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Multi-granular Intuitionistic Fuzzy Three-Way Decision Model Based on the Risk Preference Outranking Relation

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Abstract

As an important extension of decision-theoretic rough sets, three-way decision theory provides a new perspective for people to deal with uncertain problems. However, the traditional multi-granularity decision-theoretic rough sets model has limited ability in describing the risk preferences of decision-makers and the processing of intuitionistic fuzzy information. In addition, as far as we know, most of the risk loss functions in existing studies are based on utility theory. However, the complete compensability between attributes is not always true, and this fact may lead to inconsistencies between the final calculated results and the actual situation. We propose a multi-granular intuitionistic fuzzy three-way decision model based on the risk preference outranking relation. In this scenario, we first define the outranking relation on the intuitionistic fuzzy set and fuse it for the purpose of risk preference calculation. Next, starting from the single granularity, the relations between the membership outranking relation class, the nonmembership outranking relation class, and the rough approximation are analyzed, and the related properties are proven. Then, the single granularity is extended to construct the multi-granular intuitionistic fuzzy decision-theoretic rough sets and their corresponding three-way decision model. Furthermore, by systematically studying the decision loss costs of optimistic and pessimistic states, three-way decision rules are induced. The rationality and effectiveness of our proposed model are verified through a case study analysis and comparisons with existing methods. The results show that our proposed model can quantitatively analyze and calculate the uncertainty of decision-makers’ cognitive risk preferences, achieve global control of the decision-making process, and reduce the loss of decision-making costs.

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Abbreviations

RS:

Rough set

Pos:

Positive

Neg:

Negative

Bnd:

Boundary

DTRSs:

Decision-theoretic rough sets

3WD:

Three-way decision

TAO:

Trisecting-acting-outcome

IF3WD:

Intuitionistic fuzzy three-way decision

OR:

Outranking relation

MGIF:

Multi-granular intuitionistic fuzzy

OMGRS:

Optimistic multi-granular rough set

PMGRS:

Pessimistic multi-granular rough set

MOR:

Membership-OR

NOR:

Nonmembership-OR

IOR:

Intuitionistic-OR

RL:

Risk lover

RA:

Risk aversion

RN:

Risk neutral

IFSMR:

Intuitionistic fuzzy similarity measurement reasoning

IFMADM:

Intuitionistic fuzzy multi-attribute decision making

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Acknowledgements

The authors would like to thank Editor-in-Chief, editor, and anonymous reviewers for their valuable comments and helpful suggestions.

Funding

This work was supported by the National Natural Science Foundation of China (Grants No. 61877004 and No. 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. College of Artificial Intelligence, Beijing Normal University, Beijing, 100875, China

    Xian-wei Xin, Ji-hua Song, Jing-bo Sun & Wei-ming Peng

  2. College 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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  2. Ji-hua Song
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Contributions

X.X.: data curation, investigation, resources, software, writing—original draft. J.S.: conceptualization, funding acquisition, methodology, writing—review and editing. Z.X., J.S., and W.P.: formal analysis, project administration, supervision.

Corresponding author

Correspondence to Ji-hua Song.

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Xin, Xw., Song, Jh., Xue, Za. et al. Multi-granular Intuitionistic Fuzzy Three-Way Decision Model Based on the Risk Preference Outranking Relation. Cogn Comput 14, 1826–1843 (2022). https://doi.org/10.1007/s12559-021-09888-9

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  • DOI: https://doi.org/10.1007/s12559-021-09888-9

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