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Interval-valued Pythagorean fuzzy (IVPF) set is one the successful extension of the existing theories for handling the uncertainties during the decision-making process. Under that environment, various aggregation operators have been developed by the authors to aggregate the different preferences of the decision makers under the different attributes. But these studies have conducted under the assumption that their corresponding pairs are independent and don’t consider the interaction between the pairs of the membership degrees. In this paper, these conditions have been relaxed by considering the interrelationship between the different inputs by using Maclaurin symmetric mean (MSM) operator. Further, based on the input and MSM operator, we proposed two aggregation operators namely, IVPF Maclaurin symmetric mean and IVPF weighted Maclaurin symmetric mean operators and studied their desirable properties. A decision-making method based on these operators has been discussed for solving the decision-making problems under IVPF set environment. Finally, an illustrative example and a comparative analysis have been presented to demonstrate the proposed approach.

In this article, we combine some fundamental theories of the Pythagorean 2-tuple linguistic sets (P2TLSs) with EDAS method and design the Pythagorean 2-tuple linguistic number (P2TLN) EDAS (P2TLN-EDAS) method for multiple attribute group decision making (MAGDM) issue. Firstly, the basic concepts of P2TLSs are introduced. Next, two aggregation operators of P2TLN are defined, and then the calculation steps of EDAS method are listed briefly. Furthermore, P2TLN-EDAS method is given for MAGDM problems and computing steps are proposed in detail. Finally, a computational example related to construction safety assessment is used to expound the effectiveness of the designed method. Meanwhile, we also carried out some comparative analysis between P2TLN-EDAS method and P2TLWA/P2TLWG operators and another P2TLN-TODIM method. The results show that P2TLN-EDAS method derives the same best alternative as P2TLWA, P2TLWG operators and P2TLN-TODIM method. [ABSTRACT FROM AUTHOR]

In this paper, a new set of intuitionistic fuzzy aggregation operators have been introduced under the environment of intuitionistic fuzzy sets (IFSs). For this, firstly focused on some existing aggregation operators and then new operational rules known as Dombi operation have been pro- posed which make the advancement of flexibility behavior with the parameter. Based on Dombi operation laws, some new averaging and geometric aggregation operators namely, intuitionistic fuzzy Dombi weighted averaging, ordered weighted averaging and hybrid weighted averaging operator, classified as IFDWA, IFDOWA and IFDHWA operators respectively and intuitionistic fuzzy Dombi geometric, ordered weighted geometric and hybrid weighted geometric operators, labeled as IFDWG, IFDOWG and IFDHWG operators respectively have been proposed. Further, some properties such as idempotency, boundedness, monotonicity and commutative are inves- tigated. Finally, a multi-attribute decision-making model has been developed for the proposed operators to select the best mutual fund for investment. The execution of the comparative study has been examined with the existing operators in this environment. [ABSTRACT FROM AUTHOR]

In this paper, we present the 2-tuple linguistic neutrosophic CODAS model based on the traditional fuzzy CODAS (combinative distance-based assessment) model and some fundamental theories of 2-tuple linguistic neutrosophic information. Firstly, we briefly review the definition of 2-tuple linguistic neutrosophic sets (2TLNSs) and introduce the score function, the accuracy function, operation laws and some aggregation operators of 2TLNNs. Then, the calculation steps of traditional fuzzy CODAS model are briefly presented. Furthermore, by combining the traditional fuzzy CODAS model with 2TLNNs information, the 2-tuple linguistic neutrosophic CODAS model is established and the computing steps for multiple attribute group decision making (MAGDM) are simply depicted. Our presented model is more accurate and effective for considering the combinative form of two distance measurements, including fuzzy weighted Hamming distance (HD) and fuzzy weighted Euclidean distance (ED). Finally, a numerical example for safety assessment of construction project has been given to illustrate this new model and some comparisons between 2TLNNs CODAS model and two 2TLNNs aggregation operators are also made to further illustrate the advantages of the new method. [ABSTRACT FROM AUTHOR]

In this paper, we present the 2-tuple linguistic neutrosophic MABAC model based on the traditionalMABAC (multi-attributive border approximation area comparison) model and some fundamental theories of 2-tuple linguistic neutrosophic information. Firstly, we briefly review the definition of 2-tuple linguistic neutrosophic sets (2TLNNSs) and introduce the score function, accuracy function, operation laws and some aggregation operators of 2TLNNs. Then, the calculation steps of traditional MABAC model are briefly presented. Furthermore, combine the traditional MABAC model with 2TLNNs information, the 2-tuple linguistic neutrosophic MABAC model is established for multiple attribute group decision making (MAGDM) and the computing steps are simply depicted. In our presented model; it's more accuracy and effective for computing the distance between each alternatives and the border approximation area (BAA). Finally, a numerical example for safety assessment of construction project has been given to illustrate this new model and some comparisons between 2TLNNsMABAC model and two 2TLNNs aggregation operators are also conducted to further illustrate advantages of the new method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making problems based on the Bonferroni mean operators with dual Pythagorean hesitant fuzzy information. Firstly, we introduce the concept and basic operations of the dual hesitant Pythagorean fuzzy sets, which is a new extension of Pythagorean fuzzy sets. Then, motivated by the idea of Bonferroni mean operators, we have developed some Bonferroni mean aggregation operators for aggregating dual hesitant Pythagorean fuzzy information. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the dual hesitant Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example for supplier selection in supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we extend MM operator and dual MM (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs) and then to solve the MADM problems. Firstly, we develop some interval-valued Pythagorean fuzzy Muirhead mean operators by extending MM and DMM operators to IVPFNs. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present some new methods to deal with MADM problems with the IVPFNs based on the proposed MM and DMM operators. Finally, we verify the validity and reliability of our methods by using an application example for green supplier selections, and analyse the advantages of our methods by comparing it with other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making problems with Pythagorean fuzzy information. Then, we utilize arithmetic and geometric operations to develop some Pythagorean fuzzy interaction aggregation operators: Pythagorean fuzzy interaction weighted average (PFIWA) operator, Pythagorean fuzzy interaction weighted geometric (PFIWG) operator, Pythagorean fuzzy interaction ordered weighted average (PFIOWA) operator, Pythagorean fuzzy interaction ordered weighted geometric (PFIOWG) operator, Pythagorean fuzzy interaction hybrid average (PFIHA) operator, Pythagorean fuzzy interaction hybrid geometric (PFIHG) operator, Pythagorean fuzzy interaction correlate aggregation operators, Pythagorean fuzzy interaction induced aggregation operators, Pythagorean fuzzy interaction induced correlate aggregation operators, Pythagorean fuzzy interactive power arithmetic and geometric aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example for selecting the service outsourcing provider of communications industry is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with interval-valued dual hesitant fuzzy uncertain linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we propose some aggregation operators for aggregating intervalvalued dual hesitant fuzzy uncertain linguistic information. Then, we have utilized these operators to develop some approaches to solve the interval-valued dual hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example for selecting the service outsourcing provider of communications industry is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making problems with picture fuzzy information. Then, we utilize arithmetic and geometric operations to develop some picture fuzzy aggregation operators: picture fuzzy weighted average (PFWA) operator, picture fuzzy weighted geometric (PFWG) operator, picture fuzzy ordered weighted average (PFOWA) operator, picture fuzzy ordered weighted geometric (PFOWG) operator, picture fuzzy hybrid average (PFHA) operator and picture fuzzy hybrid geometric (PFHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the picture fuzzy 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. [ABSTRACT FROM AUTHOR]

Bipolar 2-tuple linguistic aggregation operators are developed in the current study for aggregation operations including weighted average, weighted geometric average, ordered weighted average, ordered weighted geometric average, hybrid average and hybrid geometric average. We investigate the characteristics of these operators, and present methods that apply these operators to solving the bipolar 2-tuple linguistic multiple attribute decision making problems. A real-world example is then analyzed to illustrate the relevance and effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

Hamacher product is a t-norm and Hamacher sum is a t-conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Hamacher operations to develop some hesitant Pythagorean fuzzy aggregation operators: hesitant Pythagorean fuzzy Hamacher weighted average (HPFHWA) operator, hesitant Pythagorean fuzzy Hamacher weighted geometric (HPFHWG) operator, hesitant Pythagorean fuzzy Hamacher ordered weighted average (HPFHOWA) operator, hesitant Pythagorean fuzzy Hamacher ordered weighted geometric (HPFHOWG) operator, hesitant Pythagorean fuzzy Hamacher hybrid average (HPFHHA) operator and hesitant Pythagorean fuzzy Hamacher hybrid geometric (HPFHHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the hesitant Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making problems with Pythagorean 2-tuple linguistic information. Then, we utilize arithmetic and geometric operations to develop some Pythagorean 2-tuple linguistic aggregation operators. 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 MADM 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. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making problems based on the aggregation operators with hesitant bipolar fuzzy information. Then, motivated by the ideal of arithmetic and geometric operation, we have developed some aggregation operators for aggregating hesitant bipolar fuzzy information: hesitant bipolar fuzzy weighted average (HBFWA) operator, hesitant bipolar fuzzy weighted geometric (HBFWG) operator, hesitant bipolar fuzzy ordered weighted average (HBFOWA) operator, hesitant bipolar fuzzy ordered weighted geometric (HBFOWG) operator, hesitant bipolar fuzzy hybrid average (HBFHA) operator and hesitant bipolar fuzzy hybrid geometric (HBFHG) operator. Then, we have utilized these operators to develop some approaches to solve the hesitant bipolar fuzzy multiple attribute decision making problems. Finally, an illustrative example for evaluating the constructional engineering software quality is then analyzed to illustrate the relevance and effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

The article investigates the multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of triangular fuzzy information. Motivated by the ideal of power aggregation, in this paper some power aggregation operators for aggregating triangular fuzzy information are developed and then applied in order to develop some models for multiple attribute group decision making with triangular fuzzy information. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

With respect to multiple attribute decision making (MADM) problems in which attribute values take the form of fuzzy number intuitionistic fuzzy values, a new decision making analysis method is developed. First, some operational laws of fuzzy number intuitionistic fuzzy values, score function and accuracy function of fuzzy number intuitionistic fuzzy values are introduced. Then, we have developed two fuzzy number intuitionistic fuzzy Choquet integral aggregation operators: fuzzy number intuitionistic fuzzy Choquet ordered averaging (FNIFCOA) operator and fuzzy number intuitionistic fuzzy Choquet ordered geometric mean (FNIFCOGM) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of the FNIFCOA and FNIFCOGM operators, such as commutativity, idempotency and monotonicity, and applied the FNIFCOA and FNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information. Finally an illustrative example has been given to show the developed method. [ABSTRACT FROM AUTHOR]