Some q ‐rung orthopair uncertain linguistic aggregation operators and their application to multiple attribute group decision making

Abstract

q‐Rung orthopair fuzzy sets (q‐ROFSs), originally presented by Yager, are a powerful fuzzy information representation model, which generalize the classical intuitionistic fuzzy sets and Pythagorean fuzzy sets and provide more freedom and choice for decision makers (DMs) by allowing the sum of the qnormaltnormalh power of the membership and the qnormaltnormalh power of the nonmembership to be less than or equal to 1. In this paper, a new class of fuzzy sets called q‐rung orthopair uncertain linguistic sets (q‐ROULSs) based on the q‐ROFSs and uncertain linguistic variables (ULVs) is proposed, and this can describe the qualitative assessment of DMs and provide them more freedom in reflecting their belief about allowable membership grades. On the basis of the proposed operational rules and comparison method of q‐ROULSs, several q‐rung orthopair uncertain linguistic aggregation operators are developed, including the q‐rung orthopair uncertain linguistic weighted arithmetic average operator, the q‐rung orthopair uncertain linguistic ordered weighted average operator, the q‐rung orthopair uncertain linguistic hybrid weighted average operator, the q‐rung orthopair uncertain linguistic weighted geometric average operator, the q‐rung orthopair uncertain linguistic ordered weighted geometric operator, and the q‐rung orthopair uncertain linguistic hybrid weighted geometric operator. Then, some desirable properties and special cases of these new operators are also investigated and studied, in particular, some existing intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are proved to be special cases of these new operators. Furthermore, based on these proposed operators, we develop an approach to solve the multiple attribute group decision making problems, in which the evaluation information is expressed as q‐rung orthopair ULVs. Finally, we provide several examples to illustrate the specific decision‐making steps and explain the validity and feasibility of two methods by comparing with other methods.

Aggregation operators and VIKOR method based on complex q-rung orthopair uncertain linguistic informations and their applications in multi-attribute decision making

“…From the above discussions, we get the result; our established approach is more refillable and extensive consistence then existing methods (Liu and Jin 2012 ; Lu and Wei 2017 ; Liu et al 2019b ), due to its constraints. Therefore, the established approaches in this manuscript are more reliable and more efficient then CIFS and CPFS to cope with uncertain and awkward information in realistic decision theory.…”

“…The advantage of the CQRULS is that it contains the uncertain linguistic variable, truth and falsity grades with a conditions that is the sum of q-power of the real parts (also for imaginary parts) of the truth and falsity grades are not exceeded from unit interval. Further, to explore the proficiency and validity of the established operators based on the novel CQROULVs, we choose some existing operators based on intuitionistic uncertain linguistic variables (Liu and Jin 2012 ), Pythagorean uncertain linguistic variables (Lu and Wei 2017 ), q-rung orthopair uncertain linguistic variables (Liu et al 2019b ), complex intuitionistic uncertain linguistic variables (Special case of the explored operators), complex Pythagorean uncertain linguistic variables (Special case of the explored operators), and complex q-rung orthopair uncertain linguistic variables. Further, we choose the complex Pythagorean uncertain linguistic information, which is discussed in Table 11 , and solve it by using some existing methods (Liu and Jin 2012 ; Lu and Wei 2017 ; Liu et al 2019b ).…”

“…(Liu and Jin 2012 ) is discussed below. The authors chose the intuitionistic uncertain linguistic information, which is discussed in Table 15 , and solved it by using some existing methods (Liu and Jin 2012 ; Lu and Wei 2017 ; Liu et al 2019b ).…”

“…Liu et al ( 2017 ) examined the Pythagorean uncertain linguistic partitioned Bonferroni mean operators. The q-rung orthopair fuzzy uncertain linguistic aggregation operators was explored by Liu et al ( 2019b ).…”

The q-Rung Orthopair Hesitant Fuzzy Uncertain Linguistic Aggregation Operators and Their Application in Multi-Attribute Decision Making

“…Wang et al [31] combined uncertain linguistic variables with q-rung orthopair fuzzy sets and proposed the q-rung orthopair fuzzy uncertain linguistic sets (q-ROFULSs). Liu et al [32] studied the aggregation operators of the q-rung orthopair fuzzy uncertain linguistic sets and their applications in multi-attribute decision-making. However, the intuitionistic uncertain linguistic set cannot describe the degree of hesitant of the decision maker.…”