Abstract
The intuitionistic fuzzy set (IFS) and bipolar fuzzy set (BFS) are all effective models to describe ambiguous and incomplete cognitive knowledge with membership, non-membership, negative membership, and hesitancy sections. But in daily life problems, there are some situations where we cannot apply the ordinary models of IFS and BFS, separately. Hence, there is a need to combine both the models of IFS and BFS into a single one. A tripolar fuzzy set (TFS) is a generalization of IFS and BFS. In circumstances where BFS and IFS models cannot be used individually, a tripolar fuzzy model is more dependable and efficient. Further, the IFS and BFS models are reduced to corollaries due to the proposed model of TFS. For this purpose in this article, we first consider some novel operations on tripolar fuzzy information. These operations are formulated on the basis of well-known Dombi T-norm and T-conorm, and the desirable properties are discussed. By applying the Dombi operations, arithmetic and geometric aggregation operators of TFS are proposed, and we introduce the concepts of a TF-Dombi weighted average (TFDWA) operator, a TF-Dombi ordered weighted average (TFDOWA) operator, and a TF-Dombi hybrid weighted (TFDHW) operator and explore their fundamental features including idempotency, boundedness, monotonicity, and others. In the second part, we propose TF-Dombi weighted geometric (TFDWG) operator, TF-Dombi ordered weighted geometric (TFDOWG) operator, and TF-Dombi hybrid geometric (TFDHG) operator. The features and specific cases of the mentioned operators are examined. Enterprise resource planning (ERP) is a management and integration approach that organizations employ to manage and develop many aspects of their operations. The study's primary contribution is to employ TFS to create certain decision-making strategies for the selection of optimal ERP systems. The proposed operators are then used to build several techniques for solving multiattribute decision-making (MADM) issues with TF information. Finally, an example of ERP system selection is investigated to demonstrate that the techniques suggested are trustworthy and realistic.
Highlights
Decision making (DM) is a method of resolving real-world problems by selecting the ideal choice from a range of viable options
Decision-making methods have been used in several areas of modern science, for example, Xu [4] developed the use of intuitionistic fuzzy set (IFS) in arithmetic aggregation operators (AOPs) and initiated many valuable operators
We presented various AOPs in a TF environment by using an expanded idea of IFS and bipolar fuzzy set (BFS). e following points describe the novelty of proposed operators: (i) e ability of a tripolar fuzzy set (TFS) is to express IFS and BFS information at once in a single notion called tripolar fuzzy environment which makes it exceptional in literature. e qualitative characteristics of IFS and BFS are combined in a single TFS
Summary
Decision making (DM) is a method of resolving real-world problems by selecting the ideal choice from a range of viable options. Decision-making methods have been used in several areas of modern science, for example, Xu [4] developed the use of IFS in arithmetic aggregation operators (AOPs) and initiated many valuable operators. E bipolar fuzzy set (BFS) [20, 21] was developed to measure the uncertain and cognitive information presented in the form of positive polarity and negative polarity in real-world scenarios. Dombi [30] studied decision methods by developing some arithmetic and geometric AOPs with the help of Dombi operations and BFSs. e topics in fuzzy information aggregation operators are developing rapidly, and many researchers are involved to construct feasible and advanced models to deal with decision processes. (i) e ability of a TFS is to express IFS and BFS information at once in a single notion called tripolar fuzzy environment which makes it exceptional in literature.
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