On the mathematical theory of evidence in navigation

• Autorzy: Filipowicz W.

Identyfikatory

DOI

10.17402/100

• Języki publikacji: EN

Abstrakty

EN

In most problems encountered in navigation, imprecision and uncertainty dominate. Methods of their processing rely on rather obsolete formalisms based on probability and statistics. Available solutions exploit a limited amount of available data, and knowledge is necessary to interpret the achieved results. Profound a posteriori analysis is rather limited; thus, the informative context of solutions is rather poor. Including knowledge in a nautical data processing scheme is impossible. Remaining stuck with the traditional formal apparatus, based on probability theory, one cannot improve the informative context of obtained results. Traditional approaches toward solving problems require assumptions imposed by the probabilistic model that exclude possibility of modelling uncertainty. It should be noticed that the flexibility of exploited formalism decide the quality of upgrading models and, subsequently, on the universality of the final results. Therefore, extension of the available formalisms is a challenge to be met. Many publications devoted to the mathematical theory of evidence (MTE) and its adaptation for nautical science in order to support decision making in navigational processes have enabled one to submit and defend the following proposition. Many practical problems related to navigational ship conducting and to feature uncertainty can be solved with MTE; the informative context of the obtained results is richer when compared to those acquired by traditional methods. Additionally, a posteriori analysis is an inherent feature of the new foundations. The brief characteristics of a series of publications devoted to the new methodology are the main topics of this paper.

Słowa kluczowe

EN

nautical evidence; uncertainty; belief structures; position fixing; fix accuracy; systematic errors evaluation

• Wydawca: Wydawnictwo Naukowe Akademii Morskiej w Szczecinie
• Czasopismo: Zeszyty Naukowe Akademii Morskiej w Szczecinie
• Rocznik: 2016
• Tom: nr 45 (117)
• Strony: 159--167
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Filipowicz W.

• Gdynia Maritime University 81/83 Morska St., 81-225 Gdynia, Poland

Bibliografia

• 1. Ayoun, A. & Smets, P. (2001) Data Association in Multi- -Target Detection Using the Transferable Belief Model. International Journal of Intelligent Systems 16. pp. 1167– 1182.
• 2. Burrus, N. & Lesage, D. (2004) Theory of Evidence. Technical Report No. 0307-07/07/03. Activity: CSI Seminar, Place: EPITA Research and Development Laboratory, Cedex France.
• 3. Dempster, A.P. (1968) A generalization of Bayesian inference. Journal of the Royal Statistical Society, Series B 30 (2). pp. 205–247.
• 4. Denoeux, T. (2000) Modelling vague beliefs using fuzzy valued belief structures. Fuzzy Sets and Systems 116, pp. 167–199.
• 5. Filipowicz, W. (2009) Application of the Theory of Evidence in Navigation. Knowledge Engineering and Export Systems. Warsaw: Academic Editorial Board EXIT. pp. 599– 614.
• 6. Filipowicz, W. (2009a) Belief Structures and their Applications in Navigation. Methods of Applied Informatics 3. pp. 53–82.
• 7. Filipowicz, W. (2010) Fuzzy Reasoning Algorithms for Position Fixing. Measurements Automatics Control 12. pp. 1491–1495.
• 8. Filipowicz, W. (2011) Fuzzy Evidence in Terrestrial Navigation. Navigational Systems and Simulators: Marine Navigation and Safety of Sea Transportation. A. Weintrit (Ed.) Leiden: CRC Press/Balkema. pp. 65–73.
• 9. Filipowicz, W. (2011a) Evidence Representation and Reasoning in Selected Applications. Lecture Notes in Artificial Intelligence. Jędrzejowicz P, Ngoc Thanh Nguyen, Kiem Hoang (Eds). Berlin, Heidelberg: Springer-Verlag. pp. 251– 260.
• 10. Filipowicz, W. (2012) Evidence Representations in Position Fixing. Electrical Review 10b. pp. 256–260.
• 11. Filipowicz, W. (2014) Fuzzy evidence reasoning and navigational position fixing. Recent advances in knowledge-based paradigms and applications, advances in intelligent systems and computing, 234. Tweedale, J.W., Jane, L.C. (Eds). Heildelberg, New York, London: Springer. pp. 87–102.
• 12. Filipowicz, W. (2014a) Mathematical Theory of Evidence in Navigation. Belief Functions: Theory and Applications. Fabio Cuzzolin (Ed.) Third International Conference, BELIEF 2014 Oxford, UK, Springer International Publishing Switzerland. pp. 199–208.
• 13. Filipowicz, W. (2014b) Systematic errors handling with MTE. Procedia Computer Science 35. pp. 1728–1737.
• 14. Shafer, G. (1976) A mathematical theory of evidence. Princeton: Princeton University Press.
• 15. Srivastava, R.P., Dutta, S.K. & Johns, R. (1996) An Expert System Approach to Audit Planning and Evaluation in the Belief-Function Framework. International Journal of Intelligent Systems in Accounting, Finance and Management 5(3). pp. 165–183.
• 16. Sun, L., Srivastava, R.P. & Mock, T. (2006) An Information Systems Security Risk Assessment Model under Dempster-Shafer Theory of Belief Functions. Journal of Management Information Systems 22(4), pp. 109–142.
• 17. Yager, R.R. (1996) On the normalization of fuzzy belief structures. International Journal of Approximate Reasoning 14 (2–3). pp. 127–153.
• 18. Yen, J. (1990) Generalizing the Dempster-Shafer theory to fuzzy sets. IEEE Transactions on Systems, Man and Cybernetics 20 (3). pp. 559–570.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.