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Introduction to U-Number Calculus


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Abstract

Commonsense reasoning plays a pivotal role in the development of intelligent systems for decision-making, system analysis, control and other applications. As Prof. L. Zadeh mentions a kernel of the theory of commonsense is the concept of usuality. Zadeh suggested main principles of the theory of usuality, unfortunately up to present day; a fundamental and systemic approach to reasoning with usual knowledge is not developed. In this study, we develop a new approach to calculus of usual numbers (U-numbers). We consider a U-number as a Z-number, where the second component is “usually”. Validity of the suggested approach is verified by examples.


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Pages

Total Pages: 6
Pages: 211-216

DOI
10.1080/10798587.2017.1330311


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Published

Volume: 24
Issue: 1
Year: 2018

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References

Aliev R.A. Soft computing: fuzzy logic, neural networks and distributed artificial intelligence

Aliev, Rafik Aziz. "Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions." Studies in Fuzziness and Soft Computing (2013): n. pag. Crossref. Web. https://doi.org/10.1007/978-3-642-34895-2

Aliev, Rafik, and Konul Memmedova. "Application ofZ-Number Based Modeling in Psychological Research." Computational Intelligence and Neuroscience 2015 (2015): 1-7. Crossref. Web. https://doi.org/10.1155/2015/760403

Aliev, Rafik, and Alex Tserkovny. "Systemic Approach to Fuzzy Logic Formalization for Approximate Reasoning." Information Sciences 181.6 (2011): 1045-1059. Crossref. Web. https://doi.org/10.1016/j.ins.2010.11.021

Aliev R.A. Fuzzy sets theory and its application

ALIEV, R. A., W. PEDRYCZ, and O. H. HUSEYNOV. "DECISION THEORY WITH IMPRECISE PROBABILITIES." International Journal of Information Technology & Decision Making 11.02 (2012): 271-306. Crossref. Web. https://doi.org/10.1142/S0219622012400032

Aliev, Rafik A et al. "The Arithmetic of Z-Numbers." (2015): n. pag. Crossref. Web. https://doi.org/10.1142/9575

Aliev, R.A., A.V. Alizadeh, and O.H. Huseynov. "The Arithmetic of Discrete Z-Numbers." Information Sciences 290 (2015): 134-155. Crossref. Web. https://doi.org/10.1016/j.ins.2014.08.024

Charles M. Introduction to probability

Jamshidi, M. "Fuzzy Control of Complex Systems." Soft Computing - A Fusion of Foundations, Methodologies and Applications 1.1 (1997): 42-56. Crossref. Web. https://doi.org/10.1007/s005000050005

Kóczy L.T. J. BUSEFAL

Pedrycz W. Fuzzy Systems Engineering. Toward Human-centric Computing

Schwartz, Daniel G. "A Logic for Qualified Syllogisms." Advanced Techniques in Computing Sciences and Software Engineering (2009): 45-50. Crossref. Web. https://doi.org/10.1007/978-90-481-3660-5_8

Shafer G. A Mathematical Theory of Evidence

Springer M.D. The Algebra of Random Variables

Whalen, Thomas, and Brian Schott. "Usuality, Regularity, and Fuzzy Set Logic." International Journal of Approximate Reasoning 6.4 (1992): 481-504. Crossref. Web. https://doi.org/10.1016/0888-613X(92)90001-G

Williamson, R.C. (1989). Probabilistic Arithmetic. (Ph.D. thesis). University of Queensland, Australia, http://theorem.anu.edu.au/~williams/papers/thesis300

Williamson, Robert C., and Tom Downs. "Probabilistic Arithmetic. I. Numerical Methods for Calculating Convolutions and Dependency Bounds." International Journal of Approximate Reasoning 4.2 (1990): 89-158. Crossref. Web. https://doi.org/10.1016/0888-613X(90)90022-T

WISE, Ben P., and Max HENRION. "A Framework for Comparing Uncertain Inference Systems to Probability." Machine Intelligence and Pattern Recognition (1986): 69-83. Crossref. Web. https://doi.org/10.1016/B978-0-444-70058-2.50010-3

Yager R.R. On Implementing Usual Values. UAI ‘86: Proceedings of the Second Annual Conference on Uncertainty in Artificial Intelligence

Zadeh, L.A. "Probability Measures of Fuzzy Events." Journal of Mathematical Analysis and Applications 23.2 (1968): 421-427. Crossref. Web. https://doi.org/10.1016/0022-247X(68)90078-4

Zadeh, L.A. "The Role of Fuzzy Logic in the Management of Uncertainty in Expert Systems." Fuzzy Sets and Systems 11.1-3 (1983): 199-227. Crossref. Web. https://doi.org/10.1016/S0165-0114(83)80081-5

Zadeh L.A. Fuzzy sets and common sense reasoning

Zadeh, Lofti A. "Syllogistic Reasoning in Fuzzy Logic and Its Application to Usuality and Reasoning with Dispositions." IEEE Transactions on Systems, Man, and Cybernetics SMC-15.6 (1985): 754-763. Crossref. Web. https://doi.org/10.1109/TSMC.1985.6313459

Zadeh, L. A. "Outline of a Theory of Usuality Based on Fuzzy Logic." Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems (1996): 694-712. Crossref. Web. https://doi.org/10.1142/9789814261302_0035

Zadeh, Lotfi A. "A Note on Z-Numbers." Information Sciences 181.14 (2011): 2923-2932. Crossref. Web. https://doi.org/10.1016/j.ins.2011.02.022

JOURNAL INFORMATION


ISSN PRINT: 1079-8587
ISSN ONLINE: 2326-005X
DOI PREFIX: 10.31209
10.1080/10798587 with T&F
IMPACT FACTOR: 0.652 (2017/2018)
Journal: 1995-Present




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