| | | |

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

#### Aliya Fahmi [1] , Saleem Abdullah [2] , Fazli Amin [3]

##### 65 60

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.

Trapezoidal cubic fuzzy number, aggregation operators, multi-criteria decision making
• [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).
Birincil Dil en Mühendislik Araştırma Makalesi Yazar: Aliya Fahmi Yazar: Saleem Abdullah Yazar: Fazli Amin
 Bibtex @araştırma makalesi { jnt414107, journal = {Journal of New Theory}, issn = {}, eissn = {2149-1402}, address = {Gaziosmanpaşa Üniversitesi}, year = {2018}, volume = {}, pages = {51 - 65}, doi = {}, title = {Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems}, key = {cite}, author = {Abdullah, Saleem and Amin, Fazli and Fahmi, Aliya} } 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. Retrieved from http://dergipark.gov.tr/jnt/issue/36299/414107 MLA 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". Journal of New Theory (2018): 51-65 Chicago 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". Journal of New Theory (2018): 51-65 RIS TY - JOUR T1 - Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems AU - Aliya Fahmi , Saleem Abdullah , Fazli Amin Y1 - 2018 PY - 2018 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 51 EP - 65 VL - IS - 22 SN - -2149-1402 M3 - UR - Y2 - 2018 ER - EndNote %0 Journal of New Theory Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems %A Aliya Fahmi , Saleem Abdullah , Fazli Amin %T Expected Values of Aggregation Operators on Cubic Trapezoidal Fuzzy Number and its Application to Multi-Criteria Decision Making Problems %D 2018 %J Journal of New Theory %P -2149-1402 %V %N 22 %R %U 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 (Mart 2018): 51-65.