Dual Linguistic Term Set and Its Application Based on the Normal Cloud Model

In recent years, some complex linguistic expression techniques with probabilistic information, such as proportional linguistic terms, probabilistic linguistic term sets, have been proposed to describe the uncertainty of opinions and preferences. However, the probability information is expressed as the crisp numbers, which is usually difficult to be estimated and information losses may exist. To capture the inherent fuzziness and vagueness of decision information more comprehensively and accurately, in this article, we introduce a novel concept named dual linguistic term set (DLTS), which consists of two linguistic variables. The DLTS can allow the decision makers to express the probabilistic information by the means of linguistic variables. To describe the hesitant information of the decision makers, a more general concept named hesitant fuzzy DLTS is developed. Afterwards, a multicriteria decision making method with dual linguistic information is proposed based on the normal cloud model. To do so, the DLTS is first transformed into an equivalent two-tuple consisting of two independent normal clouds. Then, new multiplication operation and power operation of normal clouds are defined to obtain the expectation for each attribute value. After aggregating the evaluation information, we further develop a new score function to rank alternatives reasonably. Finally, an illustrative example is given to verify the effectiveness and feasibility of the proposed method, also some comparisons and analyses are provided to show the advantages of the proposed method.