A novel trigonometric operation-based q -rung orthopair fuzzy aggregation operator and its fundamental properties
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ORIGINAL ARTICLE
A novel trigonometric operation-based q-rung orthopair fuzzy aggregation operator and its fundamental properties Harish Garg1 Received: 22 August 2019 / Accepted: 14 March 2020 Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The q-rung orthopair fuzzy sets (q-ROFSs) are a prominent idea to express the fuzzy information in the decision-making process and are the generalization of the existing intuitionistic fuzzy set and Pythagorean fuzzy set. The q-ROFSs can dynamically adapt the information by changing the parameter q 1 based on the membership degree and therefore support more innumerable possibilities. Driven by these requisite characteristics, this paper aspires to present some sine trigonometric operations laws for q-ROFSs. The sine trigonometry function preserves the periodicity and symmetric about the origin, and hence, it satisfies the decision-maker preferences toward the evaluation of the objects. Associated with these laws, we define a series of new aggregation operators named as sine trigonometry weighted averaging and geometric operators to aggregate the q-rung orthopair fuzzy information. The fundamental relations between the proposed operators are also examined. Afterward, we present a group decision-making technique to solve the multiple attribute group decisionmaking problems based on proposed operators and illustrate with a numerical example to verify it. The superiors, as well as the advantages of the proposed operators, are also discussed in it. Lastly, the influence of the membership degrees on the operations has been investigated and found that when the parameter q increases from 2 to 4 and then from 4 to 7, then there is the certain change in the range of the score values. Keywords q-rung orthopair Sine trigonometric operations Operational laws Aggregation operators, group decision making
1 Introduction Multiple attribute group decision-making (MAGDM) process is one of the most famous and emerging topics which represent a way to elect the finest alternative with a group of decision-makers and attributes. In this process, there are two critical tasks. The first one is to describe the environment where the values of different attributes are measured efficiently, while the second task is to aggregate the described information. Traditionally, the information which represents the objects is mostly taken in the form of the deterministic or crisp. However, with the developing
& Harish Garg [email protected]; [email protected] http://sites.google.com/site/harishg58iitr/ 1
School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala, Punjab 147004, India
complexities of the systems day by day, it is very challenging to collect the information, from the logbooks, resources and experts, in crisp form. Thus, to reveal the information more clearly, a theory of fuzzy sets [42] and its extensions such as the intuitionistic fuzzy set (IFS) [3] and Pythagorean fuzzy se
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