Hexagonal fuzzy number inadvertences and its applications to MCDM and HFFLS based on complete ranking by score functions

Abstract

Zadeh introduced fuzzy set theory in the year 1965 to overcome the enigma and obscurity in the real world problems. The underlying power of fuzzy sets is that linguistic / qualitative variables can be used along with quantitative variables to represent continuous imprecise concepts. The continuous anagram concepts need to be modeled by continuous fuzzy numbers instead of intervals and real numbers. So, many researchers developed various fuzzy numbers such as triangular fuzzy numbers, trapezoidal fuzzy numbers, hexagonal fuzzy numbers, octagonal fuzzy numbers and decagonal fuzzy numbers based on shapes in literature. While offering these fuzzy numbers, there are some inadvertences in the existing definition of hexagonal, octagonal and decagonal fuzzy numbers. In this study, some flaws in the concept of hexagonal fuzzy numbers in literature are rectified and a new definition of hexagonal fuzzy numbers in the general form is proposed. Moreover, a complete ranking of hexagonal fuzzy numbers using score functions has also been proposed and is validated through fuzzy Multi Attribute Decision Making (MADM) problem and fuzzy linear system. Further, an algorithm for solving fully fuzzy generalized hexagonal fuzzy linear system of equations as an application of proposed ranking principle is given and is numerically illustrated.