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The use of a new technology for online teaching and learning, impacts the educational productivity by accelerating the rate of learning. E-learning is one of the most used strategic applications of information technology, more related to the educational field of teaching and learning. E-learning has been recognized as electronic learning via internet tool that allows teachers and students to interact together, and as a key determinant in increasing the performance of the education sector (Naveed et al., 2020). E-Learning Systems play an essential role in promoting new teaching methods. Learning Management Systems (LMS) are software platforms that deliver the learning material online. LMS in the academic field aimed to form good students with deep knowledge, and are also synonymous with e-learning in accordance with the use of web inside classroom (A. Khan & Q.Ullah, 2021). Google Classroom was introduced in 2014 as a LMS platform (Lapowsky, 2014), and has been evaluated as the best used in terms of discussing new knowledge out of time and distance (Falvo & Johnson, 2007). Moodle, Blackboard, Google Classroom are Learning Management System (LMS) become a prevalent tool in higher education institutions developed to support the implementation of distance teaching and learning processes (Alshehri et al., 2019). Among of them is mentioned the platform Google Classroom, being the most prevalent tool that has been integrated into higher education (Jakkaew & Hemrungrote, 2017). In the study of Jordan (Jordan & Duckett, 2018) are compared two LMS such as Blackboard and Google Classroom. Their comparison is first done in the context of how quickly students adapt each LMS respectively. The second point deals with the properties, the functionality of an LMS that can influence student engagement. The results of their study showed that students preferred Google Classroom because it was easy to use, free mobile app, files all in one place on Google Drive, so all these benefits makes the work easy in group. This application is effective for both students and teachers, so they can keep their files more organized, while being connected with a stream line of communication for sending/receiving their works within the deadlines. In order to explain the factors that impact the use of Google Classroom, were developed some theories that made predictions in the adoption and use of a new technology. Among of them the most widely used is the technology adoption model (TAM3) (Fishbein & Ajzen, 1975), with high prediction of technology adoption and use defined from (Davis et al., 1989) also Adams (Adams et al., 1992), and Venkatesh (Venkatesh & Davis, 2000). This theoretical model has been regarded as a base model in innovations adoption behaviour. TAM3 especially posits the individual behavioural intention to use an IT via two constructs: Perceived Usefulness and Perceived Ease of Use. Following Davis, Bagozzi, and Warshaw (Davis et al., 1992) PU defines the degree of believing that the use of an IT will increase a personal job performance (Venkatesh & Bala, 2008), while PEOU defines the degree for which an individual believes that the use of an IT have no exertion (Venkatesh et al., 2003). TAM3 has been considered as the most potencial model (Davis et al., 1989) with great impact in innovations adoption behavior (Pavlou, 2003). Making complex decisions in a better way is really complicated. The multi criteria decision making problems (MCDM) are a group of methods focused in the determination of the best choice for o complex problem (T. L. Saaty, 1978). The most popular among them is mentioned the AHP-method, that decomposes a complex problem in a hierarchical structure with criteria and alternatives by evaluating their weights and finally rank them according their importance to each other. To deal with uncertainty (Cheng et al., 1999) the AHP is expressed with fuzzy numbers (Zadeh, 1965), as Fuzzy AHP (FAHP). The expansion of AHP is in fact FAHP (Van Laarhoven & Pedrycz, 1983) in producing better decisions, and to tolerate the ambiguity and vagueness of information (Lee et al., 2008). There are some ways to construct the decision matrix for FAHP while calculating the relative importance of the attributes of the problem. An alternative way is the integration of TAM3 model results as the initializing for constructing the decision matrix in crisp numbers, then it is converted with fuzzy numbers applying all the steps of AHP and finally the deffuzification of fuzzy numbers into crisp numbers. The types of fuzzy numbers used are the trapezoidal fuzzy numbers. The FAHP is a better way for ranking criteria/alternatives under uncertainty (Aliyev et al., 2020).