A New Extended-MULTIMOORA Technique for Selecting Efficient Water Purification Strategy Under ff'-Fractional Linguistic Term Set

The main objective of water purification processes is to remove harmful chemical compounds and microorganisms from water sources to produce suitable water for human consumption. Water purification plays a pivotal role in meeting the critical demand for clean drinking water across diverse industries, including medical, pharmaceutical, and chemical sectors. Its significance extends beyond industry needs, impacting the resilience and prosperity of nations. As a result, experts around the world are studying several potential technologies to increase and maintain water supplies. In regions susceptible to drought, the need for innovative water purification strategies is even more critical. This article presents a novel approach, the "Extended MULTIMOORA" method utilizing ff' -fractional linguistic term sets ff' -FLTSs), to address the challenge of selecting the most effective water purification process. This article introduces the concepts of arithmetic mean, geometric mean, weighted averaging, and weighted geometric operators for ff' -FLTSs and investigate its several important key features. In decision-making problems, when the weights of the decision makers are unknown, the decision-making process is more difficult, we introduce an entropy measure and a distance measure to find the weight information. Furthermore, we effectively apply the proposed technique and newly defined operators to select the best technique for purifying water at a commercial scale. At last, we establish a comparative analysis to show the validity and feasibility of the proposed techniques compared to existing methods.