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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]