Recommender systems leveraging deep learning models have been crucial for assisting users in selecting items aligned with their preferences and interests. However, a significant challenge persists in single-criteria recommender systems, which often overlook the diverse attributes of items that have been addressed by Multi-Criteria Recommender Systems (MCRS). Shared embedding vector for multi-criteria item ratings but have struggled to capture the nuanced relationships between users and items based on specific criteria. In this study, we present a novel representation for Multi-Criteria Recommender Systems (MCRS) based on a multi-edge bipartite graph, where each edge represents one criterion rating of items by users, and Multiview Dual Graph Attention Networks (MDGAT). Employing MDGAT is beneficial and important for adequately considering all relations between users and items, given the presence of both local (criterion-based) and global (multi-criteria) relations. Additionally, we define anchor points in each view based on similarity and employ local and global contrastive learning to distinguish between positive and negative samples across each view and the entire graph. We evaluate our method on two real-world datasets and assess its performance based on item rating predictions. The results demonstrate that our method achieves higher accuracy compared to the baseline method for predicting item ratings on the same datasets. MDGAT effectively capture the local and global impact of neighbours and the similarity between nodes.