Picture Fuzzy Soft-Hypersoft Sets, Information Measures and Aggregation Operators in Decision-Making Applications

Abstract

The thesis titled “Picture Fuzzy Soft-Hypersoft Sets, Information Measures & Aggregation Operators in Decision-Making Applications” explores picture fuzzy information within the framework of soft-hypersoft sets and their applications in decision-making using various information measures and aggregation operators. It introduces extensions of picture fuzzy sets, including bi-parametric discriminant measures, picture fuzzy soft sets, picture fuzzy hypersoft sets/matrices, and q-rung picture fuzzy sets,with applications in hydrogen fuel cell technology, sustainable agrifarming, renewable energy source selection, and green supply chain management. The thesis begins with a comprehensive background on picture fuzzy sets and their extensions, including definitions, operations, and a literature survey. A bi-parametric picture fuzzy discriminant measure is proposed, mathematically validated, and integrated with modified VIKOR and TOPSIS methods to assess hydrogen fuel cell technologies. Modified picture fuzzy soft Dombi aggregation operators and their algebraic properties are introduced and applied within the EDAS methodology to prioritize factors for sustainable agrifarming. Furthermore, the concept of picture fuzzy hypersoft sets and similarity measures is developed, with the proposed properties validated through numerical illustrations and comparative analyses. Picture fuzzy hypersoft matrices are constructed to organize information, and new choice and value matrices are introduced to address renewable energy source selection problems. In addition this, a modified q-rung picture fuzzy AHP/WASPAS methodology is presented, overcoming restrictions on uncertainty components. This methodology is applied to green supply chain management for strategic planning in the energy sector. The thesis concludes by summarizing its findings and contributions, highlighting the theoretical advancements and practical applicability of the proposed methodologies. Additionally, potential directions for future work are discussed, including further generalizations of picture fuzzy hypersoft sets and their applications to more complex multi-criteria decision-making problems across diverse domains.