Derived fuzzy importance of attributes based on the weakest triangular norm-based fuzzy arithmetic and applications to the hotel services

The correlation between the performance of attributes and the overall satisfaction such as they are perceived by the customers is often used to calculate the importance of attributes in the crisp case. Recently, the method was extended, based on the standard Zadeh extension principle, to the fuzzy case, taking into account the specificity of the human thinking. The difficulties of calculation are important and only approximations of the analytic results can be obtained. In the present paper we give a simplified and exact method to compute the derived importance of the attributes in the case of input data given by triangular fuzzy numbers. The effective calculation is based on the $T_{W}$-extension principle and it uses reasonable computer resources even if a large number of attributes and customers is considered. The proposed derived method is later on compared with other methods of calculation of the fuzzy importance of attributes. The results of a survey with respect to the quality of hotel services in Oradea (Romania) are subject to the application of the proposed method.