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A decision-making framework based on complex fuzzy bipolar soft sets for investment strategy optimization.

Fazli Amin^1,2, Zia Ullah³, Sidra Niaz⁴

¹Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, Pakistan. fazliamin@hu.edu.pk.

Scientific Reports

|June 24, 2026

Summary

This study introduces a new Complex Fuzzy Bipolar Soft Set (CFBSS) framework to improve decision-making under uncertainty and time-varying conditions. The CFBSS framework enhances ranking stability and adaptability for complex real-world problems.

Keywords:

Aggregation operators Bipolar soft sets Complex fuzzy sets Investment strategy MCDM

Related Experiment Videos

Area of Science:

Decision Sciences
Fuzzy Set Theory
Soft Set Theory

Background:

Existing fuzzy and soft set models struggle with decision-making under uncertainty, bipolarity, and periodic behaviors, leading to information loss and unstable rankings.
Complex fuzzy sets offer amplitude-phase representations for periodicity, while bipolar soft sets handle positive-negative assessments.

Purpose of the Study:

To propose the Complex Fuzzy Bipolar Soft Set (CFBSS) framework, integrating complex fuzzy sets with bipolar soft sets.
To develop novel operational laws, score/accuracy functions, distance/entropy measures, and aggregation operators for the CFBSS framework.
To introduce a Multi-Criteria Decision Making (MCDM) algorithm using the CFBSS framework and assess its performance.

Main Methods:

Integration of complex fuzzy set theory (for periodicity) and bipolar soft set theory (for bipolarity).
Development of new mathematical operations, including aggregation operators (CFBSSWA, CFBSOWA, CFBSHWA) and their properties.
Application of a novel MCDM algorithm to a case study on solar panel selection for investment strategy optimization.

Main Results:

The proposed CFBSS framework demonstrates preliminary improvements in ranking stability, adaptability, and interpretability compared to existing methods.
Novel operational laws, distance/entropy measures, and aggregation operators were successfully developed and their mathematical properties verified.
The MCDM algorithm applied to solar panel selection showed promising results in optimizing investment strategies under uncertainty.

Conclusions:

The CFBSS framework offers a robust approach to handle dual and time-varying uncertainties in decision-making processes.
The developed MCDM algorithm provides a stable and adaptable method for complex selection problems.
Potential applications span finance, healthcare, engineering, and other fields requiring sophisticated uncertainty management.