Innovative Bonferroni Mean Product and Linear Diophantine Fuzzy Bipartite Decision Graphs With Application to Sustainable Development

Abstract

In multi-criteria decision-making (MCDM) situations, it is widely noticed that the resolution method is impacted by the existence of imprecise information and uncertainty in the decision maker’s assessment. Existing fuzzy models are insufficient in controlling these uncertainties to achieve a suitable balance in decision-making processes. Linear Diophantine fuzzy sets (LDFSs) are a powerful fuzzy model that uses control (reference) parameters to address these difficult challenges. This work proposes two unique concepts: linear Diophantine fuzzy bipartite decision graphs and Bonferroni mean linear Diophantine fuzzy aggregation operators. A strong MCDM framework is provided, based on linear Diophantine fuzzy bipartite decision graphs and Bonferroni mean linear Diophantine fuzzy aggregation operators. The concept of the linear Diophantine fuzzy degree provides a metric value that reflects the impact and relevance of vertices in a linear Diophantine fuzzy network, hence improving decision-making. The result of this research is the development of a complete decision-making system that makes use of the linear Diophantine fuzzy bipartite decision graph and the Bonferroni mean product. The use of this strategy to eliminate poverty in Pakistan demonstrates its effectiveness and versatility in dealing with real-world challenges. This research shows great promise for addressing complex socioeconomic challenges, providing critical information for policymakers, analysts, and academic researchers looking for novel solutions across several sectors.

Keywords

• Linear Diophantine fuzzy set
• Bonferroni mean
• aggregation operator
• fuzzy graphs
• decision-making