Spherical fuzzy sets (SFSs) provide more free space for decision makers (DMs) to express preference information from four aspects: approval, objection, abstention and refusal. The partitioned Maclaurin symmetric mean (PMSM) operator is an effective information fusion tool, which can fully capture the interrelationships among any multiple attributes in the same block whereas attributes in different block are unrelated. Therefore, in this paper,we first extendPMSM operator to spherical fuzzy environment and develop spherical fuzzy PMSM (SFPMSM) operator as well as spherical fuzzy weighted PMSM (SFWPMSM) operator. Meanwhile, we discuss some properties and special cases of these two operators. To diminish the impact of extreme evaluation values on decision-making results, then we integrate power average (PA) operator and PMSM operator to further develop spherical fuzzy power PMSM (SFPPMSM) operator and spherical fuzzy weighted power PMSM (SFWPPMSM) operator and also investigate their desirable properties. Subsequently, a new multiple attribute group decision making (MAGDM) method is established based on SFWPPMSM operator under spherical fuzzy environment. Finally, two numerical examples are used to illustrate the proposed method, and comparative analysis with the existing methods to further testy the validity and superiority of the proposed method.

The linguistic q-rung orthopair fuzzy (L q-ROF) set is an important implement in the research area in modelling vague decision information by incorporating the advantages of q- rung orthopair fuzzy sets and linguistic variables. This paper aims to investigate the multicriteria decision group decision making (MCGDM) with L q-ROF information. To do this, utilizing Hamacher t-norm and t-conorm, some L q-ROF prioritized aggregation operators viz., L q- ROF Hamacher prioritized weighted averaging, and L q-ROF Hamacher prioritized weighted geometric operators are developed in this paper. The defined operators can effectively deal with different priority levels of attributes involved in the decision making processes. In addition, Hamacher parameters incorporated with the proposed operators make the information fusion process more flexible. Some prominent characteristics of the developed operators are also wellproven. Then based on the proposed aggregation operators, an MCGDM model with L q-ROF context is framed. A numerical example is illustrated in accordance with the developed model to verify its rationality and applicability. The impacts of Hamacher and rung parameters on the achieved decision results are also analyzed in detail. Afterwards, a comparative study with other representative methods is presented in order to reflect the validity and superiority of the proposed approach.

The purpose of this article is to develop a multicriteria group decision making (MCGDM) method in dual hesitant fuzzy (DHF) environment by evaluating the weights of the decision makers from the decision matrices using two newly defined prioritized aggregation operators based on score function to remove the inconsistencies in choosing the best alternative. Prioritized weighted averaging operator and prioritized weighted geometric operator based on Einstein operations are described first for aggregating DHF information. Some of their desirable properties are also investigated in details. A method for finding the rank of alternatives in MCGDM problems with DHF information based on priority levels of decision makers is developed. An illustrative example concerning MCGDM problem is considered to establish the application potentiality of the proposed approach. The method is efficient enough to solve different real life MCGDM problems having DHF information.

The recently proposed q-rung orthopair fuzzy set (q-ROFS) characterized by a membership degree and a non-membership degree is powerful tool for handling uncertainty and vagueness. This paper proposes the concept of q-rung orthopair linguistic set (q-ROLS) by combining the linguistic term sets with q-ROFSs. Thereafter, we investigate multi-attribute group decision making (MAGDM) with q-rung orthopair linguistic information. To aggregate q-rung orthopair linguistic numbers ( q-ROLNs), we extend the Heronian mean (HM) to q-ROLSs and propose a family of q-rung orthopair linguistic Heronian mean operators, such as the q-rung orthopair linguistic Heronian mean (q-ROLHM) operator, the q-rung orthopair linguistic weighted Heronian mean (q-ROLWHM) operator, the q-rung orthopair linguistic geometric Heronian mean (q-ROLGHM) operator and the q-rung orthopair linguistic weighted geometric Heronian mean (q-ROLWGHM) operator. Some desirable properties and special cases of the proposed operators are discussed. Further, we develop a novel approach to MAGDM within q-rung orthopair linguistic context based on the proposed operators. A numerical instance is provided to demonstrate the effectiveness and superiorities of the proposed method.

The difficulty of innovation risk assessment makes it necessary to use a multi-criteria analysis.

Innovative projects are related to unstructured problems and the uncertainty, therefore,

the use of fuzzy logic in the innovation risk assessment is analyzed. This paper proposes

a method of determining the weights of criteria in order to innovation risk assessment. The

weights are determined by 5 general criteria and 14 detailed criteria of innovation risk assessment.

The proposed method is an extension of the fuzzy AHP method. The extension

consists in taking into consideration the group decision-making approach with experts’ psychological

conditions. The groups of experts have been chosen based on an elaborated form.

The form makes it possible to characterize the persons within the scope of different psychological

conditions. The proposed method provides objective and rational decision-making.

The paper presents also a comparison of results with the fuzzy AHP method without the

group decision making. The weights obtained by the proposed method are more diversified

and bring out the most important criteria.