A MATLAB Toolbox for Fuzzy Relational Calculus in Variety of Fuzzy Algebras

The paper presents a comprehensive MATLAB software package designed to model and solve a broad class of problems in fuzzy relational calculus: inverse problem for fuzzy linear systems of equations and fuzzy linear systems of inequalities; behaviour, reduction and minimization for finite fuzzy machines; optimization of linear objective function under fuzzy linear system of equations or inequalities constraints. The software supports a variety of fuzzy algebras, such as max−min, min−max, max−product, Goguen, Gödel, and Łukasiewicz, offering tools for direct and inverse problem resolution. The implementation is based on well-established theoretical results in fuzzy logic and fuzzy algebraic structures, providing a robust foundation for exact and efficient computation. We begin by outlying the mathematical background and the principles behind the implemented algorithms. The development history of the package is briefly reviewed to highlight the motivations and design choices. A selection of examples is presented to illustrate the use of the software in different problem settings. The package is freely available and has been downloaded over 2100 times from MATLAB File Exchange, indicating the interest in applying fuzzy relational methods in computational environments.