Abstract
An interpretation of problem-solving with uncertainty supported by fuzzy paraset methodology is presented. Using the concept of uncertainty by Shafer, Zadeh and Dubois-Prade, a rough algorithm for general problem-solving with uncertainty is proposed. To measure uncertainty for subsets of a basic space, the known functions of plausibility and belief are used, as well as the possibility and necessity measures. The algorithm is outlined not only for a finite, but also for an infinite basic space. To improve the effect of the procedure proposed, specific methodological tools are designed: an evidence paraset and an uncertainty paraset.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Shafer, G.: A Mathematical Theory of Evidence. Univ. Press, Princeton (1976)
Dempster, A. P.: Upper and Lower Probabilities Induced a Multivalued Mapping. Annals of Math. Stat. 38 (1967) 325–339
Zadeh, L.A.: Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1 (1978) 3–28
Dubois, D., Prade, H.: Representation and Combination of Uncertainty with Belief Functions and Possibility Measures. Univ. P. Sabatier, 31062 Toulouse Cédex, France, (1978) 244–264
Klir, G.J.: Uncertainty in the Dempster-Shafer Theory: A Critical Re-Examination. Int. J. General Systems 18 (1990) 155–166
Yager, R.R.: On the Normalization of Fuzzy Belief Structures. Int. J. of Approximate Reasoning 14 (1996) 127–153
Sajda, J.: Introduction to the Intuitive Theory of General Abstract Parasets. Proc. of the 7th World Congress IFSA’97, Prague (1997) 67–72
Sajda, J.: Elliptic Parasets. Proc. of the 7th Int. Conf. on AI and Inf.-Control Systems of Robots’97, Smolenice Castle-Bratislava (1997) 333–346
Sajda, J.: A Fuzzification of Paraset Methodology. Proc. of the 6`h Fuzzy Colloquium, Zittau, Germany (1998) 44–49
De Beats, B., Cooman, G., Kerre, E.: The Construction of Possibility Measures from Samples on T-semi-partitions. J. of Information Sciences 106 (1998) 3–22
Harmanec, D., Klir, G.J., Wang, Z.: Modal Logic Interpretation of Dempster-Shafer Theory: An Infinite Case. J. of Approximate Reasoning 14 (1996) 81–93
Churn-Jung, L.: Possibilistic Residuated Implication Logics with Applications. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 6 (1998) 365–385
Goodman, I.R., Nguyen, H.T.: Uncertainty Models for Knowledge-Based Systems. North-Holland, Amsterdam (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Šajda, J. (2000). Using Fuzzy Parasets in Problem-Solving Under Uncertainty. In: Hampel, R., Wagenknecht, M., Chaker, N. (eds) Fuzzy Control. Advances in Soft Computing, vol 6. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1841-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1841-3_10
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1327-2
Online ISBN: 978-3-7908-1841-3
eBook Packages: Springer Book Archive