MULTI-CRITERIA DECISION-MAKING METHOD BASED ON INDUCED INTUITIONISTIC NORMAL FUZZY RELATED AGGREGATION OPERATORS

2012 ◽  
Vol 20 (04) ◽  
pp. 559-578 ◽  
Author(s):  
JIAN-QIANG WANG ◽  
KANG-JIAN LI ◽  
HONG-YU ZHANG
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Ordered Weighted Averaging ◽  
Averaging Operator ◽  
Relative Closeness ◽  
Ordered Weighted Averaging Operator

In this paper, we first defined intuitionistic normal fuzzy numbers as well as their operational laws and score function. Next, we proposed some aggregation operators including ordered intuitionistic normal ordered fuzzy weighted averaging operator, intuitionistic normal fuzzy ordered weighted geometric averaging operator, intuitionistic normal fuzzy related ordered weighted averaging operator, intuitionistic normal fuzzy related ordered weighted geometric averaging operator, induced intuitionistic normal fuzzy related ordered weighted averaging operator and induced intuitionistic normal fuzzy related ordered weighted geometric averaging operator. After that, similarity measure between two intuitionistic normal fuzzy numbers is defined. For multi-criteria decision making problems, in which the criteria are interactive and the criteria values are intuitionistic normal fuzzy numbers, an approach based on induced intuitionistic normal fuzzy related aggregation operators is proposed. And the comprehensive evaluation values of all alternatives can be derived by applying induced intuitionistic normal fuzzy related aggregation operators. Finally, the ranking of the whole alternatives set can be obtained by comparing the relative closeness of alternatives to the ideal solution. In the end, an example is given to show the validity and the feasibility of the method.

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.

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.

A LINGUISTIC AGGREGATION OPERATOR INCLUDING WEIGHTS FOR LINGUISTIC VALUES AND EXPERTS IN GROUP DECISION MAKING

2013 ◽  
Vol 21 (06) ◽  
pp. 927-943 ◽  
Author(s):  
ZHENG PEI ◽  
LI ZOU ◽  
LIANGZHONG YI
Keyword(s):  
Decision Making ◽  
Aggregation Operator ◽  
Point Of View ◽  
Weighted Averaging ◽  
Ordered Weighted Averaging ◽  
Averaging Operator ◽  
Aggregation Processes ◽  
Decision Making Problem ◽  
Ordered Weighted Averaging Operator ◽  
Linguistic Decision Making

Different linguistic aggregation methods have been proposed and applied in the linguistic decision making problems. Generally, weights for experts or criteria are considered in linguistic aggregation processes. In this paper, we provide a method to discovery new forms to compute weights and new interpretations in the linguistic ordered weighted averaging operator. In linguistic decision analysis, it can be noticed that some of initial linguistic values used by experts have priority over others linguistic values in evaluation processes. We formalize the priority over initial linguistic values as weights for linguistic values, by considering weights for linguistic values as well as weights for experts, we provide an alternative method to discovery weights information of the linguistic ordered weighted averaging operator, its properties show that such linguistic aggregation operator is extensions of the 2-tuple arithmetic mean, the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator. By an illustrative example, we compare the linguistic aggregation operator with the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator in a decision making problem. From the practical point of view, we provide an optimization model to obtain such weights information in linguistic aggregation processes, examples show the linguistic aggregation operator as an alternative linguistic ordered weighted averaging operator in practice.

scholarly journals Generalized complex q-rung orthopair fuzzy Einstein averaging aggregation operators and their application in multi-attribute decision making

2020 ◽  
Author(s):  
Peide Liu ◽  
Zeeshan Ali ◽  
Tahir Mahmood
Keyword(s):  
Decision Making ◽  
Detailed Comparison ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Ordered Weighted Averaging ◽  
Averaging Operator ◽  
Special Cases ◽  
Generalized Complex ◽  
Multi Attribute Decision Making ◽  
Ordered Weighted Averaging Operator

Abstract The recently proposed q-rung orthopair fuzzy set, which is characterized by a membership degree and a non-membership degree, is effective for handling uncertainty and vagueness. This paper proposes the concept of complex q-rung orthopair fuzzy sets (Cq-ROFS) and their operational laws. A multi-attribute decision making (MADM) method with complex q-rung orthopair fuzzy information is investigated. To aggregate complex q-rung orthopair fuzzy numbers, we extend the Einstein operations to Cq-ROFSs and propose a family of complex q-rung orthopair fuzzy Einstein averaging operators, such as the complex q-rung orthopair fuzzy Einstein weighted averaging operator, the complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator, the generalized complex q-rung orthopair fuzzy Einstein weighted averaging operator, and the generalized complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator. Desirable properties and special cases of the introduced operators are discussed. Further, we develop a novel MADM approach based on the proposed operators in a complex q-rung orthopair fuzzy context. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods.

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