Informatica

Public-private partnership (PPP) is regarded as an innovative way to the procurement of public projects. Models vary with PPP projects due to their differences. The evaluation criteria are usually complex and the judgments offered by decision makers (DMs) show the characteristics of fuzziness and uncertainty. Considering these cases, this paper first analyses the risk factors for PPP models and then proposes a new method for selecting them in the setting of single-valued neutrosophic hesitant fuzzy environment. To achieve these purposes, two single-valued neutrosophic hesitant fuzzy correlation coefficients are defined to measure evaluated PPP models. Considering the weights of the risk factors and their interactions, two single-valued neutrosophic hesitant fuzzy 2-additive Shapley weighted correlation coefficients are defined. When the 2-additive measure on the risk factor set is not exactly known, several distance measure-based programming models are constructed to determine it. Based on these results, an algorithm for evaluating PPP models with single-valued neutrosophic hesitant fuzzy information is developed. Finally, a practical numerical example is provided to verify the validity and feasibility of the new method.

Linguistic hesitant fuzzy sets (LHFSs) permit the decision maker to apply several linguistic terms with each having several membership degrees to denote his/her preference of one thing. This type of fuzzy sets can well address the qualitative and quantitative cognitions of the decision maker as well as reflect his/her hesitancy, uncertainty and inconsistency. This paper introduces a distance measure between any two LHFSs and then defines a correlation coefficient of LHFSs. Considering the application of LHFSs, the weighted distance measure and the weighted correlation coefficient of LHFSs are defined. To address the interactions between elements in a set, the Shapley weighted distance measure and the Shapley weighted correlation coefficient are presented. It is worth noting that when the elements are independent, they degenerate to the associated weighted distance measure and the weighted correlation coefficient, respectively. After that, their application to pattern recognition is studied. Furthermore, an approach to multi-attribute decision making under linguistic hesitant fuzzy environment is developed. Meanwhile, numerical examples are offered to show the concrete application of the developed procedure.