A Comparison of Some t-Norms and t-Conorms over the Steady State of a Fuzzy Markov Chain

1. Araiza, R., Xiang, G., Kosheleva, O., Skülj, D.: Under interval and fuzzy uncertainty, symmetric Markov chains are more difficult to predict. In: 2007 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), vol. 26, pp. 526–531. IEEE (2007)

   Google Scholar 

2. Avrachenkov, K.E., Sanchez, E.: Fuzzy Markov chains: specificities and properties. In: IEEE (ed.) 8th IPMU’2000 Conference, Madrid, Spain, pp. 1851–1856. IEEE (2000)

   Google Scholar 

3. Avrachenkov, K.E., Sanchez, E.: Fuzzy Markov chains and decision-making. Fuzzy Optim. Decis. Mak. 1(2), 143–159 (2002)

   Article  MathSciNet  Google Scholar 

4. Campos, M.A., Dimuro, G.P., da Rocha Costa, A.C., Kreinovich, V.: Computing 2-step predictions for interval-valued finite stationary Markov chains. Tech. rep., UTEP-CS-03-20 (2003)

   Google Scholar 

5. Figueroa-García, J.C.: Interval type-2 fuzzy Markov chains: an approach. In: 2007 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), vol. 28, No. 1, pp. 1–6 (2010)

   Google Scholar 

6. Figueroa-García, J.C.: Advances in Type-2 Fuzzy Sets and Systems, vol. 301, chap. Interval Type-2 Fuzzy Markov Chains, pp. 49–64. Springer (2013)

   Google Scholar 

7. Figueroa-García, J.C., Kalenatic, D., Lopéz, C.A.: A simulation study on fuzzy Markov chains. Commun. Comput. Inf. Sci. 15(1), 109–117 (2008)

   MATH  Google Scholar 

8. Figueroa-García, J.C., Kalenatic, D., Lopez, C.A.: Scalarization of fuzzy Markov chains. Lect. Notes Comput. Sci. 6215(1), 110–117 (2010)

   Google Scholar 

9. Figueroa-García, J.C., Kalenatic, D., López-Bello, C.A.: Interval type-2 fuzzy Markov chains: type reduction. Lect. Notes Comput. Sci. 6839(1), 211–218 (2011)

   Google Scholar 

10. Gavalec, M.: Reaching matrix period is np-complete. Tatra Mt. Math. Publ. 12(1), 81–88 (1997)

    MathSciNet  MATH  Google Scholar 

11. Gavalec, M.: Periods of special fuzzy matrices. Tatra Mt. Math. Publ. 16(1), 47–60 (1999)

    MathSciNet  MATH  Google Scholar 

12. Gavalec, M.: Computing orbit period in max-min algebra. Discret. Appl. Math. 100(1), 49–65 (2000)

    Article  MathSciNet  Google Scholar 

13. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers (2009)

    Google Scholar 

14. Kurano, M., Yasuda, M., Nakagami, J.: Interval methods for uncertain Markov decision processes. In: International Workshop on Markov Processes and Controlled Markov Chains (1999)

    Google Scholar 

15. Kurano, M., Yasuda, M., Nakagami, J., Yoshida, Y.: A fuzzy approach to Markov decision processes with uncertain transition probabilities. Fuzzy Sets Syst. 157(16), 2674–2682 (2007)

    MathSciNet  MATH  Google Scholar 

16. Sanchez, E.: Resolution of eigen fuzzy sets equations. Fuzzy Sets Syst. 1(1), 69–74 (1978)

    Article  MathSciNet  Google Scholar 

17. Sanchez, E.: Eigen fuzzy sets and fuzzy relations. J. Math. Anal. Appl. 81(1), 399–421 (1981)

    Article  MathSciNet  Google Scholar 

18. Skulj, D.: Regular finite Markov chains with interval probabilities. In: 5th International Symposium on Imprecise Probability: Theories and Applications, Prague, Czech Republic, 2007 (2007)

    Google Scholar 

19. Zeng, J., Liu, Z.Q.: Type-2 fuzzy Markov random fields to handwritten character recognition. In: 18th International Conference on Proceedings of Pattern Recognition, 2006, ICPR 2006, vol. 1, pp. 1162–1165 (2006)

    Google Scholar 

Download references