International Journal of Nonlinear Analysis and Applications

Consideration of fuzzy zero based on transmission average

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran

Abstract

Fuzzy field and arithmetic operators based on transmission average (TA) and neutral member are dealt by  Abbasi et al. \cite{2}. Many examples are exist such that based on their definition $ \tilde{A}.\tilde{0}_{\tilde{A}} \tilde{0}_{\tilde{A}}.\tilde{A}) $ is not equal to $ \tilde{0}_{\tilde{A}} $. Therefore, we investigate the conditions that $ \tilde{A}.\tilde{0}_{\tilde{A}}(=\tilde{0}_{\tilde{A}}.\tilde{A})=\tilde{0}_{\tilde{A}} $. Numerical examples show the applicability of theorems and mentioned problems.

Keywords

[1] F. Abbasi, T. Allahviranloo, and S. Abbasbandy, A new attitude coupled with fuzzy thinking to fuzzy rings and fields, J. Intell. Fuzzy Syst. 29 (2015), 851-–861.
[2] S. Abdullah, M. Aslam, T.A. Khan, and M. Naeem, A new type of fuzzy normal subgroups and fuzzy cosets, J. Intell. Fuzzy Syst. 25 (2013), 37—47.
[3] T. Allahviranloo and S.‘Abbasbandy, A new attitude coupled with the basic thinking to ordering for ranking fuzzy numbers, Int. J. Ind. Math. 8 (2016), no. 4, 365–375.
[4] T. Allahviranloo, I. Perfilieva and F. Abbasi, A new attitude coupled with fuzzy thinking for solving fuzzy equations, Soft Comput. 22 (2018), 3077–3095.
[5] F. Babakordi and M. Adabitabar Firozja, Solving fully fuzzy dual matrix system with optimization problem, Int. Ind. Math. 12 (2020), 109–119.
[6] F. Babakordi and T. Allahviranloo, A Cramer method for solving fully fuzzy linear systems based on transmission average, Control Optim. Appl. Math. 2 (2022), 115—130.
[7] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980.
[8] G. Gebray and B. Krishna Reddy, Fuzzy set field and fFuzzy metric, Adv. Fuzzy Syst. 2014 (2014), 15–15.
[9] F. Khalili Goodarzi, N.A. Taghinezhad, and S.H. Nasseri, A new fuzzy approach to solve a novel model of open shop scheduling problem, Appl. Math. Phys. 76 (2014), 199-210.
[10] G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall PTR, Upper Saddle River, 1995.
[11] S. Markov, A non-standard subtraction of intervals, Serdica 3 (1977), 359—370.
[12] S. Markov, On the algebra of intervals and convex bodies, J. Univer. Comput. Sci. 4 (1998), 34—47.
[13] S.H. Nasseri, N.A. Taghi-Nezhad and A. Ebrahimnejad, A novel method for ranking fuzzy quantities using center of incircle and its application to a petroleum distribution center evaluation problem, Int. J. Ind. Syst. 27 (2017), no. 4, 457–484.
[14] L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets Syst. 161 (2010), 1564–1584.
[15] F. Taleshian, J. Fathali and N.A. Taghi-Nezhad, Fuzzy majority algorithms for the 1-median and 2-median problems on a fuzzy tree, Fuzzy Inf. Engin. 10 (2018), no. 2, 225–248.
[16] G. Wenxiang and L. Tu, Fuzzy linear spaces, Fuzzy Sets Syst. 49 (1992), 377—380.
International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 6
June 2024
Pages 349-353
  • Receive Date: 05 February 2023
  • Revise Date: 13 April 2023
  • Accept Date: 05 May 2023