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<p>Matrices are a unifying concept that permeates diverse fields of study and provides a common framework for expressing and solving problems in all fields, including decision-making. In most decision-making scenarios, addressing uncertainty is paramount as real-world scenarios often involve incomplete information, ambiguous data, and unpredictable factors. The aptness of a picture fuzzy hypersoft set as a parameterization tool becomes evident when dealing with the complexities and challenges associated with managing imprecise data. In this article, we have initially developed the notions of the picture fuzzy hypersoft matrices (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44196_2025_997_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\( {\textbf{P}^{\mathbb{F}\mathbb{H}}}_{\mathbb{S}\mathbb{M}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <msup> <mi mathvariant="bold">P</mi> <mrow> <mi mathvariant="double-struck">F</mi> <mi mathvariant="double-struck">H</mi> </mrow> </msup> </mrow> <mrow> <mi mathvariant="double-struck">S</mi> <mi mathvariant="double-struck">M</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) and their basic operations based on the enhanced framework of the picture fuzzy hypersoft set. We then proposed the ideas of fundamental operational principles for picture fuzzy hypersoft numbers based on the structure of picture fuzzy hypersoft matrices. Furthermore, the concepts for picture fuzzy hypersoft geometric aggregation operators have been presented. The application of picture fuzzy hypersoft geometric aggregation operators to energy policy design signifies a bridge between theoretical advancements and practical decision-making. The inclusion of a decision-making approach, explanatory example, and comparative analysis enhances the understanding of how the developed theory can be effectively used and demonstrates its potential contributions to the field of informed decision-making using human intuitionistic data.</p>

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Assimilation of Matrix Operations with Picture Fuzzy Hypersoft Structures for Complex Decision Scenarios

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月6日

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  • Muhammad Imran Harl,
  • Muhammad Saeed,
  • Muhammad Haris Saeed,
  • Muhammad Salman Habib,
  • Mehran Ullah

摘要

Matrices are a unifying concept that permeates diverse fields of study and provides a common framework for expressing and solving problems in all fields, including decision-making. In most decision-making scenarios, addressing uncertainty is paramount as real-world scenarios often involve incomplete information, ambiguous data, and unpredictable factors. The aptness of a picture fuzzy hypersoft set as a parameterization tool becomes evident when dealing with the complexities and challenges associated with managing imprecise data. In this article, we have initially developed the notions of the picture fuzzy hypersoft matrices ( \( {\textbf{P}^{\mathbb{F}\mathbb{H}}}_{\mathbb{S}\mathbb{M}}\) P F H S M ) and their basic operations based on the enhanced framework of the picture fuzzy hypersoft set. We then proposed the ideas of fundamental operational principles for picture fuzzy hypersoft numbers based on the structure of picture fuzzy hypersoft matrices. Furthermore, the concepts for picture fuzzy hypersoft geometric aggregation operators have been presented. The application of picture fuzzy hypersoft geometric aggregation operators to energy policy design signifies a bridge between theoretical advancements and practical decision-making. The inclusion of a decision-making approach, explanatory example, and comparative analysis enhances the understanding of how the developed theory can be effectively used and demonstrates its potential contributions to the field of informed decision-making using human intuitionistic data.