Probabilistic fuzzy argumentation frameworks with finite fuzzy statuses

Document Type : Research Paper

Authors

1 School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

2 Business School, Shandong Normal University, Jinan 250014, China

3 School of Computer Science and Technology, Shandong Jianzhu Yniversity, Jinan 250101, China

Abstract

Randomness and fuzziness of argumentation have attracted the interest of many researchers.
However, though each of these two properties is discussed in the past, seldom literature considers both of them.
The purpose of this paper aims to explore semantics of the argumentation frameworks with these two attributes at the same time.
Firstly, we introduce probabilistic-fuzzy matrices to describe the arguments with randomness and fuzziness,
and define the mathematical form of the probabilistic-fuzzy argumentation frameworks.
In these frameworks, an argument has finite fuzzy states and each fuzzy state has a probability.
This provides a mathematical foundation for the follow-up work.
Then, we introduce a method of modifying the probabilities of the fuzzy states,
which proposes a feasible way to revise the probabilities.
Formally, it is the revision of the probabilistic-fuzzy matrices of arguments.
Finally, based on this process, we set up an extension semantics system for probabilistic-fuzzy frameworks.
The semantics enriches the theory of argumentation, and propose a way to check the probabilities.

Keywords

References

[1] P. Baroni, M. Caminada, M. Giacomin, An introduction to argumentation semantics, The Knowledge Engineering
Review, 26(04) (2011), 365-410.
[2] C. da Costa Pereira, A. G. Tettamanzi, S. Villata, Changing onei’s mind: Erase or rewind? Possibilistic belief
revision with fuzzy argumentation based on trust, Proceedings of the 22nd International Joint Conference on Artificial
Intelligence, Barcelona, (2011), 164-171.
[3] P. Dondio, Multi-valued and probabilistic argumentation frameworks, Proceedings of Computational Models of Argument, Pitlochry, (2014), 253-260.
[4] P. M. Dung, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games, Artificial Intelligence, 77(2) (1995), 321-357.
[5] P. M. Dung, P. M. Thang, Towards (probabilistic) argumentation for jury-based dispute resolution, Proceedings of
Computational Models of Argument, Amsterdam, (2010), 171-182.
[6] A. Hunter, A probabilistic approach to modeling uncertain logical arguments, International Journal of Approximate
Reasoning, 54(1) (2013), 47-81.
[7] A. Hunter, Probabilistic qualification of attack in abstract argumentation, International Journal of Approximate
Reasoning, 55(2) (2014), 607-638.
[8] A. Hunter, M. Thimm, Probabilistic reasoning with abstract argumentation frameworks, Journal of Artificial Intelligence Research, 59 (2017), 565-611.
[9] J. Janssen, M. De Cock, D. Vermeir, Fuzzy argumentation frameworks, In Information Processing and Management of Uncertainty in Knowledge-based Systems, Torremolinos, (2008), 513-520.
[10] S. Kaci, C. Labreuche, Argumentation framework with fuzzy preference relations, In International Conference on
Information Processing and Management of Uncertainty in Knowledge-Based Systems, Dortmund, (2010), 554-563.
[11] H. Li, N. Oren, T. J. Norman, Probabilistic argumentation frameworks, In International Workshop on Theories
and Applications of Formal Argumentation, Barcelona, (2011), 1-16.
[12] J. Mo, H. L. Huang, Continuous probability-interval valued fuzzy preference relations and its application in group
decision making, Iranian Journal of Fuzzy Systems, 18(4) (2021), 185-200.
[13] A. Saha, A. R. Mishra, P. Rani, T. Senapati, R. R. Yager, A dual probabilistic linguistic MARCOS approach based
on generalized Dombi operator for decision-making, Iranian Journal of Fuzzy Systems, 20(2) (2022), 83-102.
[14] J. Wu, A Boolean model for conflict-freeness in argumentation frameworks, AIMS Mathematics, 8(2) (2023), 3913-3919.
[15] J. Wu, H. Li, Probabilistic three-valued argumentation frameworks, Proceedings of the 3rd International Conference
on Logic and Argumentation, Hangzhou, (2020), 308-323.
[16] J. Wu, L. Li, W. Sun, G¨odel semantics of fuzzy argumentation frameworks with consistency degrees, AIMS Mathematics, 5(4) (2020), 4045-4064.
[17] M. Yadegari, S. A. Seyedin, Rule-based joint fuzzy and probabilistic networks, Iranian Journal of Fuzzy Systems,
17(3) (2020), 135-149.
[18] S. Zhao, J. Wu, An efficient algorithm of fuzzy reinstatement labelling, AIMS Mathematics, 7(6) (2022), 11165-11187.
Iranian Journal of Fuzzy Systems
Volume 20, Issue 3
May and June 2023
Pages 177-189

Files

Share

How to cite

Statistics