PSI - Issue 72

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

511

  1 2 , ,..., n A v v v     

(8) where + = and − = for benefit criteria, and + = and − = for cost criteria. 3. Determine the PIS and NIS separation measures:   2 1 n i ij j i S v v       (9)   2 1 n i ij j i S v v       (10) 5. Rank the alternatives according to C i in descending order. While classical TOPSIS has been widely applied in material selection problems, it has limitations in handling the uncertainty and indeterminacy present in FGM evaluation. This motivates our development of a neutrosophic extension to TOPSIS specifically for FGM selection. 3. Methodology This section presents the proposed neutrosophic TOPSIS framework for FGM selection. We first describe the evaluation criteria specific to FGMs, followed by the detailed steps of the neutrosophic TOPSIS algorithm. 3.1. Evaluation Criteria for FGM Selection The selection of FGMs requires consideration of various criteria that capture both the gradient-specific properties and conventional material performance metrics. Based on literature review and expert consultations, we identified the following key criteria categories: Thermal Performance 4. Determine how near the perfect answer you are: i    S i i i c S S   (11)

 Thermal conductivity gradient ( C 1 )  Thermal expansion compatibility ( C 2 )  Thermal shock resistance ( C 3 )  Maximum service temperature ( C 4 ) Mechanical Properties  Elastic modulus gradient ( C 5 )  Fracture toughness ( C 6 )  Fatigue resistance ( C 7 )  Wear resistance ( C 8 ) Manufacturing Considerations  Processing complexity ( C 9 )  Reproducibility ( C 10 )