Multi-criteria group sorting (MCGS) that considers linguistic preferences involves multiple individuals evaluating alternatives and assigning them to pre-determined ordered categories based on specific criteria. Nevertheless, due to the limited availability of class information and the constrained cognitive capacity of decision-makers (DMs), it becomes challenging for DMs to furnish explicit preference information to reach consensus. Besides, decision parameters such as consensus threshold and class thresholds are also too hard to be assumed in advance. Therefore, this paper studies the preference disaggregation problem in MCGS, in which DMs are allowed to provide their pairwise comparisons in flexible linguistic expressions (FLEs) as preference information. To more fully utilize the preferences, semantic granulation is introduced. First, an individual consistency recognition model is proposed to identify inconsistent preferences and provide modification directions to the corresponding individuals. Next, semantic granulation and maximum entropy are combined into a granulation-driven information transformation model to convert the preference information based on FLEs into triangular fuzzy numbers (TFNs). Subsequently, in the consensus-driven preference disaggregation model, decision parameters and sorting results can be obtained at the premise of consensus by adjusting weights. Ultimately, to substantiate the effectiveness of the proposal, two numerical applications concerning the sorting of government venture capitals and information system suppliers are presented, along with comparative analysis, sensitivity analysis, and simulation analysis.

The distance between the intuitionistic fuzzy sets (IFSs) is a notable and has been widely used information measure to enhance decision-making performance. However, different numerical results are derived when using different distance measures. Therefore, it is worthwhile to explore in depth how to select an appropriate formula for distance computation. This paper uses the line integral to define the distance between IFSs. The presented study divided into three folds. First, the existing distances between IFSs are examined, and their flaws are listed. Second, the distances between IFSs are redefined based on the analysis of the geometric importance of the line integral. More importantly, some existing distances happen to be special cases of the distance we define. Finally, we introduce the accuracy function into the defined distance for evaluating the accuracy of distance by applying the physical meaning of line integral. In other words, the distance accuracy is emphasized as a crucial standard by which to assess the effectiveness of distances between IFSs. To demonstrate the stated measures, some numerical examples are provided to show the superiority of our approach.

As a useful tool, probabilistic hesitant fuzzy set is an enhanced version for hesitant fuzzy set. It could be used to model the uncertainty very effectively. However, in probabilistic hesitant fuzzy risky multiple attribute decision making problems, the occurrence probabilities of elements in a probabilistic hesitant fuzzy element and the probability of risk status are often difficult to obtain by subjective evaluation of a decision maker. This paper aims to propose two nonlinear programming models for calculating the probabilities of elements in a probabilistic hesitant fuzzy element and the probability of risk status respectively. First, a nonlinear programming model using maximum entropy principle is established for determining the probabilities of elements in a probabilistic hesitant fuzzy element. Second, by introducing the water-filling theory, we put forward its extension and design a novel mathematical programming model to determine the probability of risk status. Moreover, we have proved that both the two mathematical programming models are convex programming models and their global optimal solutions can be found. Thirdly, the collective overall expected values of alternatives are calculated and the ranking order can be derived. Then, the selection of investment project is investigated, and comparison analysis shows the superiority of the presented approach.

Short text is becoming ubiquitous in many modern information systems. Due to the shortness and sparseness of short texts, there are less informative word co-occurrences among them, which naturally pose great difficulty for classification tasks on such data. To overcome this difficulty, this paper proposes a new way for effectively classifying the short texts. Our method is based on a key observation that there usually exists ordered subsets in short texts, which is termed ``information path'' in this work, and classification on each subset based on the classification results of some pervious subsets can yield higher overall accuracy than classifying the entire data set directly. We propose a method to detect the information path and employ it in short text classification. Different from the state-of-art methods, our method does not require any external knowledge or corpus that usually need careful fine-tuning, which makes our method easier and more robust on different data sets. Experiments on two real world data sets show the effectiveness of the proposed method and its superiority over the existing methods.