The algebraic structures Group, Ring, Field and Vector spaces are important innovations in Mathematics. Most of the theoretical concepts of Mathematics are based on the theorems related to these algebraic structures. Initially many mathematicians developed theorems related to all these algebraic structures. In 20th century most of the researchers introduced the theorems on the algebraic structures with Fuzzy and Intuitionistic fuzzy sets. Recently in 21st century the researchers concentrated on Neutrosophic sets and introduced the algebraic structures like Neutrosophic Group, Neutrosophic Ring, Neutrosophic Field, Neutrosophic Vector spaces and Neutrosophic Linear Transformation. In the current scenario of relating the spaces with the structures, we have introduced the concepts of Neutrosophic topological vector spaces. In this article, the study of Neutrosophic Topological vector spaces has been initiated. Some basic definitions and properties of classical vector spaces are generalized in Neutrosophic environment over a Neutrosophic field with continuous functions. Neutrosophic linear transformations and their properties are also included in Neutrosophic Topological Vector spaces. This article is an extension work of fuzzy and intuitionistic fuzzy vector spaces which were introduced in fuzzy and intuitionistic fuzzy environments. Even though it is an extension work, Neutrosophic Topological Vector space will play an important role in Neural Networks, Image Processing, Machine Learning and Artificial Intelligence Algorithms.

This paper introduces a new Neutrosophic Adaptive Neuro-Fuzzy Inference System paired with Explainable Artificial Intelligence to classify oral cancer from clinical photos. The ANFIS model’s interpretability and accuracy have been enhanced in resolving challenging medical images by deploying Neutrosophic logic on a 1000-image dataset to solve the word indeterminacy. A combination of Neutrosophic sets addresses ambiguity, enabling an adaptive neuro-fuzzy network to learn from data to accurately classify oral cancer. This exhibits the benefits of fuzzy logic and neural networks in action. The parameters of this model have been changed meticulously to increase sensitivity, specificity, and accuracy toward diagnostic readiness. These results reflect a substantive enhancement in the model’s ability to distinguish between benign and malignant lesions by delivering accurate and understandable diagnostic decisions existence for clinical adoption. AI medical diagnostic confidence increases the understanding of how the model makes decisions. The ideal objective is to develop a strong, dependable, and easy-to-understand tool to diagnose cancer early. The experimentation on this model can be improved as it may lead to real-time testing, more data for the testing dataset, and using how many types of cancer the model can be applied.

Cancer has been considered an incurable disease since its inception and has had an intimidating effect on mankind. Rapid technological advancement and medical breakthroughs have indeed thwarted its threat. Cancer is curable, provided it gets detected in the nascent stage. A growth or sore in the mouth that doesn't heal is the first sign of oral cancer. Despite the advanced radiation therapy and chemotherapy available, the fatality rate projects a grim picture with enormous scope for improvement. This study aims to broaden the use of artificial intelligence in the early stages of oral cancer detection. For papers that used artificial intelligence to diagnose oral cancer, a search was made between January 2018 and June 2024. Based on diverse image kinds and the use of artificial intelligence, 50 studies were included in diagnosing or detecting oral cancer. These studies were divided into different categories due to the heterogeneity of their data and the wide variety of algorithms used for analysis based on artificial intelligence. The precise prediction and identification of the onset of oral cancer may be greatly aided by artificial intelligence. Albeit, various chronological issues require attention alongside advances in artificial intelligence techniques to safely integrate with everyday clinical procedures and practices. This paper intends to act as a detailed guide for all to develop a system of similar thought processes.

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