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To date, type-2 fuzzy sets have attracted much more interest of the researchers, which are more capable to handle uncertain and imprecision information than type-1 fuzzy sets. Heronian mean is a classical mean aggregation operator which can effectively consider the interrelationships between various arguments. In this paper, we extend Heronian mean to trapezoidal interval type-2 fuzzy environment and present some aggregation operators, such as trapezoidal interval type-2 fuzzy generalized Heronian mean (TIT2FGHM) operator and trapezoidal interval type-2 fuzzy weighted generalized Heronian mean (TIT2FWGHM) operator. Then, we further discuss several desirable properties and particular cases when the parameters take diverse values in detail. Moreover, concerning multiple attribute group decision making problems in which the decision attributes are interdependent and the attribute values take the forms of interval type-2 fuzzy numbers, we propose a new approach based on TIT2FWGHM operator. Finally, we provide a numerical example of providers selection to illustrate the practicality and effectiveness of the proposed method and give a comparison analysis between the proposed method and existing methods. [ABSTRACT FROM AUTHOR]

Maclaurin symmetric mean (MSM) operator is a powerful tool to integrate multiple input arguments, which has the characteristic of considering the interrelationships among the input arguments. In this paper, we extend the traditional MSM operator to the single-valued neutrosophic interval 2-tuple linguistic environment, propose some novel aggregation operators, and develop a novel method to solve multiple attribute group decision making (MAGDM) problems. Firstly, we put forward the concept of single-valued neutrosophic interval 2-tuple linguistic sets (SVN-ITLSs) by combining the definitions of single-valued neutrosophic sets and interval 2-tuple. Secondly, the Maclaurin symmetric mean is extended to the single-valued neutrosophic interval 2-tuple linguistic environment and three new aggregation operators are proposed, such as the single-valued neutrosophic interval 2-tuple linguistic Maclaurin symmetric mean (SVN-ITLMSM) operator, the single-valued neutrosophic interval 2-tuple linguistic weighted average (SVN-ITLWA) operator and the single-valued neutrosophic interval 2-tuple linguistic weighted Maclaurin symmetric mean (SVN-ITLWMSM) operator. Some desirable properties of the proposed SVN-ITLMSM operator are investigated. Thirdly, an approach to solve MAGDM problem is developed based on the proposed operators. Finally, a numerical example is given to illustrate the application and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the multi-attribute decision making (MADM) problems under two situations that the attributes are independent and correlative, respectively, in which the attribute values take the form of dual hesitant fuzzy linguistic elements and the weights of attributes take the form of real numbers. Firstly, the concept, operational laws, score function and accuracy function of dual hesitant fuzzy linguistic element (DHFLE) are defined. For the situation that the attributes are independent, some dual hesitant fuzzy linguistic geometric aggregation operators are proposed. Considering that there exists prioritization among the attributes, we propose several dual hesitant fuzzy linguistic prioritized aggregation operators based on the prioritized average (PA) operator. Moreover, some desirable properties and special cases of these operators are investigated in detail. Based on the proposed operators, two novel approaches to MADM with dual hesitant fuzzy linguistic information are proposed. Finally, a numerical example for investment alternative selection is given to illustrate the application of the proposed methods. [ABSTRACT FROM AUTHOR]