...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 2 | Year 2017 | Article Id. IJMTT-V52P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P518

Ordering L-R type Generalized Trapezoidal Fuzzy Numbers


G.Uthra, K.Thangavelu, R.M.Umamageswari
Abstract

Methods for ordering fuzzy numbers play a vital role as decision criteria. In fuzzy literature there are many techniques for ordering fuzzy numbers. In practice, some special L-R fuzzy numbers, like triangular fuzzy number, the Gaussian fuzzy number, Cauchy fuzzy number and Trapezoidal fuzzy number are widely used various areas to deal with many vague information. Based on the recent developments in research of fuzzy number ranking,the paper extends thenew ranking approach to rank and orderGeneralized L-R Fuzzy Numbers. The purpose of this paper is to introduce a general frame work for comparing fuzzy sets with respect to fuzzy orderings in a gradual way. The approach proposed herein is relatively simple in terms of computational efforts and is efficient when ranking a large quantity of fuzzy numbers.

Keywords
Triangular fuzzy number, the Gaussian fuzzy number, Cauchy fuzzy number and Trapezoidal fuzzy.
References

[1] S. Abbasbandy, B. Asady, “Ranking fuzzy numbers by distance minimization”, Inf. Sci., 176, 2405-2416, 2006.
[2] Amit Kumar, Pushpinder Singh, ParmpreetKaur and AmarpreetKaur, “A New Approach For Ranking of L-R Type Generalized Fuzzy Numbers”,Tamsuki Oxford Journal of Information and Mathematical Sciences, 27(2), 197-211, 2011.
[3] B. Asady, Zendehnam, “A Ranking fuzzy numbers by distance minimization”, Appl. Math. Model, 31, 2589- 2598, 2007.
[4] F. N. Azman, L. A. Abdullah, “A New Centroids Method for Ranking of trapezoidal Fuzzy Numbers”, Malays. J. Fundam. Appl. Sci., doi:10.11113/jt.v68.1124, 2014.
[5] L. H. Chen, H. W. Lu, “An approximate approach for ranking fuzzy numbers based on left and right dominance”, Compt. Math. Appl., 41, 1589-1602, 2001.
[6] S.M. Chen and J. H. Chen, “Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads”, Expert Systems with Applications, 36 no.3, 6833-6842, 2009.
[7] C. H. Cheng, “A new approach for ranking fuzzy numbers by distance method”, Fuzzy Sets Syst., 5, 131- 141, 2014.
[8] T. C. Chu, S. A. Wu, “Centroid ranking approach based on fuzzy model”, Int. J. Mech. Aerosp. Ind. Mechatron. Eng. 7, 531-537, 2013.
[9] Y. Deng, Z. Zhenfu, L. Qi, “Ranking fuzzy numbers with an area method using radius of gyration”, Comput. Math. Appl., 51, 1127-1136, 2006.
[10] D. Dubois, H. Prade, “Operations on fuzzy numbers”, Int. J. Syst. Sci., 9, 613-626, 1978.
[11] Jos𝑒 A. Gonz𝑎 lez Campos and Ronald A. Manr𝑖 quez Pe𝑛 afiel, “A Method for Ordering of LR-Type Fuzzy Numbers: An Important Decision Criteria”, Axioms, 5, 22, doi:10.3390 / axioms 5030022, 2016.
[12] E. Lee, R. J. Li, “Comparision of fuzzy numbers based on the probability measure of fuzzy events”, Comput. Math. Appl., 15, 1988, 887-896.
[13] M. Modarres, S. Sadi-Nezhad, “Ranking fuzzy numbers by preference ratio”, Fuzzy Sets Syst., 118, 429-436, 2001.
[14] S. Nasseri, F. Taleshian, Z. Alizadeh, J. Vahidi, “A new method for ordering LR fuzzy numbers”, J. Math. Comput. Sci., 4, 283-294, 2012.
[15] Y. Thorani Y, P. P. B. Rao, N. R. Shankar, “Ordering generalized trapezoidal fuzzy numbers”, Int. J. contemp. Math. Sci., 7, 555-573, 2012.
[16] Y. L. P. Thorani and N. Ravi Shankar, “Ranking Generalized LR Fuzzy Numbers Using Area, Mode, Spreads and Weights”, Applied Mathematical Sciences, Vol.11, no. 39, 1943-1953, 2017.
[17] W. Wang, Z. Wang, “Total orderings defined on the set of all fuzzy numbers”, Fuzzy Sets Syst., 5, 131-141, 2014.
[18] Y. M. Wang, J. B. Yang, D. L. Xu, K. S. Chin, “On the centroids of fuzzy numbers”, Fuzzy Sets Syst., 157, 919- 926, 2006.
[19] L. A. Zadeh, “Fuzzy sets”, Information and Control, 8 no. 3, 338-353, 1965.

Citation :

G.Uthra, K.Thangavelu, R.M.Umamageswari, "Ordering L-R type Generalized Trapezoidal Fuzzy Numbers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 2, pp. 132-135, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P518

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2025 Seventh Sense Research Group® . All Rights Reserved