New prioritized aggregation operators with priority degrees among priority orders for complex intuitionistic fuzzy information

Author(s):  
Harish Garg ◽  
Dimple Rani

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Yang ◽  
Jiarong Shi ◽  
Yongfeng Pang

Some hybrid aggregation operators have been developed based on linguistic hesitant intuitionistic fuzzy information. The generalized linguistic hesitant intuitionistic fuzzy hybrid weighted averaging (GLHIFHWA) operator and the generalized linguistic hesitant intuitionistic fuzzy hybrid geometric mean (GLHIFHGM) operator are defined. Some special cases of the new aggregation operators are studied and many existing aggregation operators are special cases of the new operators. A new multiple attribute decision making method based on the new aggregation operators is proposed and a practical numerical example is presented to illustrate the feasibility and practical advantages of the new method.



2016 ◽  
Vol 15 (02) ◽  
pp. 311-352 ◽  
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen

Aggregation operators play a key role in multiple criteria decision-making (MCDM). Extensions of aggregation operators to intuitionistic fuzzy sets (IFSs) usually involve replacing the standard arithmetic operations with those defined over the membership and nonmembership of IFS, which is essentially a pair of special Archimedean triangular norm (t-norm) and triangular conorm (t-conorm), called probabilistic sum t-conorm and product t-norm, on the membership and nonmembership of IFS, respectively. In this paper, we first introduce some operations on IFSs by means of Archimedean t-norm and t-conorm. Then some generalized Archimedean intuitionistic fuzzy aggregation operators are proposed, such as generalized Archimedean intuitionistic fuzzy weighted averaging operator, generalized Archimedean intuitionistic fuzzy ordered weighted averaging (GAIFOWA) operator, and generalized Archimedean intuitionistic fuzzy hybird averaging operator. Some desirable properties of these operators are investigated. The relations between these operators and the existing intuitionistic fuzzy aggregation operators are discussed. Finally, applying these proposed operators, we develop an approach for multi-criteria decision-making with intuitionistic fuzzy information, an illustrative example is used to verify the developed approach and to demonstrate its practicality and effectiveness.



Author(s):  
HUA ZHAO ◽  
ZESHUI XU ◽  
ZEQING YAO

In fuzzy environments, some operators have been developed for aggregating intuitionistic fuzzy information which is expressed in pairs of the membership degrees and the non-membership degrees. However, the existing intuitionistic fuzzy aggregation operators cannot consider and reflect the density of intuitionistic fuzzy information distribution. To solve the issue, in this paper, we first develop some intuitionistic fuzzy density-based aggregation operators. Then by combining the developed operators with the existing intuitionistic fuzzy aggregation operators, we put forward some synthesized intuitionistic fuzzy aggregation operators. Furthermore, we utilize the synthesized intuitionistic fuzzy aggregation operators to develop an approach to group decision making based on intuitionistic preference relations, and illustrate our approach with a practical example of the evaluation of new medicines.



2020 ◽  
Vol 39 (3) ◽  
pp. 4763-4783
Author(s):  
Muhammad Akram ◽  
Xindong Peng ◽  
Ahmad N. Al-Kenani ◽  
Aqsa Sattar

Complex Pythagorean fuzzy (CPF), a worthwhile generalization of Pythagorean fuzzy set, is a powerful tool to deal with two-dimensional or periodic information. In this paper, we develop two prioritized aggregation operators (AOs) under CPF environment, namely, complex Pythagorean fuzzy prioritized weighted averaging (CPFPWA) operator and complex Pythagorean fuzzy prioritized weighted geometric (CPFPWG) operator. We consider the prioritization relationship among criteria and decision makers (DMs) to make our result more accurate as in real decision making (DM) problems, the criteria and DMs have different priority level. Further, we discuss remarkable properties of our proposed AOs. Moreover, we promote the evolution of MCDM problem by investigating an algorithm in CPF environment with its flow chart. Finally, to check the superiority and validity of proposed operators, we compare the computed results with the different existing techniques.



2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Shouzhen Zeng ◽  
Muhammad Munir ◽  
Tahir Mahmood ◽  
Muhammad Naeem

In this article, it is pointed out that the existing intuitionistic fuzzy and T-spherical fuzzy Einstein averaging and geometric operators have some limitations. To overcome these limitations, we proposed some new averaging and geometric operators in the T-spherical fuzzy environment instead of the intuitionistic fuzzy environment because the T-spherical fuzzy set is the most generalized form and the proposed operators can be particularized to the intuitionistic fuzzy environment. First, new operational laws for T-spherical fuzzy information are defined, on the basis of which Einstein geometric interaction operators and Einstein averaging interactive aggregation operators are then proposed. Some basic properties and advantages of proposed aggregation operators are also discussed. Moreover, the proposed operators are applied to the MADM problem to check their reliability. The superiority of the proposed operators over existing work is checked with the help of an example.



2021 ◽  
Vol 40 (1) ◽  
pp. 605-624 ◽  
Author(s):  
Lei Xu ◽  
Yi Liu ◽  
Haobin Liu

For the sake of better handle the imprecise and uncertain information in decision making problems(DMPs), linguistic interval-valued intuitionistic fuzzy numbers(LIVIFNs) based aggregation operators (AOS) are proposed by combining extended Copulas (ECs), extended Co-copulas (ECCs), power average operator and linguistic interval-valued intuitionistic fuzzy information (LIVIFI). First of all, ECs and ECCs, some specifics of ECs and ECCs, score and accuracy functions of LIVIFNs are gained. Then, based on ECs and ECCs, several aggregation operators are proposed to aggregate LIVIFI, which can offer decision makers (DMs) desirable generality and flexibility. In addition, the desired properties of proposed AOS are discussed. Last but not least, a MAGDM approach is constructed based on proposed AOs; Consequently, the effectiveness of the proposed approach is verified by a numerical example, and then the advantages are showed by comparing with other approaches.



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