Numerous research papers and several engineering applications have proved that the fuzzy set theory is an intelligent effective tool to represent complex uncertain information. In fuzzy multi-criteria decision-making (fuzzy MCDM) methods, intelligent information system and fuzzy control-theoretic models, complex qualitative information are extracted from expert’s knowledge as linguistic variables and are modeled by linear/non-linear fuzzy numbers. In numerical computations and experiments, the information/data are fitted by nonlinear functions for better accuracy which may be little hard for further processing to apply in real-life problems. Hence, the study of non-linear fuzzy numbers through triangular and trapezoidal fuzzy numbers is very natural and various researchers have attempted to transform non-linear fuzzy numbers into piecewise linear functions of interval/triangular/trapezoidal in nature by different methods in the past years. But it is noted that the triangular/trapezoidal approximation of nonlinear fuzzy numbers has more loss of information. Therefore, there is a natural need for a better piecewise linear approximation of a given nonlinear fuzzy number without losing much information for better intelligent information modeling. On coincidence, a new notion of Generalized Hexagonal Fuzzy Number has been introduced and its applications on Multi-Criteria Decision-Making problem (MCDM) and Generalized Hexagonal Fully Fuzzy Linear System (GHXFFLS) of equations have been studied by Lakshmana et al. in 2020. Therefore, in this paper, approximation of nonlinear fuzzy numbers into the hexagonal fuzzy numbers which includes trapezoidal, triangular and interval fuzzy numbers as special cases of Hexagonal fuzzy numbers with less loss/gain of information than other existing methods is attempted. Since any fuzzy information is satisfied fully by its modal value/core of that concept, any approximation of that concept is expected to be preserved with same modal value/core. Therefore, in this paper, a stepwise procedure for approximating a non-linear fuzzy number into a new Hexagonal Fuzzy Number that preserves the core of the given fuzzy number is proposed using constrained nonlinear programming model and is illustrated numerically by considering a parabolic fuzzy number. Furthermore, the proposed method is compared for its efficiency on accuracy in terms of loss of information. Finally, some properties of the new hexagonal fuzzy approximation are studied and the applicability of the proposed method is illustrated through the Group MCDM problem using an index matrix (IM).

许多研究论文和一些工程应用证明，模糊集理论是一种表示复杂不确定信息的智能有效工具。在模糊多准则决策（模糊MCDM）方法，智能信息系统和模糊控制理论模型中，从专家的知识中提取复杂的定性信息作为语言变量，并通过线性/非线性模糊数进行建模。在数值计算和实验中，信息/数据由非线性函数拟合以获得更好的精度，对于进行进一步处理以应用于现实生活中的问题而言，可能不难。因此，通过三角和梯形模糊数对非线性模糊数的研究是非常自然的，并且在过去的几年中，各种研究者试图通过不同的方法将非线性模糊数转换为区间/三角形/梯形的分段线性函数。但是要注意的是，非线性模糊数的三角/梯形近似具有更多的信息损失。因此，自然需要一种给定的非线性模糊数的更好的分段线性逼近，而又不会丢失太多信息以进行更好的智能信息建模。巧合的是 Lakshmana等人研究了广义六角模糊数的新概念，并研究了其在方程的多准则决策问题（MCDM）和广义六角完全模糊线性系统（GHXFFLS）中的应用。因此，本文尝试将非线性模糊数近似为包含梯形，三角形和区间模糊数的六边形模糊数，作为六边形模糊数的特例，其信息丢失/增益比其他现有方法少。由于任何模糊信息都可以通过该概念的模态值/核心完全满足，因此可以使用相同的模态值/核心保留该概念的任何近似值。因此，在本文中，利用约束非线性规划模型，提出了一种将非线性模糊数近似为新的保留给定模糊数核心的六边形模糊数的步骤，并通过考虑抛物线模糊数进行了数值说明。此外，比较了所提出的方法在信息丢失方面的准确性效率。最后，研究了新的六边形模糊逼近的一些性质，并通过使用索引矩阵（IM）的Group MCDM问题说明了该方法的适用性。比较了所提方法在信息丢失方面的准确性。最后，研究了新的六边形模糊逼近的一些性质，并通过使用索引矩阵（IM）的Group MCDM问题说明了该方法的适用性。比较了所提方法在信息丢失方面的准确性。最后，研究了新的六边形模糊逼近的一些性质，并通过使用索引矩阵（IM）的Group MCDM问题说明了该方法的适用性。