Alternative Arithmetic of Pentagonal Fuzzy Numbers

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-12
Year of Publication : 2020
Authors : Intan Arfina, Mashadi
  10.14445/22315373/IJMTT-V66I12P505

MLA

MLA Style: Intan Arfina, Mashadi  "Alternative Arithmetic of Pentagonal Fuzzy Numbers" International Journal of Mathematics Trends and Technology 66.12 (2020):28-36. 

APA Style: Intan Arfina, Mashadi(2020). Alternative Arithmetic of Pentagonal Fuzzy Numbers  International Journal of Mathematics Trends and Technology,28-36.

Abstract
In this paper, we introduce the definition of positive and negative fuzzy numbers based on the concept of area of fuzzy numbers on the right side of r-axis and the left side of r-axis (in the first quadrant and the second quadrant). From the concept of positive and negative fuzzy numbers, an alternative arithmetic for pentagonal fuzzy numbers is constructed. Then the multiplication form of pentagonal fuzzy numbers can be obtained in some cases. Finally, from the multiplication operations, it can later be applied to determine the multiplication identity and inverse of pentagonal fuzzy numbers.

Reference

[1] A. S. Abidin, Mashadi, and S. Gemawati, Algebraic modification of trapezoidal fuzzy numbers to complete fully fuzzy linear equations system using gauss-jacobi method, International Journal of Management and Fuzzy Systems,5 (2019), 40-46.
[2] Z. Desmita and Mashadi, Alternative multiplying triangular fuzzy number and applied in fully fuzzy linear system, American Scientific Research Journal for Engineering, Technology and Science, 56 (2019), 113-123.
[3] D. S. Dinagar and M. M. Jeyavuthin, Distinct methods for solving fully fuzzy linear programming problems with pentagonal fuzzy numbers, Journalof Computer and Mathematical Sciences, 10 (2019), 1253-1260.
[4] S. S. Geethaand K. Selvakumari, A new method for solving fuzzy transportation problem using pentagonal fuzzy numbers, Journal of Critical Reviews,7 (2020), 171-174.
[5] R. Helen and G. Uma, A operations and rangking on petagonal fuzzy numbers,International Journal of Mathematical Science and Application, 5(2015), 341-346.
[6] A.J. Kamble, Some notes on pentagonal fuzzy numbers, International Journal Fuzzy Mathematical Archive, 13 (2017), 113-121.
[7] H. Kholida and Mashadi, Alternative fuzzy algebra for fuzzy linear system using cramers rules on fuzzy trapozoidal Number, International Journal of Innovative Science and Research Technology, 4 (2019), 494-504.
[8] S. I. Marni, Mashadi, and S. Gemawati, Solving dual fully fuzzy linear system by use factorizations of the coefficient matrix for trapezoidal fuzzy number, Bulletin of Mathematics, 10 (2018), 145-56.
[9] Mashadi, A new method for dual fully fuzzy linear system by Use LU factorizations of The coefficient matrix, Jurnal Matematika dan Sains, 15(2010), 101-106.
[10] S. P. Mondaand M. Mandal, Pentagonal fuzzy number, its properties andapplication in fuzzy equation, Future Computing and Informatics Journal,2 (2017), 110-117.
[11] A. Panda and M. Pal, A study on pentagonal fuzzy number and its corresponding matrices, Pacific Science Review B: Humanities and Social Sciences,1 (2015), 131-139.
[12] T. Pathinathan and K. Ponnivalavan, Pentagonal fuzzy number, International Journal of Computing Algorithm, 3 (2014), 1003-1005.
[13] T. Pathinathan and E. A. Dolorosa ,Symmetric periodic fourier series using pentagonal fuzzy number, Journal of Computer and Mathematical Sciences, 10 (2019), 510-518.
[14] S. Ramliand S. H. Jaaman, Optimal solution of fuzzy optimization using pentagonal fuzzy numbers, American Institute of Physics Conference Proceedings,1974 (2018), 1-8.
[15] P. Selvam, A. Rajkumarand J. S. Easwari, Ranking of pentagonal fuzzy numbers applying incentre of centroids, International Journal of Pure and Applied Mathematics, 117 (2017), 165-174.
[16] Y. SafitriandMashadi, Alternative fuzzy algebra to solve dual fully fuzzy linear system using st decomposition method, The Internasional Organization of Scientific Research -Journal of Mathematics, 15 (2019), 32-38.
[17] D. R. A. Sari and Mashadi, New arithmetic triangular fuzzy numberfor solving fully fuzzy linear system using inverse matrix, International Journal of Science: Basic and Applied Research, 46 (2019),169-180.
[18] V. Vijayalakshmi and A. Karpagam, Pentagonal fuzzy number by Cholesky decomposition and singular value decomposition, International Journal ofMathematics Research, 11 (2019), 19-28.
[19] L. A. Zadeh,Fuzzy Sets, Information and Control, 8 (1965), 338-353.
[20] L. A. Zadeh, The Concept of a linguistic variable and its application toapproximate reasoning-I, Information Sciences, 8 (1975), 199-249.

Keywords : Fuzzy Number, Arithmetic Fuzzy Number, Pentagonal Fuzzy Number.