We introduce Quantization Aware Matryoshka Adaptation (QAMA), a unified framework for creating compact yet semantically rich embeddings through Matryoshka Representation Learning and multi-level quantization. Our approach learns nested embeddings that gracefully shrink to smaller dimensional subsets and leverages bitwise operations (XOR, NOT, POPCOUNT) for efficient retrieval. By augmenting transformer-based encoders with lightweight feedforward layers and specialized regularization (Matryoshka Loss, Orthogonality, Information Bottleneck, and Quantization Loss), we produce quantization-friendly representations that preserve essential information in early dimensions.

Small language models offer computational efficiency but often lack the performance of larger models. We introduce a novel query mechanism enabling small models to efficiently extract knowledge from large models during inference. Our approach executes the large model on a single vector prompt, significantly reducing computational overhead compared to full model execution.

This paper extends q -rung orthopair fuzzy numbers into q -rung orthopair trapezoidal fuzzy numbers to solve a multiattribute group decision-making problem. The decision-makers (DMs) provide some of their assessments in hesitant form, along with hesitancy weights. The basic operations laws, Hamming distance, weighted similarity measure, value and ambiguity indexes, weighted average aggregation operator, and weighted geometric aggregation operator, with their properties, are discussed for these extended fuzzy numbers. The value and ambiguity indexes are used in the Shannon entropy to evaluate the weights of the DMs and attributes'. These weights are then used to aggregate the DMs' assessments in the TOPSIS approach to obtain a weighted similarity measure from both the alternatives' positive and negative ideal solutions. The proposed approach's effectiveness is demonstrated by solving a waste disposal site selection problem. The approach is further validated through the basic properties of multiattribute decision making, comparative analyses, and comparing simulation results with an existing approach.