Computing with words with the use of inverse RDM models of membership functions

Andrzej Piegat ; Marcin Pluciński

International Journal of Applied Mathematics and Computer Science, Tome 25 (2015), p. 675-688 / Harvested from The Polish Digital Mathematics Library

Résumé

Computing with words is a way to artificial, human-like thinking. The paper shows some new possibilities of solving difficult problems of computing with words which are offered by relative-distance-measure RDM models of fuzzy membership functions. Such models are based on RDM interval arithmetic. The way of calculation with words was shown using a specific problem of flight delay formulated by Lotfi Zadeh. The problem seems easy at first sight, but according to the authors' knowledge it has not been solved yet. Results produced with the achieved solution were tested. The investigations also showed that computing with words sometimes offers possibilities of achieving better problem solutions than with the human mind.

Détail

Publié le : 2015-01-01

Zbl 1322.68199

EUDML-ID : urn:eudml:doc:271777

Bibliographie

[000] Aliev, R., Pedrycz, W., Fazlollahi, B., Huseynov, O., Alizadeh, A. and Guirimov, B. (2012). Fuzzy logic-based generalized decision theory with imperfect information, Information Sciences 189: 18-42. | Zbl 1247.91042

[001] Batyrshin, I. (2002). On granular derivatives and the solution of a granular initial value problem, International Journal of Applied Mathematics and Computer Science 12(3): 403-410. | Zbl 1081.34501

[002] Batyrshin, I. and Wageknecht, M. (2002). Towards a linguistic description of dependences in data, International Journal of Applied Mathematics and Computer Science 12(3): 391-401. | Zbl 1062.68122

[003] Cao, T. (2003). Conceptual graphs for modelling and computing with generally quantified statements, in J. Lawry, J. Shanahan and A. Ralescu (Eds.), Modelling with Words, Springer, Berlin/Heidelberg, pp. 80-101.

[004] De Cock, M. and Kerre, E.E. (2002). A context-based approach to linguistic hedges, International Journal of Applied Mathematics and Computer Science 12(3): 371-382. | Zbl 1062.68123

[005] Dymova, L. (2011). Soft Computing in Economics and Finance, Springer Verlag, Berlin/Heidelberg.

[006] Gemeinder, M. (2002). Imposing restrictions on density functions utilised in computing with words, International Journal of Applied Mathematics and Computer Science 12(3): 383-390. | Zbl 1062.68124

[007] Grzegorzewski, P. and Hryniewicz, O. (2002). Computing with words and life data, International Journal of Applied Mathematics and Computer Science 12(3): 337-345. | Zbl 1134.68589

[008] Hansen, E. (1975). A generalized interval arithmetic, in K. Nickel (Ed.), Interval Mathematics, Lecture Notes in Computer Science, Vol. 29, Springer Verlag, Berlin/Heidelberg, pp. 7-18.

[009] Hanss, M. (2005). Applied Fuzzy Arithmetic, Springer Verlag, Berlin/Heidelberg. | Zbl 1085.03041

[010] Herrera, F., López, E., Mendaña, C. and Rodríguez, M. (1999). A linguistic decision model to suppliers selection in international purchasing, Computing with Words in Information/Intelligent Systems 2, Physica-Verlag, Heidelberg, pp. 500-524.

[011] Kacprzyk, J. and Zadrożny, S. (1999). The paradigm of computing with words in intelligent database querying, Computing with Words in Information/Intelligent Systems 2, Physica-Verlag, Heidelberg, pp. 383-398. | Zbl 0947.68521

[012] Kacprzyk, J. and Zadrożny, S. (2002). Linguistic data summaries: Towards an increased role of natural language in data mining, Proceedings of the 8th IEEE International Conference on Methods and Models in Automation and Robotics, Szczecin, Poland, pp. 121-126.

[013] Kacprzyk, J. and Zadrożny, S. (2010). Computing with words is an implementable paradigm: Fuzzy queries, linguistic data summaries and natural language generation, IEEE Transactions on Fuzzy Systems 18(3): 461-472.

[014] Kahnemann, D. and Tversky, A. (2000). Choices, Values and Frames, Cambridge University Press, Russel Sage Foundation, Cambridge.

[015] Kaufmann, A. and Gupta, M. (1991). Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold, New York, NY. | Zbl 0754.26012

[016] Landowski, M. (2014). Differences between Moore's and RDM interval arithmetic, Proceedings of the 13th International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, Warsaw, Poland, pp. 331-340.

[017] Lawry, J. (2006). Modelling and Reasoning with Vague Concepts, Studies in Computational Intelligence, Vol. 12, Springer-Verlag, New York, NY. | Zbl 1092.68095

[018] Lyashko, M. (2005). The optimal solution of an interval system of linear algebraic equations, Reliable Computing 11(2): 105-127. | Zbl 1075.65061

[019] Mendel, J.M. (2002). An architecture for making judgments using computing with words, International Journal of Applied Mathematics and Computer Science 12(3): 325-335. | Zbl 1062.68125

[020] Moore, R. (1966). Interval Analysis, Prentice Hall, Englewood Cliffs, NJ. | Zbl 0176.13301

[021] Moore, R., Kearfott, R. and Cloud, M. (2009). Introduction to Interval Analysis, Society for Industrial and Applied Mathematics, Philadelphia, PA. | Zbl 1168.65002

[022] Pedrycz, W. and Gomide, F. (2007). Fuzzy Systems Engineering: Toward Human-Centric Computing, Wiley Interscience, Hoboken, NJ.

[023] Piegat, A. (2001). Fuzzy Modeling and Control, Physica Verlag, Heidelberg/New York, NY. | Zbl 0976.93001

[024] Piegat, A. and Landowski, M. (2012). Is the conventional interval-arithmetic correct?, Journal of Theoretical and Applied Computer Science 6(2): 27-44.

[025] Piegat, A. and Landowski, M. (2013a). Multidimensional approach to interval-uncertainty calculations, in K. Atanassov et al. (Eds.), New Trends in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, System Research Institute of the Polish Academy of Sciences, Warsaw, pp. 137-152.

[026] Piegat, A. and Landowski, M. (2013b). Two interpretations of multidimensional RDM interval arithmetic: Multiplication and division, International Journal of Fuzzy Systems 15(4): 486-496.

[027] Piegat, A. and Tomaszewska, K. (2013). Decision-making under uncertainty using info-gap theory and a new multidimensional RDM interval-arithmetic, Electrical Review 88(8): 71-76.

[028] Rajati, M. and Mendel, J. (2012). Lower and upper probability calculations using compatibility measures for solving Zadeh's challenge problems, Proceedings of the IEEE International Conference on Fuzzy Systems, Brisbane, Australia, pp. 1-8.

[029] Rajati, M., Mendel, J. and Wu, D. (2011). Solving Zadeh's Magnus challenge problem on linguistic probabilities via linguistic weighted averages, Proceedings of the IEEE International Conference on Fuzzy Systems, Taipei, Taiwan, pp. 2177-2184.

[030] Sevastjanov, P. and Dymova, L. (2009). A new method for solving interval and fuzzy equations: Linear case, Information Sciences 17: 925-937. | Zbl 1160.65010

[031] Tomaszewska, K. (2014). The application of horizontal membership function to fuzzy arithmetic operations, Proceedings of the 11th Polish Conference of Students and Young Scientists, Szczecin, Poland, pp. 1-8.

[032] Tomaszewska, K. and Piegat, A. (2014). Application of the horizontal membership function to the uncertain displacement calculation of a composite massless rod under a tensile load, Proceedings of the International Conference on Advanced Computer Systems, Międzyzdroje, Poland, pp. 63-72.

[033] Türkşen, I. (2007). Meta-linguistic axioms as a foundation for computing with words, Information Sciences 177(2): 332-359. | Zbl 1111.68135

[034] Wang, C. and Qiu, Z. (2013). Equivalent method of accurate solution to linear interval equations, Applied Mathematics and Mechanics 34(8): 1031-1042. | Zbl 1286.65058

[035] Zadeh, L. (1996a). Fuzzy logic = computing with words, IEEE Transactions on Fuzzy Systems 4(2): 103-111.

[036] Zadeh, L. (1996b). Linguistic characterization of preference relations as a basis for choice in social systems, in G. Klir and B. Yuan (Eds.), Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems, World Scientific Publishing Co., River Edge, NJ, pp. 336-354.

[037] Zadeh, L. (1996c). Outline of a theory of usuality based on fuzzy logic, in G. Klir and B. Yuan (Eds.), Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh, World Scientific Publishing Co., River Edge, NJ, pp. 694-712.

[038] Zadeh, L. (2001). A new direction in AI-toward a computational theory of perceptions, AI Magazine 22(1): 73-84. | Zbl 1043.68646

[039] Zadeh, L.A. (2002). From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions, International Journal of Applied Mathematics and Computer Science 12(3): 307-324. | Zbl 1062.68583

[040] Zadeh, L. (2004). A note on web intelligence, world knowledge and fuzzy logic, Data & Knowledge Engineering 50(3): 291-304.

[041] Zadeh, L. (2005). Toward a generalized theory of uncertainty (GTU), Special lecture, Polish Academy of Sciences, Warsaw.

[042] Zadeh, L. (2006a). Generalized theory of uncertainty (GTU)-principal concepts and ideas, Computational statistics & Data Analysis 51(1): 15-46. | Zbl 1157.62312

[043] Zadeh, L. (2006b). A new frontier in computation-computation with information described in natural language, International Conference ICAISC, Zakopane, Poland, (plenary lecture).

[044] Zadeh, L. (2009). Computing with words and perceptions-a paradigm shift, 2009 IEEE International Conference on Information Reuse and Integration, Las Vegas, NV, USA, pp. VIII-X.

[045] Zadeh, L. and Kacprzyk, J. (Eds.) (1999). Computing with Words in Information/Intelligent Systems 1: Foundations, Studies in Fuzziness and Soft Computing, Vol. 33, Physica-Verlag, Heidelberg. | Zbl 0931.00022

[046] Zhou, C. (2002). Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach, International Journal of Applied Mathematics and Computer Science 12(3): 411-421. | Zbl 1098.93023