Abstract The structure of interval-valued fuzzy sets is complex in regard to their arithmetic operations. To reduce the computational complexity of arithmetic operations on interval-valued fuzzy sets, we propose the notion of an n-polygonal interval-valued fuzzy set considering two 2 n + 2 -tuple ordered real numbers. Complete representation of n-polygonal interval-valued fuzzy sets and numbers is provided. Moreover, we demonstrate that the n-polygonal interval-valued fuzzy numbers can approximate the general interval-value fuzzy numbers with any precision. Next, we introduce arithmetic operations on n-polygonal interval-valued fuzzy numbers by capitalizing on the good characteristics of n-polygonal interval-valued fuzzy numbers. The properties of the introduced arithmetic operations are also addressed. In addition, with the aid of a concrete example, we verify the effectiveness of the approximation ability of the n-polygonal interval-valued fuzzy set. Furthermore, we study the properties of the topological space of n-polygonal interval-valued fuzzy numbers. This proves that this space is a complete, separable and local compact metric space when endowed with the newly defined distance between two n-polygonal interval-valued fuzzy numbers. By product, it shows that arithmetic operations introduced here on n-polygonal interval-valued fuzzy numbers are continuous. Finally, the practicability of n-polygonal interval-valued fuzzy numbers is verified by an example.

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关于n-多边形区间值模糊集和数

摘要 区间值模糊集的结构在算术运算方面是复杂的。为了降低区间值模糊集算术运算的计算复杂度，我们提出了考虑两个 2 n + 2 元组有序实数的 n 多边形区间值模糊集的概念。提供了 n 多边形区间值模糊集和数字的完整表示。此外，我们证明了 n 多边形区间值模糊数可以以任何精度逼近一般区间值模糊数。接下来，我们利用n-多边形区间值模糊数的优良特性，介绍了n-多边形区间值模糊数的算术运算。还介绍了引入的算术运算的特性。此外，借助一个具体的例子，我们验证了n多边形区间值模糊集逼近能力的有效性。此外，我们研究了n-多边形区间值模糊数的拓扑空间的性质。这证明了当赋予两个 n 多边形区间值模糊数之间新定义的距离时，该空间是一个完备的、可分的和局部紧的度量空间。通过产品，它表明这里介绍的对 n 多边形区间值模糊数的算术运算是连续的。最后，通过算例验证了n-多边形区间值模糊数的实用性。我们研究了n-多边形区间值模糊数的拓扑空间的性质。这证明了当赋予两个 n 多边形区间值模糊数之间新定义的距离时，该空间是一个完备的、可分的和局部紧的度量空间。通过产品，它表明这里介绍的对 n 多边形区间值模糊数的算术运算是连续的。最后，通过算例验证了n-多边形区间值模糊数的实用性。我们研究了n-多边形区间值模糊数的拓扑空间的性质。这证明了当赋予两个 n 多边形区间值模糊数之间新定义的距离时，该空间是一个完备的、可分的和局部紧的度量空间。通过产品，它表明这里介绍的对 n 多边形区间值模糊数的算术运算是连续的。最后，通过算例验证了n-多边形区间值模糊数的实用性。