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

Research Article

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

Year 2018, Issue: 22, 51 - 65, 26.03.2018

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.
[11] J Q. Wang, Study on multi-criteria decision-making approach with incomplete certain information. Central South University, 2005
[12] J P. Xu, Technique of order preference by similarity to ideal and anti-ideal alternative for multiple attribute group decision making problems based on Hausdorff metric. Systems Engineering Theory and Practice, 2002, 22(10): 84-93.
[13] Z S. Xu, Study on method for triangular fuzzy numberbased multi-attribute decision making with preference information on alternatives. Systems Engineering and Electronics, 2002, 24(8): 9-12.
[14] L. A. Zadeh, Fuzzy Sets, Inf. Control, 8 (3), 338-353: (1965).

Year 2018, Issue: 22, 51 - 65, 26.03.2018

Aliya Fahmi Saleem Abdullah Fazli Amin

Abstract

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.
[11] J Q. Wang, Study on multi-criteria decision-making approach with incomplete certain information. Central South University, 2005
[12] J P. Xu, Technique of order preference by similarity to ideal and anti-ideal alternative for multiple attribute group decision making problems based on Hausdorff metric. Systems Engineering Theory and Practice, 2002, 22(10): 84-93.
[13] Z S. Xu, Study on method for triangular fuzzy numberbased multi-attribute decision making with preference information on alternatives. Systems Engineering and Electronics, 2002, 24(8): 9-12.
[14] L. A. Zadeh, Fuzzy Sets, Inf. Control, 8 (3), 338-353: (1965).

There are 14 citations in total.

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
Published in Issue	Year 2018 Issue: 22

Cite

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.
AMA	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. March 2018;(22):51-65.
Chicago	Fahmi, Aliya, Saleem Abdullah, and Fazli Amin. “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 (March 2018): 51-65.
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	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, March 2018.
ISNAD	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 22 (March 2018), 51-65.
JAMA	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, 2018, pp. 51-65.
Vancouver	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.