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<p>Multi-objective optimization problems play a crucial role in addressing and optimizing a wide range of real-world challenges. It is often impractical to obtain a single solution that simultaneously satisfies all objectives. Nevertheless, in the realm of multi-objective programming problems, there is considerable potential to identify compromise solutions. The ideas of fuzzy and intuitionistic fuzzy sets are both expanded by the neutrosophic set, which serves as an effective tool in this context. This study focusses on the efficient solution of multi-objective non-linear optimization problems involving uncertain parameters represented by triangular single valued neutrosophic numbers. Many existing techniques for such problems rely on linear membership and non-membership functions, which may not accurately model every real-life problem. To overcome this limitation, this study extends well-established solution methodologies, including Zimmermann’s method, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:\gamma\:\)</EquationSource> </InlineEquation>-operator and Maximum additive operator method, by introducing non-linear (exponential, t-parametric) truth membership, indeterminacy membership and falsity membership functions in place of linear ones and providing supporting theorems. To illustrate the proposed technique, a numerical example of manufacturing system in a neutrosophic fuzzy environment is presented. Further, a case study on a portfolio selection model with sustainable investment is solved and the results obtained by the proposed method using various membership are compared. In conclusion, the study summarizes its findings and outline potential areas for future research based on this work.</p>

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Generalized non-linear neutrosophic fuzzy optimization technique to portfolio selection model with sustainable investment

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Swarup Jana,
  • Sahidul Islam

摘要

Multi-objective optimization problems play a crucial role in addressing and optimizing a wide range of real-world challenges. It is often impractical to obtain a single solution that simultaneously satisfies all objectives. Nevertheless, in the realm of multi-objective programming problems, there is considerable potential to identify compromise solutions. The ideas of fuzzy and intuitionistic fuzzy sets are both expanded by the neutrosophic set, which serves as an effective tool in this context. This study focusses on the efficient solution of multi-objective non-linear optimization problems involving uncertain parameters represented by triangular single valued neutrosophic numbers. Many existing techniques for such problems rely on linear membership and non-membership functions, which may not accurately model every real-life problem. To overcome this limitation, this study extends well-established solution methodologies, including Zimmermann’s method, \(\:\gamma\:\) -operator and Maximum additive operator method, by introducing non-linear (exponential, t-parametric) truth membership, indeterminacy membership and falsity membership functions in place of linear ones and providing supporting theorems. To illustrate the proposed technique, a numerical example of manufacturing system in a neutrosophic fuzzy environment is presented. Further, a case study on a portfolio selection model with sustainable investment is solved and the results obtained by the proposed method using various membership are compared. In conclusion, the study summarizes its findings and outline potential areas for future research based on this work.