PSI - Issue 72

Ruhit Bardhan et al. / Procedia Structural Integrity 72 (2025) 507–519

508

1. Introduction Functionally Graded Materials (FGMs) represent an advanced class of engineered materials characterized by spatially varying composition, microstructure, and properties (Mahamood & Akinlabi, 2017; Miyamoto et al., 1999). Unlike traditional composite materials with distinct interfaces between components, FGMs feature gradual transitions in material composition, resulting in continuous changes in physical, mechanical, and thermal properties across one or more dimensions. This gradient structure allows FGMs to combine the advantageous properties of different materials, such as the thermal resistance of ceramics with the mechanical toughness of metals, while minimizing interface-related issues like stress concentration and delamination (Koizumi, 1997). The development and application of FGMs have gained significant momentum in recent decades, driven by demanding requirements in aerospace, biomedical, energy, and defense sectors (Naebe & Shirvanimoghaddam, 2016). These materials offer tailored solutions for components exposed to severe thermal gradients, high mechanical stresses, or environments requiring specific property variations. For instance, thermal barrier coatings in gas turbines, dental implants with biocompatibility gradients, and armor materials with optimized ballistic performance all leverage the unique capabilities of FGMs (Panda et al., 2014). However, the selection of appropriate FGM compositions and gradient profiles presents a complex multi-criteria decision-making (MCDM) challenge. Engineers must simultaneously consider numerous factors, including:  Thermal properties (conductivity, expansion coefficient, resistance)  Mechanical characteristics (strength, stiffness, toughness, fatigue resistance)  Manufacturing feasibility and cost  Environmental stability and corrosion resistance  Weight and density considerations  Service life and reliability Traditional material selection approaches often struggle with the inherent complexity of FGMs due to their continuously varying nature and the interdependencies between different properties along the gradient (Jahan et al., 2010). Furthermore, the evaluation of FGMs typically involves expert judgments and experimental data that contain various degrees of uncertainty, imprecision, and inconsistency. The TOPSIS, introduced by hwang and yoon, has been widely employed for MCDM problems. Geometric distance between alternatives and the positive ideal solution and negative ideal solution are used by TOPSIS to rank them (Hwang & Yoon, 1981). While conventional TOPSIS has proven effective for many materials selection problems (Lv et al., 2013), its application to FGMs presents unique challenges due to the gradient nature of these materials and the uncertainties involved in their assessment. To address these limitations, researchers have explored extensions of TOPSIS using fuzzy set theory (Chen, 2000), intuitionistic fuzzy sets (Boran et al., 2009), and more recently, neutrosophic sets (Guerriero et al., 2014). Smarandache developed neutrosophic set theory fuzzy and intuitionistic fuzzy sets by adding three separate membership components (Smarandache, 1999): falsity, indeterminacy and truth membership (Biswas et al., 2016; Wang et al., 2010). This three-way representation provides a more comprehensive framework for handling uncertainties, particularly the indeterminacy aspects that are prevalent in FGM evaluation. An interdisciplinary approach to applied mathematics, materials science, and fuzzy logic. Their study (Sahni et al., 2025) explores the steady-state creep behavior of functionally graded SUS- ZrO₂ and Al - ZrO₂ cylinders and provides insights relevant to high-temperature engineering applications. Delving into modelling under uncertainty, such as using neutrosophic (Parikh et al., 2022; Parikh & Sahni, 2024; Shah et al., 2023) numbers to solve logistic differential equations and using intuitionistic fuzzy super matrices to enhance decision-making. The area of computational methods (Makwana et al., 2022) for solving fuzzy differential equations and redefining fuzzy numbers to improve the accuracy of fuzzy equation solutions. Together, these studies demonstrate the strong integration of advanced mathematical modelling with real world problems in materials engineering, decision science, and dynamic systems under uncertainty. Despite these advances, there remains a gap in the literature regarding specialized decision frameworks for FGM selection that can effectively capture the unique characteristics of these materials while addressing the various forms of uncertainty in the decision process. The goal of this research is to fill this gap by vreating a neutrosophic TOPSIS framework designed especially for FGM selection issues. The research primary contributions are: