The RMSE associated with the validation and training data are reported in Tables 3–5 for all conditions. Clustering parameters and epochs in which validation and training errors are minimized simultaneously are also reported in the tables. As is apparent from the tables, all ANFIS models compared to initial FIS models performed well enough. For instance, the RMSE obtained by the FIS model for estimating the velocity of longshore currents at the general condition is 0.0932 while it is equal to 0.0895 for the ANFIS model. This shows the efficiency of the training process to tune fuzzy antecedent and consequent parameters. In this model, the appropriate number of fuzzy IF-THEN rules is 4 in accordance with the following clustering parameters:

Table 3

The RMSE of training and validation data sets estimated by the FIS and ANFIS models to estimate coastal current velocities at the general condition

Model type .	FIS .	ANFIS .
Longshore direction
Training error (m/s)	0.0932	0.0895
Validation error (m/s)	0.0951	0.0893
Number of rules	4	4
Desirable epoch	125
Clustering parameters	= [0.56, 0.6, 0.3, 0.6, 0.6, 0.6, 0.6, 2]
Cross-shore direction
Training error (m/s)	0.0676	0.0575
Validation error (m/s)	0.0563	0.0545
Number of rules	4	4
Desirable epoch	104
Clustering parameters	= [0.56, 0.56, 0.3, 0.6, 0.6, 0.6, 0. 6, 2]

Model type .	FIS .	ANFIS .
Longshore direction
Training error (m/s)	0.0932	0.0895
Validation error (m/s)	0.0951	0.0893
Number of rules	4	4
Desirable epoch	125
Clustering parameters	= [0.56, 0.6, 0.3, 0.6, 0.6, 0.6, 0.6, 2]
Cross-shore direction
Training error (m/s)	0.0676	0.0575
Validation error (m/s)	0.0563	0.0545
Number of rules	4	4
Desirable epoch	104
Clustering parameters	= [0.56, 0.56, 0.3, 0.6, 0.6, 0.6, 0. 6, 2]

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Table 4

The RMSE of training and validation data sets estimated by the FIS and ANFIS models to estimate coastal current velocities at the stormy condition

Model type .	FIS .	ANFIS .
Longshore direction
Training error (m/s)	0.1034	0.0990
Validation error (m/s)	0.0970	0.0935
Number of rules	5	5
Desirable epoch	19
Clustering parameters	= [0.4, 0.6, 0.5, 0.5, 0.5, 0.6, 0.6, 2]
Cross-shore direction
Training error (m/s)	0.1015	0.0763
Validation error (m/s)	0.0769	0.0653
Number of rules	3	3
Desirable epoch	32
Clustering parameters	= [0.56, 0.56, 0.56, 0.6, 0.6, 0.6, 0. 6, 2]

Model type .	FIS .	ANFIS .
Longshore direction
Training error (m/s)	0.1034	0.0990
Validation error (m/s)	0.0970	0.0935
Number of rules	5	5
Desirable epoch	19
Clustering parameters	= [0.4, 0.6, 0.5, 0.5, 0.5, 0.6, 0.6, 2]
Cross-shore direction
Training error (m/s)	0.1015	0.0763
Validation error (m/s)	0.0769	0.0653
Number of rules	3	3
Desirable epoch	32
Clustering parameters	= [0.56, 0.56, 0.56, 0.6, 0.6, 0.6, 0. 6, 2]

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Table 5

The RMSE of training and validation data sets estimated by the FIS and ANFIS models to estimate coastal current velocities at the windy condition

Model type .	FIS .	ANFIS .
Longshore direction
Training error (m/s)	0.1071	0.1012
Validation error (m/s)	0.1028	0.0989
Number of rules	4	4
Desirable epoch	19
Clustering parameters	= [0.3, 0.5, 0.36, 0.56, 0.5, 0.5, 0.56, 2]
Cross-shore direction
Training error (m/s)	0.0588	0.0497
Validation error (m/s)	0.0534	0.0500
Number of rules	4	4
Desirable epoch	29
Clustering parameters	= [0.3, 0.3, 0.5, 0.56, 0.36, 0.56, 0.56, 2]

Model type .	FIS .	ANFIS .
Longshore direction
Training error (m/s)	0.1071	0.1012
Validation error (m/s)	0.1028	0.0989
Number of rules	4	4
Desirable epoch	19
Clustering parameters	= [0.3, 0.5, 0.36, 0.56, 0.5, 0.5, 0.56, 2]
Cross-shore direction
Training error (m/s)	0.0588	0.0497
Validation error (m/s)	0.0534	0.0500
Number of rules	4	4
Desirable epoch	29
Clustering parameters	= [0.3, 0.3, 0.5, 0.56, 0.36, 0.56, 0.56, 2]

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