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<p>This paper deals with a class of quadratic programming problems having intuitionistic fuzzy parameters and bounded constraints. Such problems are designed to handle uncertain parameters in quadratic programming and provide a better representation of many real-life situations. This study presents the utilization of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\alpha ,u)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((\beta ,v)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>β</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> cuts and a new solution methodology is suggested to obtain the lower and upper bounds of the objective function in the problem. Using the bounds obtained, we construct the membership and non-membership functions of the optimal values graphically. By expressing the optimal value through membership and non-membership functions instead of a crisp value, this method offers a more detailed and nuanced view of the data, which can lead to better-informed decision-making. Moreover, it has been found that the proposed method yields more efficient solutions, requiring less computational work. We illustrate the solution procedure of the proposed technique by applying it to a real-life problem in textile industry.</p>

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On a Novel Solution Methodology for Intuitionistic Fuzzy Quadratic Programming Problems with Application in Textile Industry

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • Shubhpreet Kaur,
  • Sumati Mahajan

摘要

This paper deals with a class of quadratic programming problems having intuitionistic fuzzy parameters and bounded constraints. Such problems are designed to handle uncertain parameters in quadratic programming and provide a better representation of many real-life situations. This study presents the utilization of \((\alpha ,u)\) ( α , u ) and \((\beta ,v)\) ( β , v ) cuts and a new solution methodology is suggested to obtain the lower and upper bounds of the objective function in the problem. Using the bounds obtained, we construct the membership and non-membership functions of the optimal values graphically. By expressing the optimal value through membership and non-membership functions instead of a crisp value, this method offers a more detailed and nuanced view of the data, which can lead to better-informed decision-making. Moreover, it has been found that the proposed method yields more efficient solutions, requiring less computational work. We illustrate the solution procedure of the proposed technique by applying it to a real-life problem in textile industry.