Generalised L-R intuitionistic fuzzy number for river water pollution classification

Real-world problems are full of uncertainties, and in most cases, decisions are made in a situation of uncertainty. Uncertainty occurs due to ambiguous, vague, inconsistent, and imprecise information. Therefore, in order to model the uncertainty information comprehensively, a mathematical set theory is needed to cater all the information. The current intuitionistic fuzzy number still lacks in the comprehensiveness of decisionmaking evaluation due to the limitation of its left and right functions that only use linear functions as the left and right functions. Therefore, the L-R intuitionistic fuzzy number (LRIFN) introduces a more comprehensive approach by incorporating non-linear functions for left and right membership and non-membership functions, showing its capacity to represent the human thinking (decision-maker) which does not always linear. However, the existing L-R intuitionistic fuzzy number does not involve the decision-makers' perspective which has different levels of knowledge, experience, and background. Therefore, this research aims to introduce a generalised L-R intuitionistic fuzzy number (GLRIFN), which consider the different heights of the core for membership and non-membership degrees which can be determined by the confidence, reliability, or sureness level of the decision-maker.