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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]

With respect to multiple attribute decision making (MADM) problems in which the attributes are inter-dependent and take the form of dual hesitant fuzzy elements, a new MADM method with dual hesitant fuzzy information is investigated in this paper. Firstly, by using the Choquet integral, some new aggregation operators are developed for aggregating the dual hesitant fuzzy information, such as the dual hesitant fuzzy Choquet ordered average (DHFCOA) operator, the dual hesitant fuzzy Choquet ordered geometric (DHFCOG) operator, the generalized dual hesitant fuzzy Choquet ordered average (GDHFCOA) operator and the generalized dual hesitant fuzzy Choquet ordered geometric (GDHFCOG) operator. Then, some special cases, desirable properties of these operators and the relationships between them are discussed. Furthermore, based on the DHFCOA operator, an approach to MADM is proposed under dual hesitant fuzzy environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [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]

This paper investigates multiple attribute decision making (MADM) problems in which the attribute values take the form of interval-valued dual hesitant fuzzy elements (IVDHFEs). Firstly, motivated by the concepts of dual hesitant fuzzy set (DHFS) and interval number, the concept, operational laws and comparison laws of interval-valued dual hesitant fuzzy elements are proposed. Then, based on the operational laws of IVDHFEs, some aggregation operators are developed for aggregating the interval-valued dual hesitant fuzzy information, such as the interval-valued dual hesitant fuzzy weighted aggregation operators, the interval-valued dual hesitant fuzzy ordered weighted aggregation operators, the generalized interval-valued dual hesitant fuzzy weighted aggregation operators, the generalized interval-valued dual hesitant fuzzy ordered weighted aggregation operators and the interval-valued dual hesitant fuzzy hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed in detail. Based on the interval-valued dual hesitant fuzzy weighted average (IVDHFWA) operator, an approach to multiple attribute decision making is proposed under interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic fuzzy linguistic elements (HIFLEs). Firstly, motivated by the idea of hesitant fuzzy linguistic elements and intuitionistic fuzzy numbers, the concept, operational laws and comparison laws of HIFLEs are defined. Then, some aggregation operators are developed for aggregating the hesitant intuitionistic fuzzy linguistic information, such as hesitant intuitionistic fuzzy linguistic weighted aggregation operators, hesitant intuitionistic fuzzy linguistic ordered weighted aggregation operators and hesitant intuitionistic fuzzy linguistic hybrid aggregation operators. Some desirable properties of these operators and the relationships between them are discussed. Furthermore, the hesitant intuitionistic fuzzy linguistic set is extended to hesitant intuitionistic fuzzy uncertain linguistic set, and some hesitant intuitionistic fuzzy uncertain linguistic aggregation operators are developed. Based on the hesitant intuitionistic fuzzy linguistic weighted average (HIFLWA) operator, an approach to MADM is proposed under hesitant intuitionistic fuzzy linguistic environment. Finally, a practical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of trapezoid fuzzy 2-tuples. Firstly, we develop some trapezoid fuzzy 2-tuple linguistic aggregation operators based on the operational laws of trapezoid fuzzy 2-tuples, such as the trapezoid fuzzy 2-tuple weighted geometric (TFTWG) operator, the trapezoid fuzzy 2-tuple ordered weighted geometric (TFTOWG) operator, the generalized trapezoid fuzzy 2-tuple weighted average (GTFTWA) operator and the generalized trapezoid fuzzy 2-tuple ordered weighted average (GTFTOWA) operator. Then, we study some desirable properties of the developed operators, such as idempotency, monotonicity, commutativity and boundedness, and analyze some special cases of these operators. Furthermore, we propose an approach to multiple attribute decision making under trapezoid fuzzy linguistic environment based on the GTFTWA and TFTWG operators. Finally, an illustrative example is given to verify the proposed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]