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<p>The objective of this study is to enhance the design and functionality of practical applications in order to satisfy user requirements and expectations. A criterion is suggested for decision-making that relies on (p, q)-fractional fuzzy neural network in order to assess the best appropriate option for the use of S-boxes in image encryption applications. The proposed decision-making context uses (p, q)-fractional fuzzy numbers and Bonferroni mean sum operator to enhance decision-making processes under uncertain conditions. This analysis primarily aims to present the mathematical perception of (p, q)-fractional fuzzy information, which enables the depiction of uncertain and imprecise data that is commonly found in real-world decision-making contexts. After that, the scoring, and accuracy functions are introduced to guarantee precise management of fuzzy input data. Additionally, the Bonferroni mean operator exhibits a higher degree of generality when compared to basic averaging or geometric aggregation operators. The (p, q)-fractional fuzzy Bonferroni Mean aggregation operators, which are based on Bonferroni norms, are crucial in the aggregation of expert opinions. During the decision-making process, we collect expert insights regarding S-boxes, represented as (p, q)-fractional fuzzy numbers, which are then analyzed using the fuzzy neural network model. Following this, we implement the proposed decision-making models to identify the most suitable S-box. The (p, q)-FFBM operators calculate values at both the hidden and output layers, utilizing activation functions to generate the final output values. These results produce a prioritized list of S-boxes evaluated based on their overall performance against various criteria. The efficacy of this novel approach is confirmed through a comparative analysis with existing multi-criteria decision-making techniques. The findings reveal that the (p, q)-fractional fuzzy neural network method surpasses old-style methods in terms of flexibility, precision, and its capacity to manage uncertain, fuzzy information. Our methodology offers a forceful decision support framework, adept at addressing composite decision-making challenges in encryption and other diverse fields.</p>

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A Novel Decision-making Analytics for S-box Selection in Image Encryption Using Fuzzy Neural Network

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月12日

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  • Saifullah,
  • Saleem Abdullah,
  • Mian Babar,
  • Shah Sawar

摘要

The objective of this study is to enhance the design and functionality of practical applications in order to satisfy user requirements and expectations. A criterion is suggested for decision-making that relies on (p, q)-fractional fuzzy neural network in order to assess the best appropriate option for the use of S-boxes in image encryption applications. The proposed decision-making context uses (p, q)-fractional fuzzy numbers and Bonferroni mean sum operator to enhance decision-making processes under uncertain conditions. This analysis primarily aims to present the mathematical perception of (p, q)-fractional fuzzy information, which enables the depiction of uncertain and imprecise data that is commonly found in real-world decision-making contexts. After that, the scoring, and accuracy functions are introduced to guarantee precise management of fuzzy input data. Additionally, the Bonferroni mean operator exhibits a higher degree of generality when compared to basic averaging or geometric aggregation operators. The (p, q)-fractional fuzzy Bonferroni Mean aggregation operators, which are based on Bonferroni norms, are crucial in the aggregation of expert opinions. During the decision-making process, we collect expert insights regarding S-boxes, represented as (p, q)-fractional fuzzy numbers, which are then analyzed using the fuzzy neural network model. Following this, we implement the proposed decision-making models to identify the most suitable S-box. The (p, q)-FFBM operators calculate values at both the hidden and output layers, utilizing activation functions to generate the final output values. These results produce a prioritized list of S-boxes evaluated based on their overall performance against various criteria. The efficacy of this novel approach is confirmed through a comparative analysis with existing multi-criteria decision-making techniques. The findings reveal that the (p, q)-fractional fuzzy neural network method surpasses old-style methods in terms of flexibility, precision, and its capacity to manage uncertain, fuzzy information. Our methodology offers a forceful decision support framework, adept at addressing composite decision-making challenges in encryption and other diverse fields.