Linguistic variable is an effective method of representation the preferences of a decision-maker for inaccuracy available information in decision making under uncertainty. This article investigates a multiple attribute ranking decision making problem with linguistic preference by using linguistic value soft rough set. Firstly, we present the definition of linguistic value fuzzy set by introduce the concept of linguistic variable into the original Zadeh’s fuzzy set. We then define the concept of linguistic value soft set and the pseudo linguistic value soft set over the alternative set and parameter set of discourse. Moreover, we investigate the basic operators and the mathematical properties of the linguistic value soft set. Subsequently, we establish the rough approximation of an uncertainty concept with linguistic value over the object set and parameter set, i.e., the linguistic value soft rough set model. Meanwhile, we discuss several deformations of the linguistic value soft rough lower and upper approximations as well as some fundamental properties of the linguistic value soft approximation operators. With reference on the exploring of the fundamental of linguistic value soft rough set, we construct a new method for handling with the multiple attribute ranking decision making problems with linguistic information by combining the proposed soft rough set and the VIKOR method. Then, we give the detailed decision procedure and steps for the established decision approach. At last, an extensive numerical example is further conducted to illustrate the process of the decision making principle and the results are satisfactory. The main contribution of this paper is twofold. One is to provide a new model of granular computing by infusion the soft set and rough set theory with linguistic valued information. Another is to try making a new way to handle multiple attribute decision making problems based on linguistic value soft rough set and the VIKOR method.

中文翻译：

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基于语言价值软粗糙集和VIKOR方法的多属性决策方法

语言变量是一种表示不确定性情况下决策者对于不准确的可用信息的偏好的有效方法。本文通过使用语言值软粗糙集研究具有语言偏好的多属性排序决策问题。首先，通过将语言变量的概念引入原始的扎德的模糊集中，提出了语言价值模糊集的定义。然后，我们在话语的替代集和参数集上定义语言价值软集合和伪语言价值软集合的概念。此外，我们研究了语言值软集的基本运算符和数学性质。随后，我们在对象集和参数集上建立具有语言值的不确定性概念的粗略近似，即语言值软粗糙集模型。同时，我们讨论了语言值软近似上下限的几种变形以及语言值软近似算符的一些基本性质。在探索语言价值软粗糙集基础的基础上，结合提出的软粗糙集和VIKOR方法，构造了一种处理语言信息的多属性排序决策问题的新方法。然后，我们为建立的决策方法提供详细的决策程序和步骤。终于，进一步通过大量的数值例子来说明决策原理的过程，结果令人满意。本文的主要贡献是双重的。一种是通过向软集和粗糙集理论中注入语言价值信息来提供一种新的粒度计算模型。另一个尝试是尝试基于语言值软粗糙集和VIKOR方法来处理多属性决策问题的新方法。