A complex fuzzy set, characterized by complex-valued membership functions, is a generalization of a fuzzy set. In this paper, we present complex fuzzy arithmetic aggregation (CFAA) operators, complex fuzzy weighted arithmetic aggregation (CFWAA) operators. Based on the partial ordering of complex fuzzy values, we develop complex fuzzy ordered weighted arithmetic aggregation (CFOWAA) operators. Highly pertinent to complex fuzzy operations is the concept of rotational. This concept has been developed for complex fuzzy aggregation operators. We show that CFAA, CFWAA and CFOWAA operators possess the property of rotational invariance. Moreover, based on the relationship between Pythagorean membership grades and complex numbers, these operators are studied under Pythagorean fuzzy values.
D.Ramot, M.Friedman, G.Langholz and A.Kandel, Complex fuzzy logic, IEEE Trans Fuzzy Syst11 (2003), 450–461.
4.
S.Dick, Towards complex fuzzy logic, IEEE Trans Fuzzy Syst13 (2005), 405–414.
5.
B.Hu, L.Bi and S.Dai, The orthogonality between complex fuzzy sets and its application to signal detection, Symmetry9 (2017), 175.
6.
L.Bi, B.Hu, S.Li and S.Dai, The parallelity of complex fuzzy sets and parallelity preserving operators, JIntell Fuzzy Syst34 (2018), 4173–4180.
7.
B.Hu, L.Bi, S.Dai and S.Li, The approximate parallelity of complex fuzzy sets, J Intell Fuzzy Syst. DOI: 10.3233/JIFS-181131
8.
G.T.Zhang, S.Dillon, K.Y.Cai, J.Ma and J.Lu, Operation properties and Ä-equalities of complex fuzzy sets, Int J Approx Reason50 (2009), 1227–1249.
9.
A.U.M.Alkouri and A.R.Salleh, Linguistic variables, hedges and several distances on complex fuzzy sets, J Intell Fuzzy Syst26 (2014), 2527–2535.
10.
D.E.Tamir, J.Lin and A.Kandel, A new interpretation of complex membership grade, Int J Intell Syst26 (2011), 285–312.
11.
D.E.Tamir and A.Kandel, Axiomatic theory of complex fuzzy logic and complex fuzzy classes, Int J Comp Comm Control6 (2011), 562–576.
12.
D.E.Tamir, M.Last and A.Kandel, Generalized complex fuzzy propositional logic, in Proc World C Soft Computing, San Francisco, CA, USA,2011.
13.
S.Greenfield, F.Chiclana and S.Dick, Interval-valued complex fuzzy logic, Fuzzy Systems (FUZZ-IEEE), 2016 IEEE International Conference on IEEE, 2016, pp. 2014–2019.
14.
S.Greenfield, F.Chiclana and S.Dick, Join and meet operations for interval-valued complex fuzzy logic, Fuzzy Information Processing Society (NAFIPS), 2016 Annual Conference of the North American IEEE, 2016, pp. 1–5.
15.
R.R.Yager, Pythagorean membership grades in multi-criteria decision making, IEEE Trans Fuzzy Syst22(4) (2014), 958–965.
16.
R.R.Yager, Pythagorean fuzzy subsets, In: Proceedings of the Joint IFSA Congress and NAFIPS Meeting, Edmonton, Canada,2013, pp. 57–61.
R.R.Yager and A.M.Abbasov, Pythagorean membership grades, complex numbers and decision-making, Int J Intell Syst28 (2013), 436–452.
19.
S.Dick, R.R.Yager and O.Yazdanbahksh, On pythagorean and complex fuzzy set operations, IEEE Trans Fuzzy Syst24 (2016), 1009–1021.
20.
R.R.Yager, On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Trans Syst Man Cyber net B18(1) (1988), 183–190.
Z.S.Xu and R.R.Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int J General Systems35 (2006), 417–433.
23.
Z.S.Xu, Intuitionistic Fuzzy Aggregation and Clustering, Springer, Berlin, 2013.
24.
S.Zeng, Z.Mu and T.Balezentis, A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making, Int J Intell Syst33 (2018), 573–585.
25.
X.L.Zhang, A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making, Int J Intell Syst31(6) (2016), 593–611.
