Women Entrepreneurship as a Socio-Managerial-Economic-Legal System: A Fuzzy Mathematical Modelling Framework With Global Applications

Women entrepreneurship is an increasingly important component of economic development, employment generation, innovation, household welfare, social transformation and sustainable development. Nevertheless, women entrepreneurs continue to experience interconnected constraints involving access to finance, family responsibilities, managerial capability, mobility, risk perception, social attitudes, institutional accessibility, digital inequality, market access and legal implementation. This paper develops an expanded Socio-Managerial-Economic-Legal Mathematical Model (SMEL-MM) for analysing women entrepreneurship as a multidimensional system. The proposed framework integrates social support, managerial effectiveness, financial inclusion, legal empowerment, human capital, digital capability, market access, risk resilience, family–business time allocation and sustainability. Because several entrepreneurial variables are qualitative or uncertain, fuzzy-set modelling is incorporated into the framework. A composite Women Entrepreneurial Sustainability Index (WESI) is formulated, followed by an enterprise-performance function and a constrained multi-objective policy optimization model. The expanded framework further identifies practical applications in financial institutions, fintech, government policy, entrepreneurship education, business incubation, digital commerce, rural entrepreneurship, social enterprises, sustainable development, AI-enabled decision-making and international policy benchmarking. The framework can therefore serve as a bridge between mathematical modelling and practical entrepreneurial governance. The paper does not treat the proposed equations as empirically established causal relationships. Instead, they constitute a testable analytical framework whose parameters, weights and hypotheses require empirical calibration using primary and secondary data.