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<p>In this paper, we introduce an extension theory of the trapezoidal intuitionistic fuzzy numbers under intuitionistic hesitant fuzzy sets called trapezoidal hesitant intuitionistic fuzzy number (THIF-number). This new theory provides very effectively to model uncertainties of some events by several different trapezoidal intuitionistic fuzzy numbers based on the same support set in the set of real numbers <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41870_2025_2642_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation>. Also, to demonstrate the application of this theory, a new multi-criteria decision-making (MCDM) method based on THIF-numbers is presented. To do this, we first propose operations of THIF-numbers with properties. We second give score, standard deviation degree, deviation degree of THIF-numbers to compare THIF-numbers. We third develop geometric operators and arithmetic operators of THIF-numbers. Finally, a numerical example is presented to illustrate the application of the developed method in THIF-numbers.</p>

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Trapezoidal hesitant intuitionistic fuzzy numbers and their applications to multiple-criteria decision making problems

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Irfan Deli

摘要

In this paper, we introduce an extension theory of the trapezoidal intuitionistic fuzzy numbers under intuitionistic hesitant fuzzy sets called trapezoidal hesitant intuitionistic fuzzy number (THIF-number). This new theory provides very effectively to model uncertainties of some events by several different trapezoidal intuitionistic fuzzy numbers based on the same support set in the set of real numbers \(\mathbb {R}\) R . Also, to demonstrate the application of this theory, a new multi-criteria decision-making (MCDM) method based on THIF-numbers is presented. To do this, we first propose operations of THIF-numbers with properties. We second give score, standard deviation degree, deviation degree of THIF-numbers to compare THIF-numbers. We third develop geometric operators and arithmetic operators of THIF-numbers. Finally, a numerical example is presented to illustrate the application of the developed method in THIF-numbers.