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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-7908-1841-3_10
Publisher Name: Physica, Heidelberg
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