Abstract
In this manuscript, the notions of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets (CFSs) are combined is to propose the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental laws. The Cq-ROFSs are an important way to express uncertain information, and they are superior to the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the real part (similarly for imaginary part) of complex-valued membership degree and the qth power of the real part (similarly for imaginary part) of complex-valued non‐membership degree is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we develop the score function, accuracy function and comparison method for two Cq-ROFNs. Based on Cq-ROFSs, some new aggregation operators are called complex q-rung orthopair fuzzy weighted averaging (Cq-ROFWA) and complex q-rung orthopair fuzzy weighted geometric (Cq-ROFWG) operators are investigated, and their properties are described. Further, based on proposed operators, we present a new method to deal with the multi‐attribute group decision making (MAGDM) problems under the environment of fuzzy set theory. Finally, we use some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.
Highlights
To dispose unknown or undetermined information in the field of decision making, Zadeh [1]proposed the innovative concept of fuzzy set (FS) in 1965, which is characterized by a membership function limited to [0, 1], and it has been proven to be a very powerful tool to deal with uncertain information in real-life problems
1, 0.8 + 0.7 = 1.5 ≥ 1 and 0.92 + 0.82 = 0.81 + 0.64 = 1.45 ≥ 1, 0.82 + 0.72 = 0.64 + 0.49 = 1.13 ≥ 1. For dealing with such types of situations, in this article we examine the novel approach of complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental operational laws
If we considered the value of parameter q = 1 in the environment of q-ROFS, the q-ROFS is converted for intuitionistic fuzzy set (IFS)
Summary
Proposed the innovative concept of fuzzy set (FS) in 1965, which is characterized by a membership function limited to [0, 1], and it has been proven to be a very powerful tool to deal with uncertain information in real-life problems. The fuzzy sets have many advantages, there are some situations where it is difficult or impossible to solve the issue by using only membership function. To handle this issue, Atanassov [4] introduced the notion of intuitionistic fuzzy set (IFS) as a generalization of FS, which is characterized by membership function, non-membership function, and indeterminacy or inconsistency belonging to [0, 1]. The concept of IFS is a more powerful tool than FS to cope with
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