scholarly journals Application of the Bipolar Neutrosophic Hamacher Averaging Aggregation Operators to Group Decision Making: An Illustrative Example

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 698 ◽  
Author(s):  
Muhammad Jamil ◽  
Saleem Abdullah ◽  
Muhammad Yaqub Khan ◽  
Florentin Smarandache ◽  
Fazal Ghani
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Neutrosophic Set ◽  
Ordered Weighted Averaging ◽  
New Methods

The present study aims to introduce the notion of bipolar neutrosophic Hamacher aggregation operators and to also provide its application in real life. Then neutrosophic set (NS) can elaborate the incomplete, inconsistent, and indeterminate information, Hamacher aggregation operators, and extended Einstein aggregation operators to the arithmetic and geometric aggregation operators. First, we give the fundamental definition and operations of the neutrosophic set and the bipolar neutrosophic set. Our main focus is on the Hamacher aggregation operators of bipolar neutrosophic, namely, bipolar neutrosophic Hamacher weighted averaging (BNHWA), bipolar neutrosophic Hamacher ordered weighted averaging (BNHOWA), and bipolar neutrosophic Hamacher hybrid averaging (BNHHA) along with their desirable properties. The prime gain of utilizing the suggested methods is that these operators progressively provide total perspective on the issue necessary for the decision makers. These tools provide generalized, increasingly exact, and precise outcomes when compared to the current methods. Finally, as an application, we propose new methods for the multi-criteria group decision-making issues by using the various kinds of bipolar neutrosophic operators with a numerical model. This demonstrates the usefulness and practicality of this proposed approach in real life.

scholarly journals Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 658 ◽  
Author(s):  
Aliya Fahmi ◽  
Fazli Amin ◽  
Florentin Smarandache ◽  
Madad Khan ◽  
Nasruddin Hassan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Linguistic Information ◽  
Ordered Weighted Averaging ◽  
Averaging Operator ◽  
Multiple Attribute ◽  
The Relationship

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach.

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
Author(s):  
Khaista Rahman ◽  
Saleem Abdullah ◽  
Muhammad Sajjad Ali Khan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Interval Valued

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

scholarly journals Group Decision Making Based on Triangular Neutrosophic Cubic Fuzzy Einstein Hybrid Weighted Averaging Operators

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 180 ◽  
Author(s):  
Aliya Fahmi ◽  
Fazli Amin ◽  
Madad Khan ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Averaging Operators ◽  
Ordered Weighted Averaging ◽  
Multiple Attribute

In this paper, a new concept of the triangular neutrosophic cubic fuzzy numbers (TNCFNs), their score and accuracy functions are introduced. Based on TNCFNs, some new Einstein aggregation operators, such as the triangular neutrosophic cubic fuzzy Einstein weighted averaging (TNCFEWA), triangular neutrosophic cubic fuzzy Einstein ordered weighted averaging (TNCFEOWA) and triangular neutrosophic cubic fuzzy Einstein hybrid weighted averaging (TNCFEHWA) operators are developed. Furthermore, their application to multiple-attribute decision-making with triangular neutrosophic cubic fuzzy (TNCF) information is discussed. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals Interval-Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on Improved Hamacher Aggregation Operators and Continuous Entropy

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Jun Liu ◽  
Ning Zhou ◽  
Li-Hua Zhuang ◽  
Ning Li ◽  
Fei-Fei Jin
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Cowa Operator ◽  
Interval Valued

Under the interval-valued hesitant fuzzy information environment, we investigate a multiattribute group decision making (MAGDM) method with continuous entropy weights and improved Hamacher information aggregation operators. Firstly, we introduce the axiomatic definition of entropy for interval-valued hesitant fuzzy elements (IVHFEs) and construct a continuous entropy formula on the basis of the continuous ordered weighted averaging (COWA) operator. Then, based on the Hamachert-norm andt-conorm, the adjusted operational laws for IVHFEs are defined. In order to aggregate interval-valued hesitant fuzzy information, some new improved interval-valued hesitant fuzzy Hamacher aggregation operators are investigated, including the improved interval-valued hesitant fuzzy Hamacher ordered weighted averaging (I-IVHFHOWA) operator and the improved interval-valued hesitant fuzzy Hamacher ordered weighted geometric (I-IVHFHOWG) operator, the desirable properties of which are discussed. In addition, the relationship among these proposed operators is analyzed in detail. Applying the continuous entropy and the proposed operators, an approach to MAGDM is developed. Finally, a numerical example for emergency operating center (EOC) selection is provided, and comparative analyses with existing methods are performed to demonstrate that the proposed approach is both valid and practical to deal with group decision making problems.

Dependent Interval 2-Tuple Linguistic Aggregation Operators and Their Application to Multiple Attribute Group Decision Making

2014 ◽  
Vol 22 (05) ◽  
pp. 717-735 ◽  
Author(s):  
Hu-Chen Liu ◽  
Qing-Lian Lin ◽  
Jing Wu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Linguistic Variables ◽  
Preference Information ◽  
Operational Laws ◽  
Multiple Attribute

Consider the various types of uncertain preference information provided by the decision makers and the importance of determining the associated weights for the aggregation operator, the multiple attribute group decision making (MAGDM) methods based on some dependent interval 2-tuple linguistic aggregation operators are proposed in this paper. Firstly some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop a dependent interval 2-tuple weighted averaging (DITWA) operator and a dependent interval 2-tuple weighted geometric (DITWG) operator, in which the associated weights only depend on the aggregated interval 2-tuple arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to them. Based on the DITWA and the DITWG operators, some approaches for multiple attribute group decision making with interval 2-tuple linguistic information are proposed. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approaches.

scholarly journals Multiple Attribute Group Decision-Making process based on Generalized Archimedean Linguistic Pythagorean Fuzzy  Averaging Aggregation Operators

2021 ◽  
Author(s):  
Rajkumar Verma ◽  
Niti Mittal
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Pythagorean Fuzzy Set ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Linguistic Scale Function

Abstract The linguistic Pythagorean fuzzy set (LPFS) is a prominent tool for comprehensively representing qualitative information data. Aggregation operators (AOs) play an essential role in multiple attribute group decision-making (MAGDM) problems. In the present manuscript, we define four new operational laws for linguistic Pythagorean fuzzy numbers (LPFNs) based on Archimedean t-norm and t-conorm. Paper also uses the linguistic scale function (LSF) in order to accommodate different semantic situations during the operational process. Next, we introduce some new generalized arithmetic AOs, including the generalized Archimedean linguistic Pythagorean fuzzy weighted averaging (GALPFWA) operator, the generalized Archimedean linguistic Pythagorean fuzzy ordered weighted averaging (GALPFOWA) operator, the generalized Archimedean linguistic Pythagorean fuzzy hybrid averaging (GALPFHA) operator along with their desirable properties. The developed AOs include several existing linguistic Pythagorean fuzzy aggregation operators as their particular and limiting cases. Finally, using the proposed AOs, a new approach for solving the MAGDM problem is given and illustrated with a real-life numerical example to demonstrate its flexibility and effectiveness.

scholarly journals Prioritized Linguistic Interval-Valued Aggregation Operators and Their Applications in Group Decision-Making Problems

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 209 ◽  
Author(s):  
Kamal Kumar ◽  
Harish Garg
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Efficient Tool ◽  
Intuitionistic Fuzzy ◽  
Quantitative Manner ◽  
Interval Valued

The linguistic interval-valued intuitionistic fuzzy (LIVIF) set is an efficient tool to represent data in the form of interval membership degrees in a qualitative rather than a quantitative manner. The LIVIF set combines the features of interval-valued intuitionistic fuzzy sets (IFSs) and the linguistic variables (LV) and hence provides more freedom to decision-makers. Under this environment, the main objective of this manuscript is to propose some new aggregation operators by capturing the prioritized relationship between the objects. For this, different weighted averaging and geometric aggregation operators are proposed in which preferences related to each object are expressed in terms of LIVIF numbers. Desirable properties of the proposed operators are studied. Further, a group decision-making (DM) approach is presented to solve the multi-attribute DM problems, and its efficiency has been verified with an illustrative example.

scholarly journals Some Generalized Single Valued Neutrosophic Linguistic Operators and Their Application to Multiple Attribute Group Decision Making

2017 ◽  
Vol 5 (2) ◽  
pp. 148-162 ◽  
Author(s):  
Ruipu Tan ◽  
Wende Zhang ◽  
Shengqun Chen
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Averaging ◽  
Attribute Weights ◽  
Ordered Weighted Averaging ◽  
Aggregate Information ◽  
Multiple Attribute

Abstract This paper proposes a group decision making method based on entropy of neutrosophic linguistic sets and generalized single valued neutrosophic linguistic operators. This method is applied to solve the multiple attribute group decision making problems under single valued neutrosophic liguistic environment, in which the attribute weights are completely unknown. First, the attribute weights are obtained by using the entropy of neutrosophic linguistic sets. Then three generalized single valued neutrosophic linguistic operators are introduced, including the generalized single valued neutrosophic linguistic weighted averaging (GSVNLWA) operator, the generalized single valued neutrosophic linguistic ordered weighted averaging (GSVNLOWA) operator and the generalized single valued neutrosophic linguistic hybrid averaging (GSVNLHA) operator, and the GSVNLWA and GSVNLHA operators are used to aggregate information. Furthermore, similarity measure based on single valued neutrosophic linguistic numbers is defined and used to sort the alternatives and obtain the best alternative. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed method.

ON GROUP DECISION MAKING UNDER LINGUISTIC ASSESSMENTS

1999 ◽  
Vol 07 (04) ◽  
pp. 301-308 ◽  
Author(s):  
CONG CUONG BUI
Keyword(s):  
Decision Making ◽  
Fuzzy Logic ◽  
Group Decision Making ◽  
Decision Model ◽  
Group Decision ◽  
Weighted Averaging ◽  
Ordered Weighted Averaging ◽  
Choice Processes ◽  
Aggregation Processes ◽  
The Individual

In this paper we consider a fuzzy logic-based model in group decision making, with a focus on the set of all alternatives and on the individual lingustic preference relations. Some choice processes are devoted to the model using consensus measures and linguistic ordered weighted averaging (LOWA) operator. A multiple criteria group decision model in linguistic setting and some aggregation processes are also considered. The model and the new processes allow to incorporate human consistency in decision support systems.

SOME ICOWA OPERATORS AND THEIR APPLICATIONS TO GROUP DECISION MAKING WITH INTERVAL FUZZY PREFERENCE RELATIONS

2013 ◽  
Vol 21 (04) ◽  
pp. 579-601 ◽  
Author(s):  
LIGANG ZHOU ◽  
ZHIFU TAO ◽  
HUAYOU CHEN ◽  
JINPEI LIU
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Optimization Model ◽  
Group Decision ◽  
Weighted Averaging ◽  
Preference Relations ◽  
Ordered Weighted Averaging ◽  
Cowa Operator ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

We develop some new cases of the induced continuous ordered weighted averaging (ICOWA) operator and study their desirable properties, which are very suitable to deal with group decision making (GDM) with interval fuzzy preference relations. First, we present the consensus indicator ICOWA (CI-ICOWA) operator which uses the consensus indicator of the interval fuzzy preference as the order inducing variable in the ICOWA operator. Then the concept of compatibility degree (CD) for two interval fuzzy preference relations is defined based on the continuous ordered weighted averaging (COWA) operator and the compatibility degree ICOWA (CD-ICOWA) operator is proposed which uses the CD as the order inducing variable in the ICOWA operator. Next, we investigate some desirable properties of the CD-ICOWA operator. Additionally, we construct an optimization model to obtain the weights of experts by minimizing the compatibility degree in the GDM. Finally, an illustrative numerical example is used to verify the developed approaches.

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