Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems

Aliya Fahmi; Saleem Abdullah; Fazli Amin

EN

Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems

Abstract

In this paper, we define trapezoidal cubic fuzzy numbers and their operational laws. Started on these operational laws, each collection operators, with trapezoidal cubic fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are purposed. Expected values, score function, and accuracy function of trapezoidal cubic fuzzy numbers are defined. Overcoming on these, mindful of trapezoidal cubic fuzzy multi-criteria decision making program is proposed. A delineation illustration example is given to exhibit the sound judgment and openness of the procedure.

Keywords

Trapezoidal cubic fuzzy number,aggregation operators,multi-criteria decision making

References

[1] K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst., 20 (1), 87--96 :(1986).
[2] A. Fahmi, S. Abdullah, F. Amin ,N. Siddque and A Ali. AGGREGATION OPERATORS ON TRIANGULAR CUBIC FUZZY NUMBERS AND ITS APPLICATION TO MULTI-CRITERIA DECISION MAKING PROBLEMS, Journal of Intelligent and Fuzzy System, 33 (2017),3323-3337.
[3] A. Fahmi, S. Abdullah, F. Amin and A. Ali, Precursor Selection for Sol--Gel Synthesis of Titanium Carbide Nanopowders by a New Cubic Fuzzy Multi-Attribute Group Decision-Making Model. Journal of Intelligent Systems. Retrieved 6 Oct. 2017, from doi:10.1515/jisys-2017-0083.
[4] A. Fahmi, S. Abdullah, F. Amin and A. Ali, Weighted Average Rating (War) Method for Solving Group Decision Making Problem Using Triangular Cubic Fuzzy Hybrid Aggregation (Tcfha), Punjab University Journal of Mathematics, Vol. 50(1)(2018) pp.23-34.
[5] A. Fahmi, S. Abdullah,F. Amin, R. Ahmed, & A. Ali. Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making. Journal of Intelligent & Fuzzy Systems, (Preprint), 1-15.
[6] A. Fahmi, S. Abdullah and F. Amin, TRAPEZOIDAL LINGUISTIC CUBIC HESITANT FUZZY TOPSIS METHOD AND APPLICATION TO GROUP DECISION MAKING PROGRAM, Year: 2017, Number: 19, Pages: 27-47.
[7] T. Chu, A fuzzy number interval arithmetic based fuzzy MCDM algorithm. Inter. J. Fuzzy Systems, 2002, 4(4): 867-872.
[8] Y. B. Jun, C. S. Kim and Ki. O. Yang, Cubic sets "Annals of Fuzzy Mathematics and Informatics,", Volume 4, No. 1, 83- 98: ( 2012).
[9] R. J. Li, Theories and applications of fuzzy multi-criteria decision making. Beijing: Science Press, 2002.
[10] J, Q. Wang, Programming method of fuzzy group multiple criteria decision making with incomplete information. Systems Engineering and Electronics, 2004, 26(11): 1604-1608.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Aliya Fahmi This is me

Saleem Abdullah This is me

Fazli Amin This is me

Publication Date

March 26, 2018

Submission Date

December 28, 2017

Acceptance Date

April 10, 2018

Published in Issue

Year 2018 Number: 22

IZ

https://izlik.org/JA63BM77YZ

APA

Fahmi, A., Abdullah, S., & Amin, F. (2018). Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems. Journal of New Theory, 22, 51-65. https://izlik.org/JA63BM77YZ

AMA

1.Fahmi A, Abdullah S, Amin F. Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems. JNT. 2018;(22):51-65. https://izlik.org/JA63BM77YZ

Chicago

Fahmi, Aliya, Saleem Abdullah, and Fazli Amin. 2018. “Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems”. Journal of New Theory, nos. 22: 51-65. https://izlik.org/JA63BM77YZ.

EndNote

Fahmi A, Abdullah S, Amin F (March 1, 2018) Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems. Journal of New Theory 22 51–65.

IEEE

[1]A. Fahmi, S. Abdullah, and F. Amin, “Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems”, JNT, no. 22, pp. 51–65, Mar. 2018, [Online]. Available: https://izlik.org/JA63BM77YZ

ISNAD

Fahmi, Aliya - Abdullah, Saleem - Amin, Fazli. “Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems”. Journal of New Theory. 22 (March 1, 2018): 51-65. https://izlik.org/JA63BM77YZ.

JAMA

1.Fahmi A, Abdullah S, Amin F. Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems. JNT. 2018;:51–65.

MLA

Fahmi, Aliya, et al. “Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems”. Journal of New Theory, no. 22, Mar. 2018, pp. 51-65, https://izlik.org/JA63BM77YZ.

Vancouver

1.Aliya Fahmi, Saleem Abdullah, Fazli Amin. Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems. JNT [Internet]. 2018 Mar. 1;(22):51-65. Available from: https://izlik.org/JA63BM77YZ