Developing Environmental Indices using Fuzzy Numbers Ordered Weighted Averaging (FN-OWA) Operators

Environmental indices (EI) are common communication tool used to describe the overall status of environmental systems (e.g. air, water, soil). Development of EI entails the use of mathematical operators to aggregate various non-commensurate input parameters in a logical manner. 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 OWA operator is realized through the concept of orness, which is a surrogate for decision maker’s attitude. For the development of environmental indices, 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. To develop EI, the concept of FN-OWA (fuzzy number OWA) operators is explored to handle the situations when one ore more input parameter has fuzzy (or linguistic) values. The proposed approach is demonstrated using data provided in an earlier study by Swamee and Tyagi (2000) for establishing water quality indices. Multiple hypothetical scenarios are also generated to highlight the utility and the sensitivity of the proposed approach.