Heptadecagonal Fuzzy Number and its Distinctive Representation, Ranking, Defuzzification Technique and Application in Fuzzy Linear Programming Problem

Abstract

In this study, distinct categories of linear and nonlinear heptadecagonal fuzzy numbers with symmetry and asymmetry and their graphical representation are proposed. The membership functions and alpha-cuts for different types of heptadecagonal fuzzy numbers are also explained. Linear and nonlinear heptadecagonal fuzzy numbers with symmetry and asymmetry serve as powerful tools for simplifying the comprehension of vagueness data across different problems. By using the alpha-cut, the arithmetic operations on linear heptadecagonal fuzzy number with symmetry are addressed. A ranking method based on the centroid formula is used to rank two heptadecagonal fuzzy numbers and the alpha-cut method is applied to compute the defuzzification for linear heptadecagonal fuzzy number with symmetry. A numerical example for the fuzzy linear programming problem has been presented to illustrate the proposed methodology.