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By applying T-S fuzzy model, we first consider a general form of T-S fuzzy QVBAMNNs with time delays. Then, by constructing appropriate Lyapunov\u2013Krasovskii functionals and employing quaternion-valued integral inequalities and homeomorphism theory, several delay-dependent sufficient conditions are obtained to guarantee the existence and GAS of the considered neural networks (NNs). In addition, these theoretical results are presented in the form of quaternion-valued linear matrix inequalities (LMIs), which can be verified numerically using the effective YALMIP toolbox in MATLAB. Finally, two numerical illustrations are presented along with their simulations to demonstrate the validity of the theoretical analysis.<\/jats:p>","DOI":"10.1007\/s11063-024-11559-3","type":"journal-article","created":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T18:01:51Z","timestamp":1710266511000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Non-separation Method-Based Global Stability Criteria for Takagi\u2013Sugeno Fuzzy Quaternion-Valued BAM Delayed Neural Networks Using Quaternion-valued Auxiliary Function-Based Integral Inequality"],"prefix":"10.1007","volume":"56","author":[{"given":"Sriraman","family":"Ramalingam","sequence":"first","affiliation":[]},{"given":"Oh-Min","family":"Kwon","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,3,12]]},"reference":[{"key":"11559_CR1","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1109\/72.712187","volume":"9","author":"X Liao","year":"1998","unstructured":"Liao X, Yu J (1998) Robust stability for interval Hopfield neural networks with time delay. 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