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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 introducing 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. [ABSTRACT FROM AUTHOR]

This article studies the rough approximation of a vague concept based on multiple granularity over two universes. With the description of the background of risk decision making problems in reality, we first present the optimistic multigranulation rough vague set, pessimistic multigranulation rough vague set and variable precision multigranulation rough vague set on the multigranulation approximation space over two universes. Then, under the multigranulation fuzzy approximate space over two universes, we establish the corresponding three types of multigranulation vague rough set over two universes. Subsequently, the interesting properties and results as well as the relationship between the multigranulation rough vague set models and multigranulation vague rough set model over two universes are investigated in detail. The results show that multigranulation vague rough set models are extensions of the existing generalized rough set models under the framework of two universes. At the same time, we construct a new approach to group decision making under uncertainty by using the theory of multigranulation vague rough set over two universes. The basic principal and the detailed steps of the decision making model given in this paper are presented in detail. Meanwhile, an example of handling a medical diagnosis group decision making problem illustrates this approach. The main contribution of this paper is twofold. One is to provide the theoretical model of multigranulation vague rough set over two universes. Another is to try making a new way to handle group decision making problems under uncertainty based on multigranulation vague rough set theory and methodologies over two universes. [ABSTRACT FROM AUTHOR]

Probabilistic approaches to rough sets are still an important issue in rough set theory. Although many studies have been written on this topic, they focus on approximating a crisp concept in the universe of discourse, with less effort on approximating a fuzzy concept in the universe of discourse. This article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space over two universes. We first present the definition of a lower and upper approximation of a fuzzy set with respect to a probabilistic approximation space over two universes by defining the conditional probability of a fuzzy event. That is, we define the rough fuzzy set on a probabilistic approximation space over two universes. We then define the fuzzy probabilistic approximation over two universes by introducing a probability measure to the approximation space over two universes. Then, we establish the fuzzy rough set model on the probabilistic approximation space over two universes. Meanwhile, we study some properties of both rough fuzzy sets and fuzzy rough sets on the probabilistic approximation space over two universes. Also, we compare the proposed model with the existing models to show the superiority of the model given in this paper. Furthermore, we apply the fuzzy rough set on the probabilistic approximation over two universes to emergency decision-making in unconventional emergency management. We establish an approach to online emergency decision-making by using the fuzzy rough set model on the probabilistic approximation over two universes. Finally, we apply our approach to a numerical example of emergency decision-making in order to illustrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]