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Abstract <p>This article presents an innovative defuzzification technique forvarious fuzzy numbers: triangular, trapezoidal, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8261_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\pi\)</EquationSource> <!--LobJMat2560623Khan-m1--> </InlineEquation>-type,cosine, increasing and decreasing concave, and heptagonal. Thestudy introduces a ranking method by utilizing the probabilitydensity function of their membership functions. To illustrate theuse of the proposed work, a production planning problem isdiscussed and solved under different fuzzy patterns. Mellintransform converts these fuzzy numbers into crisp numbers foroptimal comparison and solution. The solution process is tailoredto the decision maker’s value set.</p>

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A Comprehensive Study of Mellin’s Transformation on Diverse Fuzzy Numbers with Applications of Optimizing Production Planning

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Avesh Masood Khan,
  • Ahteshamul Haq,
  • Andrei Volodin,
  • Irfan Ali

摘要

Abstract

This article presents an innovative defuzzification technique forvarious fuzzy numbers: triangular, trapezoidal, \(\pi\) -type,cosine, increasing and decreasing concave, and heptagonal. Thestudy introduces a ranking method by utilizing the probabilitydensity function of their membership functions. To illustrate theuse of the proposed work, a production planning problem isdiscussed and solved under different fuzzy patterns. Mellintransform converts these fuzzy numbers into crisp numbers foroptimal comparison and solution. The solution process is tailoredto the decision maker’s value set.