Object recognition has become prevalent across various industries. However, most existing applications are limited to identifying objects alone, without considering their associated states. The ability to recognize both the state and object simultaneously remains less common. One approach to address this is by treating state and object as a single category during training. However, this approach poses challenges in data collection and training since it requires comprehensive data for all possible combinations. Compositional Zero-shot Learning (CZSL) emerges as a viable solution by treating the state and object as distinct categories during training. CZSL facilitates the identification of novel compositions even in the absence of data for every conceivable combination. The current state-of-the-art method, KG-SP, addresses this issue by training distinct classifiers for states and objects, while leveraging a semantic model to evaluate the plausibility of composed compositions. However, KG-SP's accuracy in state and object recognition can be further improved, and it fails to consider the weighting of states and objects during composition. In this study, we propose SASOW, an enhancement of KG-SP that considers the weighting of states and objects while improving composition recognition accuracy. First, we introduce self-attention mechanisms into the classifiers for states and objects, leading to enhanced accuracy in recognizing both. Additionally, we incorporate the weighting of states and objects during composition to generate more reasonable and accurate compositions. Our validation process involves testing SASOW on three established benchmark datasets. Experimental outcomes affirm when compared against OW-CZSL approach, KG-SP, SASOW showcases improvements of 2.1%, 1.7%, and 0.4% in terms of accuracy for unseen compositions across the MIT-States, UT Zappos, and C-GQA datasets, respectively.