Development and Applications of Penalty-Based Aggregation Operators in Multicriteria Decision Making

Abstract

This article develops a new penalty-based aggregation operator known as the penalty-based induced ordered weighted averaging (P-IOWA) operator which is an extension of penalty-based ordered weighted averaging (P-OWA) operator. Our goal is to figure out how the induced variable realigns penalties when gathering information. We extend the P-OWA and P-IOWA operators with the different means such as generalized mean and quasi-arithmetic mean. This article also includes different families of P-OWA and P-IOWA operators. The value of these new operators is demonstrated through a case study centered on investment matters. This study evaluates the economic and governance performance of seven South Asian nations utilizing nine indicators from 2021 data. The research examines 5 economic indicators including GDP growth, exports and imports (% of GDP), inflation, and labor force metrics, alongside 4 governance indicators focusing on corruption control, government effectiveness, and political stability. We use min–max normalization to standardize the varied values, which originally ranged from 0.5% to 77.7% across various metrics. Following this, the normalized inverse penalty method is used to derive optimal weights for these indicators, tackling the task of combining multidimensional data. Subsequently, we implement and evaluate various penalty-based aggregation methodologies on the normalized data, each offering a distinct approach to penalizing outliers and balancing indicator weights. The study compares the results obtained from these operators to assess their impact on country rankings and overall performance evaluation. This approach allows for a comprehensive comparison of countries’ performances, integrating both economic and governance dimensions into a single, quantifiable framework.