A Method to Multi-Attribute Group Decision-Making Problem with Complex q-Rung Orthopair Linguistic Information Based on Heronian Mean Operators

Abstract

The notions of complex q-rung orthopair fuzzy sets (Cq-ROFSs) and linguistic sets (LSs) are two different concepts to deal with uncertain information in multi-attribute group decision-making (MAGDM) problems. The Heronain mean (HM) and geometric Heronain mean (GHM) operators are an effective tool used to aggregate some q-rung orthopair linguistic fuzzy numbers (q-ROLFNs) into a single element. The purpose of this manuscript is to propose a new concept called complex q-rung orthopair linguistic sets (Cq-ROLSs) to cope with complex uncertain information in real decision-making problems. Then the fundamental laws and their examples of the Cq-ROLSs are also given. Furthermore, the notions of complex q-rung orthopair linguistic Heronian mean (Cq-ROLHM) operator, complex q-rung orthopair linguistic weighted Heronian mean (Cq-ROLWHM) operator, complex q-rung orthopair linguistic geometric Heronian mean (Cq-ROLGHM) operator, complex q-rung orthopair linguistic weighted geometric Heronian mean (Cq-ROLWGHM) operator are proposed and their basic properties are also discussed. Moreover, we develop a novel approach to MAGDM using proposed operators and a numerical example is used to describe the flexibility and explicitly of the initiated operators. In last, the comparison between proposed method and existing work is also discussed in detail.

Complex q‐rung orthopair fuzzy 2‐tuple linguistic Maclaurin symmetric mean operators and its application to emergency program selection

“…To elaborate the validity and practicability of the created method in this essay, we conduct a collection of comparative analysing with other previous decision methodologies including the method based upon complex intuitionistic fuzzy weighted averaging (CIFWA) operator proposed by Garg, 27 the method based upon complex intuitionistic BM (CIFBM) operator proposed by Garg 28 and the method based upon complex q-rung orthopair fyzzy linguistic Heronian mean (Cq-ROFLHM) operator proposed by Liu et al 39 We utilize these methods to cope with the Example 1 in this paper, the score values and ranking of alternatives are displayed in Table 11. From it, we can attain the same sorting results of alternatives based on the previous methods and the designed method in this article, which can verify the availability of the propounded method.…”

“…✓ Compared with the approach on the basis of Cq-ROFLHM operator proposed by Liu et al, 39 the following three aspects are given highlight the difference between Cq-ROFLHM and Cq-ROF2TLMSM operator. 1 .…”

“…Li et al 38 expanded the EDAS method to q-rung orthopair fuzzy context to establish DM approach. Further, Liu et al 39 presents the concept of complex q-ROFS (Cq-ROFS) and Cq-ROFLS set (Cq-ROFLS) and further advanced several Cq-ROFL Heronian mean (HM) operators to build up decision model. The above fuzzy sets can only depict information from the point of quantitative and DMs are difficult to provide the precise numerical values to express their viewpoint.…”

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

“…For better understanding the established work in the next section, we concisely review some useful notions of CQROFS (Liu et al 2019a , b ; Zadeh 1974 ) and their operational laws. The notion of linguistic term set and uncertain linguistic term set are also discussed.…”

“…But these was still a problem, when a decision maker indicate their opinion in the form of yes is and in the form of no is , then probably the sum of the squares of the real part (also for imaginary part) of the both is exceeded form the unit interval. For addressing such types of difficulties, Liu et al ( 2019a , b ) explored the complex QROFS (CQROFS) with a condition that is the sum of q-powers of the real part (also for imaginary part) of the truth and the real part (also for imaginary part) of the falsity grades is not exceeded form unit interval. CQROFS is extensive proficient technique to resolve real-decision activities.…”