PSI - Issue 72

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

509

1. Development of a comprehensive neutrosophic TOPSIS methodology for FGM selection that addresses uncertainty, imprecision, and indeterminacy in evaluation criteria. 2. Formulation of specialized FGM evaluation criteria that capture gradient specific properties and manufacturing considerations. 3. Introduction of a novel neutrosophic aggregation approach for combining expert judgments with quantitative material data. 4. Validation of the proposed framework through a practical case study involving FGM selection for high temperature aerospace applications. 5. A comparison of the neutrosophic approach’s benefits with both fuzzy and conventional TOPSIS method. The paper’s remaining sections are arranged as follows : The theoretical underpinnings of neutrosophic sets and the TOPSIS method are presented in the preliminaries and definitions section. The suggested neutrosophic TOPSIS framework for FGM selection is described in depth in the methodology. Results and discussion the framework is applied to a case study, and the findings are discussed. The conclusion provides a summary of the results and This section establishes the theoretical foundation for the proposed neutrosophic TOPSIS framework. We begin by reviewing the fundamentals of functionally graded materials, followed by definitions of neutrosophic sets and their operations. Finally, we outline the classical TOPSIS method to provide context for our neutrosophic extension. 2.1. Functionally Graded Materials Advanced composited known as FGMs are distinguished by a spatial gradient in structure and composition, which causes corresponding modification in the material’s characteristics (Mahamood & Akinlabi, 2017). Unlike conventional composites with distinct interfaces, FGMs feature continuous variations in composition, microstructure, and properties. The gradient can be one-dimensional (e.g., through-thickness), two-dimensional (e.g., radial), or three dimensional, depending on the application requirements. A Functionally Graded Material is a heterogeneous composite material characterized by a spatially varying composition C(x) and/or microstructure, resulting in a continuous gradient of material properties P(x) across one or more dimensions, where x represents the spatial coordinate. FGMs can be classified based on several criteria:  Gradient type: Continuous, stepwise, or fractional  Composition: Metal-metal, metal-ceramic, ceramic-ceramic, polymer- based  Gradient dimension: 1D, 2D, or 3D  Manufacturing method: Powder metallurgy, thermal spraying, physical/chemical vapor deposition, centrifugal casting, etc. The property distribution in an FGM typically follows mathematical functions such as power law, exponential or sigmoid as represented in Equation (1):         / B A P x P A P P f x h     (1) where P A and P B are the properties at the boundaries, ℎ is the characteristic dimension, and f(x h) ⁄ is the distribution function that can take various forms such as power law ( ℎ ) , exponential .( ℎ ) ⁄ or sigmoid functions. 2.2. Neutrosophic Sets This theory introduced by (Smarandache, 1999), is especially well suited for managing uncertainty in decision making processes because it expands on fuzzy set theory by adding indeterminacy as an independent component. Let be a universe of discourse. A single valued neutrosophic set (SVNS) over is defined as: recommendations for further study. 2. Preliminaries and Definitions