Multiple attribute group decision making based on q-rung orthopair fuzzy Heronian mean operators

Abstract

The q-rung orthopair set (q-ROFSs) can serve as a generalization of the existing orthopair fuzzy sets, including intuitionistic fuzzy sets and Pythagorean fuzzy sets. The most desirable characteristic of q-ROFSs is that they support a greater space of allowable membership grades and provide decision makers more freedom in describing their true opinions. As a classical aggregation operator, Heronian mean (HM) can model the interrelationship between attributes. In this paper, we extend the traditional HM to aggregate q-rung orthopair fuzzy information and propose the q-rung orthopair fuzzy HM and its weighted form.Further, to overcome the shortcomings of the traditional HM, considering the possible partition structure in the actual decision situations, we propose the q-rung orthopair fuzzy partitioned Heronian mean operator and the q-rung orthopair fuzzy weighted partitioned Heronian mean operator. Then, some special cases and some desirable properties are investigated and discussed. A new multiple attribute group decision-making(MAGDM) technique is developed based on the proposed q-rung orthopair fuzzy operators. Finally, a representative example is provided to verify the effectiveness and superiority of the proposed method by comparing with other several existing representative MAGDM methods. K E Y W O R D SHeronian mean, multiple attribute group decision making, partition structure, q-rung orthopair fuzzy set Multiattribute decision making (MADM) is a common activity in people's daily life and business management. In the research of MADM methods, modeling and managing assessment information is a prerequisite for obtaining the optimal solution. Since Zadeh 1 originally proposed the concept of fuzzy sets (FSs) to describe the uncertainty of object, many classical extensions of FSs have been presented to accommodate to different decision scenarios, such as intuitionistic fuzzy sets (IFSs), 2 type-2 fuzzy sets, 3 hesitant fuzzy sets, 4 Pythagorean fuzzy set (PFS), 5 etc. These different extensions have been successfully applied to many different fields, such as risk management, information recommended, pattern recognition, etc. and have achieved fruitful research results. [6][7][8][9][10][11] Recently, Bustince et al. 12 reviewed the definition, properties, and other knowledge about different extensions of ordinary FSs that have been presented in the past few decades. They also summarized and analyzed the difference and the relationships between these extensions.Among these extensions of FSs, IFSs 2 are considered as powerful tools for modeling uncertainty and fuzziness, which characterize each element with a membership degree and a nonmembership degree and satisfies the restriction that the sum of them is less than or equal to 1. In the past 30 years, many scholars have conducted in-depth exploration and research on IFSs and a large number of results within the IFS context have been achieved, including comparison and ranking methods, distance measures, correlation coefficients, operation operators, preference relat...

Research on the assessment of classroom teaching quality with q ‐rung orthopair fuzzy information based on multiparametric similarity measure and combinative distance‐based assessment

“…Meanwhile, Liu et al developed some new q ‐rung orthopair fuzzy aggregation operators based on Bonferroni mean and power Maclaurin symmetric mean for aggregating the decision‐making information given by experts. Wei et al and Liu et al explored some q ‐rung orthopair fuzzy Heronian mean operators in MCDM. Peng et al studied exponential operation and aggregation operator for q ‐ROFS based on a new score function and applied them to the selection of teaching management system.…”

“…Due to the shortcomings (counterintuitive phenomena, higher computational complexity) of the existing decision‐making algorithms for q ‐ROFSs, they may be difficult for decision‐makers to select convincible or optimal alternatives. As a consequence, the aim of this paper is to deal the two challenges mentioned above by developing two MCDM approaches to managing evaluation information for q ‐ROFSs, which not only have a lower computational complexity, but also can achieve an optimal alternative out of counterintuitive phenomena.…”

“…The effect of the four parameters () on the ordering of the alternatives are presented. The new score function for q ‐rung orthopair fuzzy number ( q ‐ROFN) is put forward for dealing the comparison problem Two proposed algorithms with some existing algorithms are compared by some examples. Their objective evaluation is carried out, and the methods which maintain consistency of their results are chosen.…”

“…Two proposed algorithms with some existing algorithms are compared by some examples. Their objective evaluation is carried out, and the methods which maintain consistency of their results are chosen.…”

Research on arithmetic operations over generalized orthopair fuzzy sets

“…Specially, Yager et al developed the OWA and Choquet aggregation operations on ‐ROFSs. Along this line of research, Liu and his colleagues introduced the weighted averaging/geometric operation, (weighted, geometric) Bonferroni mean operation, (weighted) extended Bonferroni mean operation, (weighted) Archimedean Bonferroni mean operation, power (weighted) Maclaurin symmetric mean operation, and (weighted) Heronian mean operation on ‐ROFSs. Wei et al further put forward the generalized (weighted) Heronian mean operation and (weighted) geometric Heronian mean operation for ‐ROFSs.…”