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.

Zadeh在1965年引入模糊集理论来克服现实世界中的难题和模糊性。模糊集的基本功能是可以将语言/定性变量与定量变量一起使用，以表示连续的不精确概念。连续字谜概念需要用连续的模糊数字代替间隔和实数来建模。因此，许多研究人员根据文献的形状开发出各种模糊数，例如三角形模糊数，梯形模糊数，六角形模糊数，八边形模糊数和十边形模糊数。在提供这些模糊数的同时，六角形，八边形和十边形模糊数的现有定义存在一些疏漏。在这个研究中，纠正了文献中六边形模糊数概念的一些缺陷，并提出了一般形式的六边形模糊数的新定义。此外，还提出了使用得分函数对六角形模糊数进行完整排序的方法，并通过模糊多属性决策（MADM）问题和模糊线性系统对其进行了验证。此外，给出了一种求解拟定排序原理的完全模糊广义六边形模糊线性方程组的算法，并对其进行了数值说明。