Acceso abierto

New transitivity of Atanassov’s intuitionistic fuzzy sets in a decision making model

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Advanced Machine Learning Techniques in Data Analysis (special section, pp. 549-611), Maciej Kusy, Rafał Scherer, and Adam Krzyżak (Eds.)

Cite

Asiain, M.J., Bustince, H., Mesiar, R., Kolesarova, A. and Takac, Z. (2018). Negations with respect to admissible orders in the interval-valued fuzzy set theory, IEEE Transactions on Fuzzy Systems 26(2): 556–568.10.1109/TFUZZ.2017.2686372 Search in Google Scholar

Atanassov, K.T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg.10.1007/978-3-7908-1870-3 Search in Google Scholar

Atanassov, K.T. (2008). On the intuitionistic fuzzy implications and negations, in P. Chountas et al. (Eds), Intelligent Techniques and Tools for Novel System Architectures, Springer, Berlin, pp. 381–394.10.1007/978-3-540-77623-9_22 Search in Google Scholar

Atanassov, K.T. (2012). On Intuitionistic Fuzzy Sets Theory, Springer, Heidelberg.10.1007/978-3-642-29127-2 Search in Google Scholar

Atanassov, K.T. (2016). Mathematics of intuitionistic fuzzy sets, in C. Kahraman et al. (Eds), Fuzzy Logic in Its 50th Year: New Developments, Directions and Challenges, Springer, Berlin, pp. 61–86.10.1007/978-3-319-31093-0_3 Search in Google Scholar

Beliakov, G., Bustince Sola, H., James, S., Calvo, T. and Fernandez, J. (2012). Aggregation for Atanassov’s intuitionistic and interval valued fuzzy sets: The median operator, IEEE Transactions on Fuzzy Systems 20(3): 487–498.10.1109/TFUZZ.2011.2177271 Search in Google Scholar

Bentkowska, U. (2018). New types of aggregation functions for interval-valued fuzzy setting and preservation of pos-B and nec-B-transitivity in decision making problems, Information Sciences 424: 385–399.10.1016/j.ins.2017.10.025 Search in Google Scholar

Bentkowska, U., Bustince, H., Jurio, A., Pagola, M. and Pekala, B. (2015). Decision making with an interval-valued fuzzy preference relation and admissible orders, Applied Soft Computing 35: 792–801.10.1016/j.asoc.2015.03.012 Search in Google Scholar

Burillo, P. and Bustince, H. (1995). Intuitionistic fuzzy relations: Effect of Atanassov’s operators on the properties of the intuitionistic fuzzy relation, Mathware and Soft Computing 2(2): 117–148. Search in Google Scholar

Burillo, P. and Bustince, H. (1996). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets Systems 78(3): 305–316.10.1016/0165-0114(96)84611-2 Search in Google Scholar

Deschrijiver, G., Cornelis, C. and Kerre, E.E. (2004). On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Transactions on Fuzzy Systems 12(1): 45–61.10.1109/TFUZZ.2003.822678 Search in Google Scholar

Deschrijver, G. and Kerre, E. (2003). On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems 133(2): 227–235.10.1016/S0165-0114(02)00127-6 Search in Google Scholar

Drygaś, P. (2011). Preservation of intuitionistic fuzzy preference relations, Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11), Aix-les-Bains, France, pp. 554–558. Search in Google Scholar

Dubois, D., Godo, L. and Prade, H. (2014). Weighted logics for artificial intelligence an introductory discussion, International Journal of Approximate Reasoning 55(9): 1819–1829.10.1016/j.ijar.2014.08.002 Search in Google Scholar

Dubois, D. and Prade, H. (1988). Possibility Theory, Plenum Press, New York. Search in Google Scholar

Dubois, D. and Prade, H. (2012). Gradualness, uncertainty and bipolarity: making sense of fuzzy sets, Fuzzy Sets and Systems 192: 3–24.10.1016/j.fss.2010.11.007 Search in Google Scholar

Dudziak, U. and Pękala, B. (2011). Intuitionistic fuzzy preference relations, Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11), Aix-les-Bains, France, pp. 529–536. Search in Google Scholar

Grzegorzewski, P., Hryniewicz, O. and Romaniuk, M. (2020). Flexible resampling for fuzzy data, International Journal of Applied Mathematics and Computer Science 30(2): 281–297, DOI: 10.34768/amcs-2020-0022. Search in Google Scholar

Pękala, B. (2009). Preservation of properties of interval-valued fuzzy relations, Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and the 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, pp. 1206–1210. Search in Google Scholar

Pękala, B. (2019). Uncertainty Data in Interval-Valued Fuzzy Set Theory: Properties, Algorithms and Applications, Springer, Cham.10.1007/978-3-319-93910-0 Search in Google Scholar

Pękala, B., Bentkowska, U., Bustince, H., Fernandez, J. and Galar, M. (2015). Operators on intuitionistic fuzzy relations, IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Istanbul, Turkey, pp. 1–8. Search in Google Scholar

Pękala, B., Bentkowska, U. and De Baets, B. (2016). On comparability relations in the class of interval-valued fuzzy relations, Tatra Mountains Mathematical Publications 66(1): 91–101.10.1515/tmmp-2016-0023 Search in Google Scholar

Pękala, B., Szmidt, E. and Kacprzyk, J. (2018). Group decision support under intuitionistic fuzzy relations: The role of weak transitivity and consistency, International Journal of Intelligent Systems 33(10): 2078–2095.10.1002/int.21923 Search in Google Scholar

Pradhan, R. and Pal, M. (2017). Transitive and strongly transitive intuitionistic fuzzy matrices, Annals of Fuzzy Mathematics and Informatics 13(4): 485–498.10.30948/afmi.2017.13.4.485 Search in Google Scholar

Rutkowski, T., Łapa, K. and Nielek, R. (2019). On explainable fuzzy recommenders and their performance evaluation, International Journal of Applied Mathematics and Computer Science 29(3): 595–610, DOI: 10.2478/amcs-2019-0044.10.2478/amcs-2019-0044 Search in Google Scholar

Saminger, S., Mesiar, R. and Bodenhoffer, U. (2002). Domination of aggregation operators and preservation of transitivity, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10(1): 11–35.10.1142/S0218488502001806 Search in Google Scholar

Szmidt, E. (2014). Distances and Similarities in Intuitionistic Fuzzy Sets, Springer, Cham.10.1007/978-3-319-01640-5 Search in Google Scholar

Szmidt, E. and Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems 114(3): 505–518.10.1016/S0165-0114(98)00244-9 Search in Google Scholar

Szmidt, E. and Kacprzyk, J. (2006). Distances between intuitionistic fuzzy sets: Straightforward approaches may not work, 3rd International IEEE Conference on Intelligent Systems, IS06, London, UK, pp. 716–721. Search in Google Scholar

Szmidt, E. and Kacprzyk, J. (2009). Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives, in E. Rakus-Andersson et al. (Eds), Recent Advances in Decision Making, Springer, Berlin, pp. 7–19.10.1007/978-3-642-02187-9_2 Search in Google Scholar

Szmidt, E. and Kacprzyk, J. (2017). A perspective on differences between Atanassov’s intuitionistic fuzzy sets and interval-valued fuzzy sets, Studies in Computational Intelligence 671: 221–237, DOI: 10.1007/978-3-319-47557-8_13.10.1007/978-3-319-47557-8_13 Search in Google Scholar

Taylor, A.D. (2005). Social Choice and the Mathematics of Manipulation, Cambridge University Press, New York.10.1017/CBO9780511614316 Search in Google Scholar

Xu, Y., Wanga, H. and Yu, D. (2014). Cover image weak transitivity of interval-valued fuzzy relations, Knowledge-Based Systems 63: 24–32.10.1016/j.knosys.2014.03.003 Search in Google Scholar

Xu, Z. (2007). Approaches to multiple attribute decision making with intuitionistic fuzzy preference information, Systems Engineering—Theory and Practice 27(11): 62–71.10.1016/S1874-8651(08)60069-1 Search in Google Scholar

Xu, Z. and Yager, R.R. (2009). Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group, Fuzzy Optimization and Decision Making 8(2): 123–139, DOI: 10.1007/s10700-009-9056-3.10.1007/s10700-009-9056-3 Search in Google Scholar

Zadeh, L.A. (1965). Fuzzy sets, Information and Control 8: 338–353.10.1016/S0019-9958(65)90241-X Search in Google Scholar

Zapata, H., Bustince, H., Montes, S., Bedregal, B., Dimuro, G., Takac, Z. and Baczyński, M. (2017). Interval-valued implications and interval-valued strong equality index with admissible orders, International Journal of Approximate Reasoning 88: 91–109.10.1016/j.ijar.2017.05.009 Search in Google Scholar

eISSN:
2083-8492
Idioma:
Inglés
Calendario de la edición:
4 veces al año
Temas de la revista:
Mathematics, Applied Mathematics