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Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making
Recently proposed q-rung orthopair fuzzy set (q-ROFS) is a powerful and effective tool to describe fuzziness, uncertainty and vagueness. The prominent feature of q-ROFS is that the sum and square sum of membership and non-membership degrees are allowed to be greater than one with the sum of qth power of the membership degree and qth power of the non-membership degree is less than or equal to one. This characteristic makes q-ROFS more powerful and useful than intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS). The aim of this paper is to develop some aggregation operators for fusing q-rung orthopair fuzzy information. As the Muirhead mean (MM) is considered as a useful aggregation technology which can capture interrelationships among all aggregated arguments, we extend the MM to q-rung orthopair fuzzy environment and propose a family of q-rung orthopair fuzzy Muirhead mean operators. Moreover, we investigate some desirable properties and special cases of the proposed operators. Further, we apply the proposed operators to solve multi-attribute group decision making (MAGDM) problems. Finally, a numerical instance as well as some comparative analysis are provided to demonstrate the validity and superiorities of the proposed method
Pythagorean 2-tuple linguistic power aggregation operators in multiple attribute decision making
In this paper, we investigate the multiple attribute decision making
problems with Pythagorean 2-tuple linguistic information.
Then, we utilize power average and power geometric operations
to develop some Pythagorean 2-tuple linguistic power aggregation
operators: Pythagorean 2-tuple linguistic power weighted
average (P2TLPWA) operator, Pythagorean 2-tuple linguistic power
weighted geometric (P2TLPWG) operator, Pythagorean 2-tuple linguistic
power ordered weighted average (P2TLPOWA) operator,
Pythagorean 2-tuple linguistic power ordered weighted geometric
(P2TLPOWG) operator, Pythagorean 2-tuple linguistic power
hybrid average (P2TLPHA) operator and Pythagorean 2-tuple linguistic
power hybrid geometric (P2TLPHG) operator. The prominent
characteristic of these proposed operators are studied. Then,
we have utilized these operators to develop some approaches to
solve the Pythagorean 2-tuple linguistic multiple attribute decision
making problems. Finally, a practical example for enterprise
resource planning (ERP) system selection is given to verify the
developed approach and to demonstrate its practicality and
effectiveness
Generalized Hamacher aggregation operators for intuitionistic uncertain linguistic sets: Multiple attribute group decision making methods
© 2019 by the authors. In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method
Circular Pythagorean fuzzy sets and applications to multi-criteria decision making
In this paper, we introduce the concept of circular Pythagorean fuzzy set
(value) (C-PFS(V)) as a new generalization of both circular intuitionistic
fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs)
proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle
that represents the membership degree and the non-membership degree and whose
center consists of non-negative real numbers and with the condition
. A C-PFS models the fuzziness of the uncertain information
more properly thanks to its structure that allows modelling the information
with points of a circle of a certain center and a radius. Therefore, a C-PFS
lets decision makers to evaluate objects in a larger and more flexible region
and thus more sensitive decisions can be made. After defining the concept of
C-PFS we define some fundamental set operations between C-PFSs and propose some
algebraic operations between C-PFVs via general -norms and -conorms. By
utilizing these algebraic operations, we introduce some weighted aggregation
operators to transform input values represented by C-PFVs to a single output
value. Then to determine the degree of similarity between C-PFVs we define a
cosine similarity measure based on radius. Furthermore, we develop a method to
transform a collection of Pythagorean fuzzy values to a PFS. Finally, a method
is given to solve multi-criteria decision making problems in circular
Pythagorean fuzzy environment and the proposed method is practiced to a problem
about selecting the best photovoltaic cell from the literature. We also study
the comparison analysis and time complexity of the proposed method
Multi-criteria decision-making based on Pythagorean cubic fuzzy Einstein aggregation operators for investment management
Pythagorean cubic fuzzy sets (PCFSs) are a more advanced version of interval-valued Pythagorean fuzzy sets where membership and non-membership are depicted using cubic sets. These sets offer a greater amount of data to handle uncertainties in the information. However, there has been no previous research on the use of Einstein operations for aggregating PCFSs. This study proposes two new aggregator operators, namely, Pythagorean cubic fuzzy Einstein weighted averaging (PCFEWA) and Pythagorean cubic fuzzy Einstein ordered weighted averaging (PCFEOWA), which extend the concept of Einstein operators to PCFSs. These operators offer a more effective and precise way of aggregating Pythagorean cubic fuzzy information, especially in decision-making scenarios involving multiple criteria and expert opinions. To illustrate the practical implementation of this approach, we apply an established MCDM model and conduct a case study aimed at identifying the optimal investment market. This case study enables the evaluation and validation of the established MCDM model's effectiveness and reliability, thus making a valuable contribution to the field of investment analysis and decision-making. The study systematically compares the proposed approach with existing methods and demonstrates its superiority in terms of validity, practicality and effectiveness. Ultimately, this paper contributes to the ongoing development of sophisticated techniques for modeling and analyzing complex systems, offering practical solutions to real-world decision-making problems
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