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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. [ABSTRACT FROM AUTHOR]

Intuitionistic uncertain linguistic variables (IULVs) are useful to express the qualitative and quantitative recognitions of decision makers. However, after reviewing the previous operational laws on IULVs, we find there are some limitations. To address these issues, we define several new operations on IULVs and give a new ranking method. To improve the utilization of IULVs, this paper defines two Choquet operators: the intuitionistic uncertain linguistic symmetrical Choquet averaging (IULSCA) operator and the intuitionistic uncertain linguistic symmetrical Choquet geometric mean (IULSCGM) operator, which can address the internal correlations among elements. To globally reflect the interactive characteristics of the importance of elements, two generalized Shapley intuitionistic uncertain linguistic symmetrical Choquet operators are presented. Subsequently, a new distance measure is defined, which is then used to build models to ascertain fuzzy measures on decision maker and criteria sets to address the case where the weighting information is partly known. After that, a new procedure to intuitionistic uncertain linguistic group decision making is developed. Finally, a specific example is offered to illustrate the practicality of the new procedure, and the comparison analysis is also made. [ABSTRACT FROM AUTHOR]

To denote the quantitative and qualitative fuzzy information simultaneously, this paper introduces a new type of fuzzy sets called uncertain linguistic hesitant fuzzy sets, which are denoted by an uncertain linguistic variable with several possible interval membership degrees. Considering the application of this type of fuzzy sets, several basic operational laws are defined, and several properties are studied. Meanwhile, an ordered relationship is introduced. Then, two types of uncertain linguistic hesitant fuzzy aggregation operators are defined. One uses additive measures, and the other is based on λ-fuzzy measures. Then, a similarity measure is presented, by which models for the optimal weight vector are constructed. After that, an approach to uncertain linguistic hesitant fuzzy multi-attribute decision making is developed. Finally, an illustrative example for evaluating corporate environmental performance is offered to show the concrete practicality of the procedure. [ABSTRACT FROM AUTHOR]

Interval-valued intuitionistic hesitant fuzzy sets (IVIHFSs) are useful to denote the decision makers' interval preferred, interval non-preferred and hesitant opinions simultaneously. Considering the application of IVIHFSs, this paper introduces a new decision-making method with interval-valued intuitionistic hesitant fuzzy information that extends the application scopes. To do this, the interval-valued intuitionistic hesitant fuzzy hybrid Shapley weighted averaging (IVIHFHSWA) operator and the interval-valued intuitionistic hesitant fuzzy hybrid Shapley weighted geometric (IVIHFHSWG) operator are defined to aggregate the collective attribute values of alternatives. To reflect the interactions and reduce the complexity of calculating the weights, the 2-additive measures are used to define these two hybrid Shapley weighted operators. To derive the exact weight information of attributes and ordered positions, the associated programming models for determining the optimal 2-additive measures are constructed that are based on the defined Hamming distance measure. To show the feasibility and efficiency of the new method, a practical decision-making problem is offered, which is also used to compare with the previous methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Considering the fact that the players may have different risk attitudes for the approximate values of strategies, this paper uses the possibility and necessity measures to denote the risk attitudes of the players, which are useful tools to address this issue. To do this, the concepts of possibility and necessity expectations of fuzzy variables are introduced, and several desirable properties are studied. Then, two vectors to denote the players' risk attitudes for their strategies are presented. Furthermore, the concept of possibility and necessity (PN) equilibrium strategy is defined, and the associated models are constructed, by which the optimal possibility and necessity equilibrium strategy is obtained. Meanwhile, a special case is briefly considered. Finally, a numerical example is offered to show the equilibrium strategy of the players. [ABSTRACT FROM AUTHOR]

In this paper, we shall study another coalitional value for fuzzy games with a coalition structure, which is named the proportional coalitional Shapley value. A generalized form of the proportional coalitional Shapley value for fuzzy games with a coalition structure is considered, which can be regarded as a generalization of crisp case. The axiomatic systems of this value are researched. When the original fuzzy game is fuzzy convex, the relationship between the proportional coalitional Shapley value, the fuzzy quotient core and the fuzzy quotient population monotonic allocation scheme (FQPMAS) is researched. [ABSTRACT FROM AUTHOR]