Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term, respectively. Complex neutrosophic set is an extension of the neutrosophic set. Further set theoretic operations such as complement, union, intersection, complex neutrosophic product, Cartesian product, distance measure, and δ-equalities of complex neutrosophic sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.

Agriculture has significantly aided in meeting the food needs of growing population. In addition, it has boosted economic development in irrigated regions. In this study, an assessment of the groundwater (GW) quality for agricultural land was carried out in El Kharga Oasis, Western Desert of Egypt. Several irrigation water quality indices (IWQIs) and geographic information systems (GIS) were used for the modeling development. Two machine learning (ML) models (i.e., adaptive neuro-fuzzy inference system (ANFIS) and support vector machine (SVM)) were developed for the prediction of eight IWQIs, including the irrigation water quality index (IWQI), sodium adsorption ratio (SAR), soluble sodium percentage (SSP), potential salinity (PS), residual sodium carbonate index (RSC), and Kelley index (KI). The physicochemical parameters included T°, pH, EC, TDS, K⁺, Na⁺, Mg²⁺, Ca²⁺, Cl⁻, SO₄²⁻, HCO₃⁻, CO₃²⁻, and NO₃⁻, and they were measured in 140 GW wells. The hydrochemical facies of the GW resources were of Ca-Mg-SO₄, mixed Ca-Mg-Cl-SO₄, Na-Cl, Ca-Mg-HCO₃, and mixed Na-Ca-HCO₃ types, which revealed silicate weathering, dissolution of gypsum/calcite/dolomite/ halite, rock–water interactions, and reverse ion exchange processes. The IWQI, SAR, KI, and PS showed that the majority of the GW samples were categorized for irrigation purposes into no restriction (67.85%), excellent (100%), good (57.85%), and excellent to good (65.71%), respectively. Moreover, the majority of the selected samples were categorized as excellent to good and safe for irrigation according to the SSP and RSC. The performance of the simulation models was evaluated based on several prediction skills criteria, which revealed that the ANFIS model and SVM model were capable of simulating the IWQIs with reasonable accuracy for both training “determination coefficient (R²)” (R² = 0.99 and 0.97) and testing (R² = 0.97 and 0.76). The presented models’ promising accuracy illustrates their potential for use in IWQI prediction. The findings indicate the potential for ML methods of geographically dispersed hydrogeochemical data, such as ANFIS and SVM, to be used for assessing the GW quality for irrigation. The proposed methodological approach offers a useful tool for identifying the crucial hydrogeochemical components for GW evolution assessment and mitigation measures related to GW management in arid and semi-arid environments.