Generalized Geometric Aggregation Operators Based on T-Norm Operations for Complex Intuitionistic Fuzzy Sets and Their Application to Decision-making

Complex intuitionistic fuzzy set (CIFS) is a special intuitionistic fuzzy set where the membership and non-membership degrees are expressed by a complex-valued membership degree and can more easily describe the vagueness and uncertainty in the real world. Archimedean t-conorm and t-norm (ATT), as an...

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Bibliographic Details
Published in:Cognitive computation 2020-05, Vol.12 (3), p.679-698
Main Authors: Garg, Harish, Rani, Dimple
Format: Article
Language:English
Subjects:
Artificial Intelligence
Biomedical and Life Sciences
Biomedicine
Computation by Abstract Devices
Computational Biology/Bioinformatics
Data integration
Decision making
Fuzzy sets
Mathematical functions
Multiple criterion
Neurosciences
Operators
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Summary:Complex intuitionistic fuzzy set (CIFS) is a special intuitionistic fuzzy set where the membership and non-membership degrees are expressed by a complex-valued membership degree and can more easily describe the vagueness and uncertainty in the real world. Archimedean t-conorm and t-norm (ATT), as an important class of the t-norm (TN) and t-conorm (TC), have greater flexibility in the information fusion process. In this paper, we extend the ATT to CIFSs and present some generalized geometric aggregation operators, which can be used to handle the multiple criteria decision-making (MCDM) problems. For it, we firstly define some new operational laws of the CIFSs based on ATT, then some weighted geometric aggregation operators based on proposed operations are proposed. Further, some desirable properties and special cases of them are studied. Finally, a decision-making approach is developed for the MCDM problem with complex intuitionistic fuzzy information. A practical example is given to show the availability and advantages of the proposed method by comparison with some existing methods. The proposed aggregation operators are more generalized than the existing ones to utilize the uncertain and imprecise information. Several existing operators are considered as special cases of the proposed one. Finally, the proposed method will offer various choices to the decision-maker to access the finest alternatives.
ISSN:1866-9956
1866-9964
DOI:10.1007/s12559-019-09678-4