Many consensus models in social network group decision making (SNGDM) have been reported to obtain a collective solution despite the initial opinions of decision makers (DMs) may be different. However, these models ignore the obstinacy of DMs to their initial opinions, which violates the sociological research results. Aiming at the consensus reaching of SNGDM where DMs are stubborn to their initial opinions, this paper proposes a novel consensus model based on the passive adjustment based on feedback mechanism (PA-FM) and active adjustment based on social interaction (AA-SI), which adaptively adopts AA-SI or PA-FM in each round according to the opinion distribution of DMs. Specially, the proposed consensus model assimilates the advantage of PA-FM and AA-SI, where adjustment intensity of DMs affects the consensus level of PA-FM, and stubbornness degree of DMs affects that of AA-SI. To elucidate the performance and advantages of the proposed consensus model, a hypothetical application and three simulation analyses are constructed. The results show that (1) In the decision-making group that is stubborn to the initial opinions, social interaction has a beneficial or harmful effect on the consensus reaching, depending on the stubbornness degree and opinion distribution of DMs; and (2) Given any stubbornness degree and adjustment intensity, the proposed consensus model outperforms existing consensus methods in consensus efficiency and success rate.

The Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method has been developed as one of the effective techniques to accomplish the best alternative selection of multicriteria decision-making (MCDM) problems. However, the existing PROMETHEE methods fail to adjust the representation range of uncertain information. Moreover, the weight determination and information aggregation in the PROMETHEE model still suffer from an excessive dependence of decision makers' (DMs') subjective judgments and the lack of considering the interrelationship among criteria. To solve the aforementioned drawbacks and provide DMs with a reliable and robust method of MCDM, a novel PROMETHEE method based on the q-rung orthopair fuzzy sets, that is, q-ROF-PROMETHEE model, is presented herein. First, the PROMETHEE-II method is extended to q-rung orthopair fuzzy (q-ROF) environment, which not only handles the uncertainty of human cognition but also provides DMs with a broader space to represent their decisions information. Second, a new optimization model is constructed based on the proposed cross entropy and q-ROF entropy, which is capable of leveraging the preference of DMs to obtain the optimal objective weights among criteria. In addition, the q-ROF weighted Hamy mean operator is embedded in the preference information aggregation of the PROMETHEE method so as to deal with the interrelationship among criteria. Finally, q-ROF-PROMETHEE is applied to a hospital performance evaluation case to demonstrate the proposed method's superiority, validity, and feasibility.

In this paper, a new tool, called q-rung orthopair uncertain linguistic numbers (q-ROULNs), is developed and a new multiattribute group decision making (MAGDM) method for q-ROULNs is proposed. First, the concept of q-rung orthopair uncertain linguistic sets (q-ROULSs) is introduced, and some operational laws, expected function, accuracy function, and distance measure of q-ROULSs are defined. Further, to effectively aggregate q-ROULNs, we take advantage of partitioned Heronian mean operator and power average operator and propose the q-rung orthopair uncertain linguistic power partitioned Heronian mean operator and its weighted form. The proposed operators not only deal with this situations where attributes are divided into several parts and attributes in the same part are interrelated each other, whereas attributes in different parts have no relationship, but also reduce the negative influence of unreasonable attribute values provided by decision makers on final results. Some desirable properties and special cases of the proposed operators are also investigated. Finally, a MAGDM method based on the proposed operators is developed and a numerical instance as well as comparative analysis is conducted to illustrate the effectiveness and advantages of the proposed method.

Pythagorean fuzzy set (PFS) whose main feature is that the square sum of the membership degree and the non-membership degree is equal to or less than one, is a powerful tool to express fuzziness and uncertainty. The aim of this paper is to investigate aggregation operators of Pythagorean fuzzy numbers (PFNs) based on Frank t-conorm and t-norm. We first extend the Frank t-conorm and t-norm to Pythagorean fuzzy environments and develop several new operational laws of PFNs, based on which we propose two new Pythagorean fuzzy aggregation operators, such as Pythagorean fuzzy Choquet–Frank averaging operator (PFCFA) and Pythagorean fuzzy Choquet–Frank geometric operator (PFCFG). Moreover, some desirable properties and special cases of the operators are also investigated and discussed. Then, a novel approach to multi-attribute decision making (MADM) in Pythagorean fuzzy context is proposed based on these operators. Finally, a practical example is provided to illustrate the validity of the proposed method. The result shows effectiveness and flexible of the new method. A comparative analysis is also presented.