Bivariate Grid Scale based Multiple Attribute Evaluation Technique (GAMETE) with Incomplete Information on Weights

In this paper, we have devised a novel Multiple Attribute Decision Making (MADM) method referred to as the bivariate Grid Scale based Multiple Attribute Evaluation Technique (GAMETE) method to deal with MADM decision problems involving tangible and intangible attributes under incomplete weight information. The proposed method innovatively incorporates an Attractiveness GRID Scale (AGRIDS) to evaluate intangible attributes, grounded in cognitive psychological principles— particularly the separability and independence of positive and negative aspects in human judgement. Additionally, a new bi-dimensional positional advantage operator (bi-pao) is introduced to compute the intangible attractiveness index. Further, linear programming models are formulated in order to construct the pairwise dominance matrix. Afterwards, we rank alternatives using a dominance intensity measure and the Boolean matrix. Furthermore, the proposed method is illustrated through a logistics center location problem. We also perform a comparison with several state-of-the-art linguistic Intuitionistic Fuzzy Sets (LIFS) and linguistic Pythagorean Fuzzy Sets (LPFS) based MADMs with the aim of showing the applicability and feasibility of the method suggested. Notably, GAMETE provides a multidimensional decision-making framework suitable for addressing complex technological and economic challenges where both quantitative and qualitative factors coexist. Its flexibility and interpretability make it a promising tool for real-world strategic decision scenarios.