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. 2025 Jul 1;15(1):20706.
doi: 10.1038/s41598-025-07896-5.

A decision-theoretic framework for wastewater treatment performance assessment based on a fuzzy parameterized fuzzy hypersoft set approach

Muhammad Haris Saeed  1 , Fatima Razaq  2 , Muhammad Saeed  2 , Muhammad Salman Habib  3 , Seung-June Hwang  4
Affiliations

A decision-theoretic framework for wastewater treatment performance assessment based on a fuzzy parameterized fuzzy hypersoft set approach

Muhammad Haris Saeed et al. Sci Rep. .

Abstract

The economic development of a country is profoundly influenced by how it protects and utilizes its natural resources, one of which is wastewater, with emphasis on environmental sustainability. For this multi-factorial sustainability analysis, this study introduces a novel Fuzzy Parameterized Fuzzy Hypersoft Set (FPFHSS) structure to develop a comprehensive decision-making and performance evaluation system for wastewater treatment facilities. The practicality of the designed system is explored by highlighting its ability to evaluate urban projects and work as a decision-making system for environmental policy design. The study introduces an algorithm based on the hypersoft structure, allowing the division of attributes into sub-attributes for a more concise analysis. The sub-parametric values are first parameterized into fuzzy numbers and then evaluated based on their relative importance. With proper fuzzy parameterization of each sub-attribute, novel specialized FPFHSS based Technique of Ordered Preference Similar to Ideal Solution (TOPSIS) and Multi-Objective Optimization on the basis of a Ratio Analysis (MULTIMOORA) approaches are developed that provide a versatile analysis in addition to the newly developed algorithm. With these 3 specialized systems, 4 case studies were developed based on 19 pseudo-realistic environmental, social, technical, and economic factors each simulating a different scenario faced by nations highlighting sustainability, technical performance and the environment allowing for informed decision-making while addressing uncertainty making them highly suitable as a computational AI solution for real-data analysis. This fuzzy analysis offers a reference for making informed decisions in the context of environmental remediation and complex scenario simulations.

Keywords: Decision Making; Environmental Policy Design; Fuzzy Set; Hypersoft Set; Optimization; Sustainability; Wastewater.

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Conflict of interest statement

Declarations. Competing interests: The authors don’t have competing interest to declare.

Figures

Fig. 1
Fig. 1
Design of the Study.
Fig. 2
Fig. 2
A sub-attributive division of criteria considered for performance analysis.
Fig. 3
Fig. 3
Graphical Representation of Rankings obtained from the Simulation Analysis.
See this image and copyright information in PMC

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