17. Stoyanova, D., More on Cartesian product over intuitionistic fuzzy sets, BUSEFAL, Vol. 54, 1993, 9–13.
  18. Cornelis, C., G. Deschrijver, G., E. E. Kerre, Implication in intuitionistic fuzzy and interval–valued fuzzy set theory: Construction, application, International Journal of Approximate Reasoning, Vol. 35, 2004, 55–95.
  19. Buhaescu, T., On the convexity of intuitionistic fuzzy sets, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca,1988, 137–144.
  20. Gerstenkorn, T., J. Manko, Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 44, 1991, 39–43.
  21. Stoyanova, D., K. T. Atanassov, Relation between operators, defined over intuitionistic fuzzy sets, Preprint IM-MFAIS, Sofia, Bulgaria, 1990, 46–49.
  22. Stoyanova, D., More on Cartesian product over intuitionistic fuzzy sets, BUSEFAL, Vol. 54, 1993, 9–13.
  23. Mahapatra, G. S., T. K. Roy, Reliability evaluation using triangular intuitionistic fuzzy numbers arithmetic operations, Proceedings of World Academy of Science, Engineering and Technology, Vol. 38, 2009, 587–595.
  24. Hajeeh, M. A., Reliability and availability of a standby system with common cause failure, International Journal of Operational Research, Vol. 11, 2011, No. 3, 343–363.
  25. Persona, A., F. Sqarbossa, H. Pham, Systemability function to optimization reliability in random environment, International Journal of Mathematics in Operational Research, Vol. 1, 2009, No. 3, 397–417.
  26. Praba, B., R. Sujatha, S. Srikrishna, Posfust reliability of a unified fuzzy Markov model, International Journal of Reliability and Safety, Vol. 5, No. 1, 83–94, 2011.
  27. Nikolaidis, E., Z.P. Mourelatos, Imprecise reliability assessment when the type of the probability distribution of the random variables is unknown, International Journal of Reliability and Safety, Vol. 5, 2011, No. 2, 140–157.
  28. Kumar, M., S.P. Yadav, S. Kumar, A new approach for analyzing the fuzzy system reliability using intuitionistic fuzzy number, International Journal of Industrial and Systems Engineering, Vol. 8, 2011, No. 2, 135–156.
  29. Wang, Y., Imprecise probabilities based on generalized intervals for system reliability assessment, International Journal of Reliability and Safety, Vol. 4, 2010, No. 4, 319–342.
  30. Shaw, A. K., T. K. Roy, Trapezoidal Intuitionistic Fuzzy Number with some arithmetic operations and its application on reliability evaluation, Int. J. Mathematics in Operational Research, Vol. 5, 2013, No. 1, 55–73.
  31. Adak, A. K., M. Bhowmik, M. Pal, intuitionistic fuzzy block matrix and its some properties, Annals of Pure and Applied Mathematics, Vol. 1, 2012, No. 1, 13–31.
  32. Varghese, A., S. Kuriakose, Centroid of an intuitionistic fuzzy number, Notes on Intuitionistic Fuzzy Sets, Vol. 18, 2012, No. 1, 19–24.
  33. Mondal, S. P., T. K. Roy, First order linear homogeneous ordinary differential equation in fuzzy environment based on Laplace transform, Journal of Fuzzy Set Valued Analysis, Vol. 2013, 2013, 1–18.
  34. Bansal, A., Some non linear arithmetic operations on triangular fuzzy numbers (m, α, β), Advances in Fuzzy Mathematics, Vol. 5, 2010, No. 2, 147–156.
  35. Vahidi, J., S. Rezvani, Arithmetic operations on trapezoidal fuzzy numbers, Journal Nonlinear Analysis and Application, Vol. 2013, 2013, 1–8.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

Retrieved from "https://ifigenia.org/index.php?title=Issue:Non-linear_arithmetic_operation_on_generalized_triangular_intuitionistic_fuzzy_numbers&oldid=12952"