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A novel intuitionistic fuzzy three-way decision model based on an intuitionistic fuzzy incomplete information system

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Abstract

As a new method of granular computing, the three-way decision (3WD) approach has unique advantages in handling uncertain and imprecise problems. Based on decision-theoretic rough sets (DTRSs) and Bayesian minimum risk theory, conditional probability and loss function are the key research issues in 3WD. Many approaches for handling deterministic and complete information have been developed. However, few studies have focused on the construction of an intuitionistic fuzzy three-way decision (IF3WD) model for an intuitionistic fuzzy incomplete information system (IFIIS). In this paper, an IF3WD model based on an IFIIS is proposed to improve the ability to process complex fuzzy incomplete information systems, which extends the application range of the traditional 3WD. Concretely, we first propose a calculation method to measure the degree of information retention of missing data and describe it in two dimensions: coarse-grained and fine-grained. Next, an intuitionistic fuzzy number approximation (IFNA) strategy for missing data is presented. Then, a loss function with three states is given. Furthermore, combined with the Choquet integral, the interaction and influence between acceptance, rejection, and delay decision costs are investigated, and the corresponding IF3WD rules are induced. Finally, the rationality and effectiveness of our proposed model are verified through case analysis and are compared with those of existing methods.

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Abbreviations

RSs:

Rough sets

Pos:

Positive

Neg:

Negative

Bnd:

Boundary

IFSs:

Intuitionistic fuzzy sets

IFN:

Intuitionistic fuzzy number

UIS:

Uncertain information system

3WD:

Three-way decision

TAO:

Trisecting-acting-outcome

DTRSs:

Decision-theoretic rough sets

TIFN:

Triangular intuitionistic fuzzy number

IF3WD:

Intuitionistic fuzzy three-way decision

IFNA:

Intuitionistic fuzzy number approximation

IFIIS:

Intuitionistic fuzzy incomplete information system

IFPM:

Intuitionistic fuzzy possibility measure

3WGrC:

Three-way granular computing

IFMADM:

Intuitionistic fuzzy multiattribute decision making

IFPWA:

Intuitionistic fuzzy power weighted average

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Acknowledgements

The authors would like to thank the editor-in-chief, the editor, and the anonymous reviewers for their valuable comments and helpful suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61877004 and 62007004), the Major Program of National Social Science Foundation of China (Grant No. 18ZDA295) and the Doctoral Interdisciplinary Foundation Project of Beijing Normal University (Grant No. BNUXKJC1925).

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Authors and Affiliations

  1. School of Artificial Intelligence, Beijing Normal University, Beijing, 100875, China

    Xian-Wei Xin, Jing-Bo Sun, Ji-Hua Song & Wei-Ming Peng

  2. School of Computer and Information Engineering, Henan Normal University, Xinxiang, China

    Zhan-Ao Xue

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  1. Xian-Wei Xin
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Contributions

XX: Data curation, investigation, resources, software, and writing the original draft. JH and WM: Conceptualization, funding acquisition, methodology, writing-review and editing. ZA and JB: Formal analysis, project administration, and supervision.

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Correspondence to Wei-Ming Peng.

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Xin, XW., Sun, JB., Xue, ZA. et al. A novel intuitionistic fuzzy three-way decision model based on an intuitionistic fuzzy incomplete information system. Int. J. Mach. Learn. & Cyber. 13, 907–927 (2022). https://doi.org/10.1007/s13042-021-01426-1

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