College of Computer Science and Mathematics

Discussion of a master’s thesis in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“Novel Enhancements to The Fuzzy Transform and its Applications in Approximating Functions and Solving Differential Equations’’

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Sunday, 2025\8\31.

master’s thesis by Student Ashwaq Abdul Qadir Khidr Al-Rawi

under the supervision of Assist. Prof. Dr. Edrees M. Nori Mahmood

Two important improvements on the framework of the Fuzzy Transform (FT) methodology are discussed in this thesis, which would ultimately be prepared for its applications in function approximation and numerical analysis with uncertainties in data. The first novelty is hybrid FT-PCHIP methodology, which includes low-dimensional fuzzy approximations that can generate the same global trend as well as local accuracy to be preserved shape from the Piecewise Cubic Hermite Interpolating Polynomial method (PCHIP). This contribution took into account the limitations of standalone FT when it comes to handling local variations through interpolation of the PCHIP, monotonic and minimizing oscillations while dealing with the residuals. The performance of the method was compared through experiments, where the mean square error was improved by more than 98% over classical FT. In this sense, the framework effectively connects discrete empirical readings with continuous modeling and analytical applications and hence is the best fit for engineering and experimental applications for sensor or irregularly sample data.The second contribution is a GA-based optimization framework for FT, which allays intrinsic problems like fixed node placement and local optima inaccuracy. The method traverses through a dual-phase GA, which first adaptively derives the little number of nodes required for any ε-convergence and then optimizes FT coefficients via a truly global search mechanism. The time complexity of vectorized implementation: real- valued GA is O(N).

 The thesis ends by discussing the new findings and giving some suggestions for their future application.

The scientific committee included the following members:

• Dr. Maysoun Mal Allah Aziz– Chairman
• Prof. Dr. Fatima Mahmoud Hassan – Member.
• Prof. Dr. Hisham Mohammed Khader – Member.
• Prof. Dr. Edrees M. Nori Mahmood – Member and supervisor