A Comprehensive Study of Mellin’s Transformation on Diverse Fuzzy Numbers with Applications of Optimizing Production Planning

This article presents an innovative defuzzification technique for various fuzzy numbers: triangular, trapezoidal, $$\pi$$ -type, cosine, increasing and decreasing concave, and heptagonal. The study introduces a ranking method by utilizing the probability density function of their membership functions. To illustrate the use of the proposed work, a production planning problem is discussed and solved under different fuzzy patterns. Mellin transform converts these fuzzy numbers into crisp numbers for optimal comparison and solution. The solution process is tailored to the decision maker’s value set.