Developing environmental indices using fuzzy numbers ordered weighted averaging (FN-OWA) operators

Environmental indices (EI) constitute a common communication tool that is often used to describe the overall status of environmental systems (air, water and soil). EI development entails the use of mathematical operators to aggregate various non-commensurate input parameters in a logical manner. The ordered weighted averaging (OWA) operator is a general mean type operator that provides flexibility in the aggregation process such that the aggregated value is bounded between minimum and maximum values of the input parameters. This flexibility of the OWA operator is realized through the concept of orness, which is a surrogate for decision maker’s attitude. The type of input parameters also affects the choice of aggregation operators. If the input parameters are linguistic or fuzzy, the aggregation through OWA operators is not possible, and the use of fuzzy arithmetic is warranted. The concept of fuzzy number OWA (FN-OWA) operators is explored to handle situations in which one or more input parameter has fuzzy (or linguistic) values. The proposed approach is demonstrated using data provided in an earlier study by Swamee and Tyagi (ASCE J Environ Eng 126(5):451–455, 2000) for establishing water quality indices. Multiple hypothetical scenarios are also generated to highlight the utility and sensitivity of the proposed approach.