Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices

Abstract

This paper explores the application of ordered weighted averaging (OWA) operators to develop water quality index, which incorporates an attitudinal dimension in the aggregation process. The major thrust behind selecting the OWA operator for aggregation of multi-criteria is its capability to encompass a range of operators bounded between minimum and maximum. A new approach for generating OWA weight distributions using probability density functions (PDFs) is proposed in this paper. The basic parameters (mean and standard deviation) of the probability density functions can be determined using the number of criteria (e.g., water quality indicators) in the aggregation process. The proposed approach is demonstrated using data provided in a study by Swamee and Tyagi [Swamee, P.K., Tyagi, A., 2000. Describing water quality with aggregate index. ASCE Journal of Environmental Engineering 126 (5), 451–455] for establishing water quality indices. The Normal distribution and its inverse form were found suitable for compromising or normative decisions, whereas the Exponential and its inverse form were found suitable for pro-risk and risk-averse decisions, respectively. The proposed OWA weight distributions are also compared with the commonly used regular increasing monotone (RIM) functions for generating OWA weights. Sensitivity analyses are carried out to highlight the utility of the proposed approach for multi-criteria decision-making and establishing water quality indices.