A cubic bipolar fuzzy set (CBFS) is a new approach in computational intelligence and decision-making under uncertainty. This model is the generalization of bipolar fuzzy sets to deal with two-sided contrasting features which can describe the information with a bipolar fuzzy number and an interval-valued bipolar fuzzy number simultaneously. In this paper, the Dombi’s operations are analyzed for information aggregation of cubic bipolar fuzzy numbers (CBFNs). The Dombi’s operations carry the advantage of more pliability and reliability due to the existence of their operational parameters. Owing to the pliable nature of Dombi’s operators, this research work introduces new aggregation operators named as cubic bipolar fuzzy Dombi weighted averaging (CBFDWA) operator and cubic bipolar fuzzy Dombi ordered weighted averaging (CBFDOWA) operator with -order and -order, respectively. Additionally, this paper presents some significant characteristics of suggested operators including, idempotency, boundedness and monotonicity. Moreover, a robust multi-criteria decision making (MCDM) technique is developed by using -CBFDWA and -CBFDWA operators. Based on the suggested operators a practical application is demonstrated towards MCDM under uncertainty. The comparison analysis of suggested Dombi’s operators with existing operators is also given to discuss the rationality, efficiency and applicability of these operators.
AtanassovK.T., Intuitionistic fuzzy sets, In: Intuitionistic Fuzzy Sets, Studies in Fuzziness and Soft Computing, 35. Physica, Heidelberg35 (1999), 1–137. https://doi.org/10.1007/978-3-7908-1870-31.
5.
XuZ.S. and YagerR.R., Some geometric aggregation operators basedon intuitionistic fuzzy sets, International Journal of GeneralSystems35 (2006), 417–433.
6.
YagerR.R., Pythagorean fuzzy subsets, Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting (2013), 57–61.
7.
YagerR.R., Pythagorean membership grades in multicriteria decisionmaking, IEEE Transactions on Fuzzy Systems22(4) (2014), 958–965.
8.
ZhangX. and XuZ., Extension of TOPSIS to multiple criteriadecision making with Pythagorean fuzzy sets, InternationalJournal of Intelligent Systems29(12) (2014), 1061–1078.
ZhangW.R., Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis, NAFIPS/IFIS/NASA94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige (1994), 305–309.
11.
ZhangW.R., Bipolar fuzzy sets, Proceedings of IEEE Inrenational Conference on Fuzzy Systems (1998), 835–840.
12.
LeeK.M., Bipolar-valued fuzzy sets and their basic operations, Proceedings of Internatinal Conference, Bangkok, Thailand, (2000), 307–317.
13.
LeeK.M., Comparison of interval-valued fuzzy sets, intuitionisticfuzzy sets, and bipolar-valued fuzzy sets, Journal of KoreanInstitute of Intelligent Systems14(2) (2004), 125–129.
WeiG., WeiC. and GaoH., Multiple attribute decision making withinterval-valued bipolar fuzzy information and their application toemerging technology commercialization evaluation, IEEE Access6 (2018), 60930–60955.
16.
JunY.B., KimC.S. and YangK.O., Cubic sets, Annals of FuzzyMathematics and Informatics4(1) (2012), 83–98.
17.
AslamM., AbdullahS. and UllahK., Bipolar fuzzy soft set and itsapplication in decision making, Journal of Intelligent & FuzzySystems27(2) (2014), 729–742.
18.
MahmoodT., MehmoodF. and khanQ., Multiple criteria decisionmaking based on bipolar-valued fuzzy set, Annals of FuzzyMathematics and Informatics11(6) (2016), 1003–1009.
19.
KaraaslanF., Neutrosophic Soft Set with Applications in DecisionMaking, International Journal of Information Science andIntelligent System4(2) (2015), 1–20.
20.
NazM. and ShabirM., On fuzzy bipolar soft sets, their algebraicstructures and applications, Journal of Intelligent & FuzzySystems26(4) (2014), 1645–1656.
21.
WeiG., AlsaadiF.E., HayatT. and AlsaediA., Bipolar fuzzy Hamacheraggregation operators in multiple attribute decision making, International Journal of Fuzzy Systems33(6) (2017), 1–12.
22.
DeliI., AliM. and SmarandacheF., Bipolar neutrosophic sets and their application based on multi-criteria decision making problems, Proceedings of the 2015 International Conference on Advanced Mechatronic Systems, Beijing, China, (2015).
23.
Akram ShumaizaM. and ArshadM., Bipolar fuzzy TOPSIS and bipolarfuzzy ELECTRE-I methods to diagnosis, Journal of Computationaland Applied Mathematics39 (2019), 1–21.
24.
YagerR.R., On ordered weighted averaging aggregation operators inmulti-criteria decision making, IEEE Transactions on Systems,Man and Cybernetics18(1) (1988), 183–190.
XuZ.S. and CaiX., Intuitionistic fuzzy information aggregation: theory and applications, SpringerHeidelberg New York Dordrecht London, (2012).
27.
PengX.D. and YuangH., Fundamental properties of Pythagorean fuzzyaggregation operators, Fundamenta Informaticae147(2016), 415–446.
28.
KhanF., KhanM.S.A., ShahzadM. and AbdullahS., Pythagorean cubicfuzzy aggregation operators and their apllication to multi-criteriadecision making problems, Journal of Intelligent & FuzzySystems36(1) (2019), 595–607.
29.
KaurG. and GargH., Multi-attribute decision-making based onBonferroni mean operators under cubic intuitionistic fuzzy setenvironment, Entropy20(1) (2018), 1–26.
30.
GargH., A new possibility degree measure for interval-valued q-rungorthopair fuzzy sets in decisionmaking, International Journalof Intelligent Systems36(1) (2021), 526–557.
31.
RiazM., GargH., FaridH.M.A. and ChinramR., Multi-criteriadecision making based on bipolar picture fuzzy operators and newdistance measures, Computer Modeling in Engineering andSciences127(2) (2021), 771–800.
32.
RiazM., PamucarD., FaridH.M.A. and HashmiM.R., q-Rung orthopair fuzzy prioritized aggregation operators and their application towards green supplier chain management, Symmetry12(6) (2020), 1–33.
33.
AshrafS., AbdullahS. and KhanS., Fuzzy decision support modelingfor internet finance soft power eval uation based on sinetrigonometric Pythagorean fuzzy information, Journal of Ambient Intelligence and Humanized Computing12(3) (2021), 3101–3119.
34.
DombiJ., A general class of fuzzy operators, the demorgan class offuzzy operators and fuzziness measures induced by fuzzy operators, Fuzzy Sets and Systems8(2) (1982), 149–163.
35.
LiuP., LiuJ. and ChenS.M., Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making, Journal of the Operational Research Society69(1) (2017), 1–24.
36.
LiuZ., WangS. and LiuP., Multiple attribute group decision makingbased on q-rung orthopair fuzzy Heronian mean operators, International Journal of Intelligent Systems33(3) (2018), 2341–2363.
37.
LiuZ., WangX., LiL., ZhaoX. and LiuP., Q-rung orthopair fuzzy multiple attribute group decision-making method based on normalized bidirectional projection model and generalized knowledge-based entropy measure, Journal of Ambient Intelligence and Humanized Computing12(8) (2021), 2715–2730.
38.
LiuP. and WangP., Some q-rung orthopair fuzzy aggregationoperators and their applications to multipleattribute decisionmaking, International Journal of Intelligent Systems33(4) (2017), 1–22.
39.
JanaC., PalM. and WangJ.Q., Bipolar fuzzy Dombi aggregationoperators and its application in multipleattribute decision-makingprocess, Journal of Ambient intelligence and HumanizedComputing10 (2019), 3533–3549.
40.
AkramM., DudekW.A. and DarJ.M., Pythagorean Dombi fuzzyaggregation operators with application in multicriteriadecision-making, International Journal of Intelligent Systems34(3) (2019), 3000–3019.
41.
KhanA.A., AshrafS., AbdullahS., QiyasM., LuoJ. and KhanS.U., Pythagorean fuzzy Dombi aggregation operators and their applicationin decision support system, Symmetry11(3) (2019), 1–19.
42.
ChenJ. and YeJ., Some single-valued neutrosophic Dombi weightedaggregation operators for multiple attribute decision-making, Symmetry9(6) (2017), 82.
43.
RiazM. and HashmiM.R., A novel approach to censuses process byusing Pythagorean m-polar fuzzy Dombi’s aggregation operators, Journal of Intelligent & Fuzzy Systems38(2) (2020), 1977–1995.
44.
ShiL. and YeJ., Dombi aggregation operators of neutrosophic cubicsets for multiple attribute decisionmaking, Algorithms11(3) (2018), 29.
45.
RiazM. and TehrimS.T., Multi-attribute group decision making basedon cubic bipolar fuzzy information using averaging aggregationoperators, Jouranl of Intelligent & Fuzzy Systems37(2) (2019), 2473–2494.
46.
RiazM. and TehrimS.T., Cubic bipolar fuzzy ordered weightedgeometric aggregation operators and their application using internaland external cubic bipolar fuzzy data, Computational andApplied Mathematics38(2) (2019), 87.
47.
RiazM. and TehrimS.T., Cubic bipolar fuzzy set with application tomulti-criteria group decision making using geometric aggregationoperators, Soft Computing24(16) (2020), 16111–16133.
