Computing with words with the use of inverse RDM models of membership functions
By: Andrzej Piegat and Marcin Pluciński
References
- 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.
- 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.
- 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.
- 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.
- 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.
- Dymova, L. (2011). Soft Computing in Economics and Finance, Springer Verlag, Berlin/Heidelberg.
- 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.
- Grzegorzewski, P. and Hryniewicz, O. (2002). Computing with words and life data, International Journal of AppliedMathematics and Computer Science 12(3): 337-345.
- 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.
- Hanss, M. (2005). Applied Fuzzy Arithmetic, Springer Verlag, Berlin/Heidelberg.
- 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.
- 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.
- 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.
- 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.
- Kahnemann, D. and Tversky, A. (2000). Choices, Values and Frames, Cambridge University Press, Russel Sage Foundation, Cambridge.
- Kaufmann, A. and Gupta, M. (1991). Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold, New York, NY.
- 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.
- Lawry, J. (2006). Modelling and Reasoning with Vague Concepts, Studies in Computational Intelligence, Vol. 12, Springer-Verlag, New York, NY.
- Lyashko, M. (2005). The optimal solution of an interval system of linear algebraic equations, Reliable Computing 11(2): 105-127.
- 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.
- Moore, R. (1966). Interval Analysis, Prentice Hall, Englewood Cliffs, NJ.
- Moore, R., Kearfott, R. and Cloud, M. (2009). Introduction to Interval Analysis, Society for Industrial and Applied Mathematics, Philadelphia, PA.
- Pedrycz,W. and Gomide, F. (2007). Fuzzy Systems Engineering: Toward Human-Centric Computing, Wiley Interscience, Hoboken, NJ.
- Piegat, A. (2001). Fuzzy Modeling and Control, Physica Verlag, Heidelberg/New York, NY.
- Piegat, A. and Landowski, M. (2012). Is the conventional interval-arithmetic correct?, Journal of Theoretical and Applied Computer Science 6(2): 27-44.
- 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.
- 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.
- 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.
- 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.
- 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.
- Sevastjanov, P. and Dymova, L. (2009). A new method for solving interval and fuzzy equations: Linear case, Information Sciences 17: 925-937.
- 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.
- 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, Mi˛edzyzdroje, Poland, pp. 63-72.
- Türk¸sen, I. (2007). Meta-linguistic axioms as a foundation for computing with words, Information Sciences 177(2): 332-359.
- Wang, C. and Qiu, Z. (2013). Equivalent method of accurate solution to linear interval equations, Applied Mathematics and Mechanics 34(8): 1031-1042.
- Zadeh, L. (1996a). Fuzzy logic = computing with words, IEEE Transactions on Fuzzy Systems 4(2): 103-111.
- 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.
- 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.
- Zadeh, L. (2001). A new direction in AI-toward a computational theory of perceptions, AI Magazine 22(1): 73-84.
- 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.
- Zadeh, L. (2004). A note on web intelligence, world knowledge and fuzzy logic, Data & Knowledge Engineering 50(3): 291-304.
- Zadeh, L. (2005). Toward a generalized theory of uncertainty (GTU), Special lecture, Polish Academy of Sciences, Warsaw.
- Zadeh, L. (2006a). Generalized theory of uncertainty (GTU)-principal concepts and ideas, Computational statistics & Data Analysis 51(1): 15-46.
- Zadeh, L. (2006b). A new frontier in computation-computation with information described in natural language, International Conference ICAISC, Zakopane, Poland, (plenary lecture).
- 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.
- Zadeh, L. and Kacprzyk, J. (Eds.) (1999). Computing withWords in Information/Intelligent Systems 1: Foundations, Studies in Fuzziness and Soft Computing, Vol. 33, Physica-Verlag, Heidelberg.
- 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.
Language: English
Page range: 675 - 688
Submitted on: Feb 3, 2014
Published on: Sep 30, 2015
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Related subjects:
© 2015 Andrzej Piegat, Marcin Pluciński, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.