<p>Complex fuzzy aggregation operators generalize the traditional fuzzy aggregation operators by associating complex-valued membership functions, providing a significant mathematical framework for modeling uncertainty and imprecision in decision-making problems. The problem addressed in this paper is the need for effective aggregation operators (AOs) in the complex fuzzy set (CFS) environment, particularly for decision-making in signal processing. Existing methods cannot handle probabilistic sum-based aggregation while maintaining normalization. To solve this, we introduced the concepts of new AOs in the environment of CFSs, called complex fuzzy normalized probabilistic sum aggregation operator (CFNPSAO) and complex fuzzy weighted normalized probabilistic sum aggregation operator (CFWNPSAO). Various properties of the AOs have been studied. A new distance measure (DM) was introduced based on CFSs. To demonstrate their effectiveness, we propose a decision-making algorithm for signal processing that utilizes CFNPSAO and complex fuzzy distance measure (CFDM) to select a reference signal among multiple signals. A numerical example illustrates the algorithm’s performance, achieving a choice function <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3220_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="77" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {C}}_{1}=0.912$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">C</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.912</mn> </mrow> </math></EquationSource> </InlineEquation> of the first signal, which is nearly close to threshold frequency <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3220_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta =0.9$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </math></EquationSource> </InlineEquation>. These findings underscore the potential of CFS-based techniques in advanced decision-making and signal processing applications.</p>

Some new aggregation operators and distance measures for complex fuzzy sets and their applications in decision-making problems

期刊论文
发表日期：

2025年5月3日

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Hikmat Ullah,
Madad Khan,
Zohaib Ahmad Khan,
Muhammad Zeeshan,
Sohail Iqbal,
Zeeshan Ali

摘要

Complex fuzzy aggregation operators generalize the traditional fuzzy aggregation operators by associating complex-valued membership functions, providing a significant mathematical framework for modeling uncertainty and imprecision in decision-making problems. The problem addressed in this paper is the need for effective aggregation operators (AOs) in the complex fuzzy set (CFS) environment, particularly for decision-making in signal processing. Existing methods cannot handle probabilistic sum-based aggregation while maintaining normalization. To solve this, we introduced the concepts of new AOs in the environment of CFSs, called complex fuzzy normalized probabilistic sum aggregation operator (CFNPSAO) and complex fuzzy weighted normalized probabilistic sum aggregation operator (CFWNPSAO). Various properties of the AOs have been studied. A new distance measure (DM) was introduced based on CFSs. To demonstrate their effectiveness, we propose a decision-making algorithm for signal processing that utilizes CFNPSAO and complex fuzzy distance measure (CFDM) to select a reference signal among multiple signals. A numerical example illustrates the algorithm’s performance, achieving a choice function ${\mathbb {C}}_{1}=0.912$ $C_{1} = 0.912$ of the first signal, which is nearly close to threshold frequency $\delta =0.9$ $δ = 0.9$ . These findings underscore the potential of CFS-based techniques in advanced decision-making and signal processing applications.