Q-rung orthopair normal fuzzy aggregation operators and their application in multi-attribute decision-making

© 2019 by the authors. Q-rung orthopair fuzzy set (q-ROFS) is a powerful tool to describe uncertain information in the process of subjective decision-making, but not express vast objective phenomenons that obey normal distribution. For this situation, by combining the q-ROFS with the normal fuzzy number, we proposed a new concept of q-rung orthopair normal fuzzy (q-RONF) set. Firstly, we defined the conception, the operational laws, score function, and accuracy function of q-RONF set. Secondly, we presented some new aggregation operators to aggregate the q-RONF information, including the q-RONF weighted operators, the q-RONF ordered weighted operators, the q-RONF hybrid operator, and the generalized form of these operators. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Meanwhile, we applied the proposed operators to the multi-attribute decision-making (MADM) problem and established a novel MADM method. Finally, the proposed MADM method was applied in a numerical example on enterprise partner selection, the numerical result showed the proposed method can effectively handle the objective phenomena with obeying normal distribution and complicated fuzzy information, and has high practicality. The results of comparative and sensitive analysis indicated that our proposed method based on q-RONF aggregation operators over existing methods have stronger information aggregation ability, and are more suitable and flexible for MADM problems

Large-Scale Green Supplier Selection Approach under a Q-Rung Interval-Valued Orthopair Fuzzy Environment

As enterprises pay more and more attention to environmental issues, the green supply chain management (GSCM) mode has been extensively utilized to guarantee profit and sustainable development. Greensupplierselection(GSS),whichisakeysegmentofGSCM,hasbeeninvestigated to put forward plenty of GSS approaches

Group Decision Algorithm for Aged Healthcare Product Purchase Under q-Rung Picture Normal Fuzzy Environment Using Heronian Mean Operator

With the intensification of the aging, the health issue of the elderly is arousing public concern increasingly. Various healthcare products for the elderly are emerging from the market, thus how to select suitable aged healthcare product is critical to the well-being of the elderly. In the literature, nonetheless, a comprehensive and standardized evaluation framework to support healthcare product purchase decision for the aged is currently lacking. This paper proposes a novel group decision-making method to aid the decision-making of aged healthcare product purchase based on q-rung picture normal fuzzy Heronian mean (q-RPtNoFHM) operators. In it, firstly, a new fuzzy variable called the q-rung picture normal fuzzy set (q-RPtNoFS) is defined to reasonably describe different responses to healthcare product evaluation, for which, some definitions including operational laws, a score function, and an accuracy function of q-RPtNoFSs are introduced. Then, two q-RPtNoFHM operators are presented to aggregate group decision information. In addition, some properties of q-RPtNoFHM operators, such as monotonicity, commutativity, and idempotency, are discussed. Finally, an example on antihypertensive drugs purchase is gave to illustrate the practicality of the proposed method, and conduct sensitivity analysis to analyze the effectiveness and flexibility of proposed methods

Improved Knowledge Measures for q-Rung Orthopair Fuzzy Sets

The q-rung orthopair fuzzy set (qROFS) defined by Yager is a generalization of Atanassov intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFSs). In this paper, we define the knowledge measure for qROFS by using the cosine inverse function. The information precision and information content are two facets of knowledge measure. Both facets of knowledge measure are considered. The properties of knowledge measure and their graphical explanations are discussed. An application of the knowledge measure in multi-attribute group decision-making (MAGDM) problem under the confidence level approach is given. A numerical example of the selection of renewable energy sources is discussed

q-rung logarithmic Pythagorean neutrosophic vague normal aggregating operators and their applications in agricultural robotics

The article explores multiple attribute decision making problems through the use of the Pythagorean neutrosophic vague normal set (PyNVNS). The PyNVNS can be generalized to the Pythagorean neutrosophic interval valued normal set (PyNIVNS) and vague set. This study discusses $q$-rung log Pythagorean neutrosophic vague normal weighted averaging ($q$-rung log PyNVNWA), $q$-rung logarithmic Pythagorean neutrosophic vague normal weighted geometric ($q$-rung log PyNVNWG), $q$-rung log generalized Pythagorean neutrosophic vague normal weighted averaging ($q$-rung log GPyNVNWA), and $q$-rung log generalized Pythagorean neutrosophic vague normal weighted geometric ($q$-rung log GPyNVNWG) sets. The properties of $q$-rung log PyNVNSs are discussed based on algebraic operations. The field of agricultural robotics can be described as a fusion of computer science and machine tool technology. In addition to crop harvesting, other agricultural uses are weeding, aerial photography with seed planting, autonomous robot tractors and soil sterilization robots. This study entailed selecting five types of agricultural robotics at random. There are four types of criteria to consider when choosing a robotics system: robot controller features, cheap off-line programming software, safety codes and manufacturer experience and reputation. By comparing expert judgments with the criteria, this study narrows the options down to the most suitable one. Consequently, $q$ has a significant effect on the results of the models

A novel approach to multi-attribute group decision-making based on interval-valued intuitionistic fuzzy power Muirhead mean

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method