Novel concept of linguistic fractional fuzzy information for effective water filtration decision-making problem based on WASPAS method

The main purpose of water filtration techniques is to eliminate poisonous chemicals and microbes from sources of water in order to provide clear and safe water. Water purification is necessary for supplying the vital need for clean water to consume in a variety of areas, which involves the biological, medication, and health care industries. Despite the demands of manufacturing, its importance affects a country's stability and success. Experts throughout the globe are thus investigating a number of promising methods to expand and preserve water supply. Finding the optimal water filtration technique for optimizing the health of humans requires the implementation of multi-criteria decision-making (MCDM) techniques. Therefore, the current manuscript addresses the task of identifying the best water filtration technique by introducing a novel method called the "LFF-WASPAS technique," relying on the implementation of linguistic fractional fuzzy set (LFFS). An LFFS serves as a generalization of all linguistic fuzzy sets. For this reason, at first, we address the linguistic fractional fuzzy sets along with their weighted averaging and weighted geometric aggregation operators (AoPs), in addition to various basic properties of all of these AoPs. Finding the weight data used in decision-making situations becomes more challenging whenever the experts' weights are missing. To address this, we present an entropy measure and an Analytic Hieratical Process (AHP). Additionally, we successfully use the freshly described operators and the suggested strategy to choose the most efficient approach for water filtration on a commercial scale. Finally, we investigate the sensitive hypothesis over the suggested method in relation to water filtration techniques. Additionally, by contrasting the suggested decision-making method with those that already are available, we assess their effectiveness and reliability.