An approach for consensual analysis on Typical Hesitant Fuzzy Sets via extended aggregations and fuzzy implications based on admissible orders
Resumo
Typical Hesitant Fuzzy Logic (THFL) is founded on the theory of Hesitant Fuzzy Sets, which consider as membership degrees the finite and non-empty subsets of the unit interval, called Typical Hesitant Fuzzy Elements (THFE). THFL provides the modelling for situations where there exists not only data uncertainty, but also indecision or hesitation among experts about the possible values for preferences regarding collections of objects. In order to reduce the information collapse for comparison and/or ranking of alternatives in the preference relationships, this thesis develops new ideas on THFL connectives, investigated under the scope of three admissible orders. In particular, properties of negations and aggregations are studied, as t-norms and OWA operators, with special interest in the axiomatic structures defining the implications and preserving their algebraic properties and representability. As the main contribution, we present a model that formally builds consensus measures on THFE through extended aggregation functions and fuzzy negation, using admissible orders for comparison and further, differentiating an analysis of consistency over preference matrices. Main theoretical results are submitted to multiple expert and mutiple criteria decision making problems.
Palavras-chave:
Typical hesitant fuzzy sets, Consensus measures, Fuzzy implications, Extended aggregation functions, Admissible orders.
Referências
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1):87–96.
Bedregal, B., Reiser, R., Bustince, H., Lopez-Molina, C., and Torra, V. (2014a). Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms. Information Sciences, 255:82 – 99.
Beliakov, G., Calvo, T., and James, S. (2014). Consensus measures constructed from aggregation functions and fuzzy implications. Knowledge-Based Systems, 55:1 – 8.
Bustince, H., Barrenechea, E., Pagola, M., Fernández, J., Xu, Z., Bedregal, B. R. C., Montero, J., Hagras, H., Herrera, F., and Baets, B. D. (2016). A historical account of types of fuzzy sets and their relationships. IEEE Transactions Fuzzy Systems,24(1):179–194.
Bustince, H., Fernandez, J., Kolesárová, A., and Mesiar, R. (2013). Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets and Systems, 220:69– 77. Theme: Aggregation functions.
Bustince, H., Marco-Detchart, C., Fernández, J., Wagner, C., Garibaldi, J. M., and Takác, Z. (2020). Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders. Fuzzy Sets Syst., 390:23–47.
Farhadinia, B. and Xu, Z. (2020).A novel distance-based multiple attribute decision-making with hesitant fuzzy sets. Soft Comput., 24(7):5005–5017.
Farhadinia, B., Aickelin, U., and Khorshidi, H. A. (2020). Uncertainty measures for probabilistic hesitant fuzzy sets in multiple criteria decision making. Int. J. Intell. Syst., 35(11):1646–1679.
García-Lapresta, J. and Llamazares, B. (2001). Majority decisions based on difference of votes. Journal of Mathematical Economics, 35(3):463–481. cited By 41.
García-Lapresta, J. L. and Llamazares, B. (2010). Preference intensities and majority decisions based on difference of support between alternatives. Group Decision and Negotiation, 19(6):527–542.
Grattan-Guinness, I. (1976). Fuzzy membership mapped onto intervals and many-valued quantities. Mathematical Logic Quarterly, 22(1):149–160.
Li, C., Rodríguez, R. M., Martínez, L., Dong, Y., and Herrera, F. (2018). Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions. Knowledge-Based Systems, 145:156–165.
Lima, A. A. d. (2019).Multidimensional Fuzzy Sets. PhD thesis, Federal University of Rio Grande do Norte, Center for Exact and Earth Sciences, Department of Informatics and Applied Mathematics, Graduate Program in Systems and Computing, Natal, Rio Grande do Norte, Brazil.
Llamazares, B., Pérez-Asurmendi, P., and García-Lapresta, J. (2013). Collective transitivity in majorities based on difference in support. Fuzzy Sets and Systems, 216:3–15. cited By 9.
Matzenauer, M., Santos, H., Bedregal, B., Bustince, H., and Reiser, R. (2021b). On admissible total orders for typical hesitant fuzzy consensus measures. International Journal of Intelligent Systems, pages 1–23.
Matzenauer, M., Reiser, R., Santos, H., Bedregal, B., and Bustince, H. (2021a). Strategies on admissible total orders over typical hesitant fuzzy implications applied to decision making problems. International Journal of Intelligent Systems, pages 1–50. In press.
Miguel, L. D., Bustince, H., Fernandez, J., Induráin, E., Kolesárová, A., and Mesiar, R. (2016). Construction of admissible linear orders for interval-valued atanassov intuitionistic fuzzy sets with an application to decision making. Information Fusion,27:189 – 197.
Rezaei, K. and Rezaei, H. (2020). New distance and similarity measures for hesitant fuzzy sets and their application in hierarchical clustering. J. Intell. Fuzzy Syst.,39(3):4349–4360.
Rodríguez, R. M., Xu, Y., Martínez-López, L., and Herrera, F. (2018).Exploring consistency for hesitant preference relations in decision making: Discussing concepts, meaning and taxonomy. Multiple-Valued Logic and Soft Computing, 30(2-3):129–154.
Schneider, G. B., Moura, B. M. P., Yamin, A. C., and Reiser, R. H. S. (2020). Int-FLBCC:Model for load balancing in cloud computing using fuzzy logic type-2 and admissible orders. RITA, 27(3):102–117.
Torra, V. (2010). Hesitant fuzzy sets. Int. Journal of Intelligent Systems, 25:529–539.
Torra, V. and Narukawa, Y. (2009). On hesitant fuzzy sets and decision. In FUZZ-IEEE 2009, IEEE Int. Conference on Fuzzy Systems, Korea, 2009, Proceedings, pages1378–1382.
Unzu, J. A. and Vorsatz, M. (2011). Measuring consensus concepts, comparisons, and properties. In Consensual Processes, pages 195–211. Springer Berlin Heidelberg, Berlin, Heidelberg.
Wang, Z., Wu, J., Liu, X., and Garg, H. (2021). New framework for fcms using dual hesitant fuzzy sets with an analysis of risk factors in emergency event. Int. J. Comput. Intell. Syst., 14(1):67–78.
Xia, M. and Xu, Z. (2011). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3):395 – 407.
Zadeh, L. (1971). Quantitative fuzzy semantics.Information Sciences, 3:159 – 176.
Zadeh, L. (1975). The concept of a linguistic variable and its application to approximate reasoning – I.Information Sciences, 8(3):199 – 249.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3):338–353.
Zanotelli, R. M., Reiser, R., and Bedregal, B. R. C. (2020).n-dimensional (S,N)-implications. Int J Approx Reason, 126:1–26.
Zeng, W., Ma, R., Yin, Q., and Xu, Z. (2020).Similarity measure of hesitant fuzzy sets based on implication function and clustering analysis. IEEE Access,8:119995–120008.
Zhu, B., Xu, Z., and Xia, M. (2012). Hesitant fuzzy geometric bonferroni means. Information Sciences, 205:72 – 85
Bedregal, B., Reiser, R., Bustince, H., Lopez-Molina, C., and Torra, V. (2014a). Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms. Information Sciences, 255:82 – 99.
Beliakov, G., Calvo, T., and James, S. (2014). Consensus measures constructed from aggregation functions and fuzzy implications. Knowledge-Based Systems, 55:1 – 8.
Bustince, H., Barrenechea, E., Pagola, M., Fernández, J., Xu, Z., Bedregal, B. R. C., Montero, J., Hagras, H., Herrera, F., and Baets, B. D. (2016). A historical account of types of fuzzy sets and their relationships. IEEE Transactions Fuzzy Systems,24(1):179–194.
Bustince, H., Fernandez, J., Kolesárová, A., and Mesiar, R. (2013). Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets and Systems, 220:69– 77. Theme: Aggregation functions.
Bustince, H., Marco-Detchart, C., Fernández, J., Wagner, C., Garibaldi, J. M., and Takác, Z. (2020). Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders. Fuzzy Sets Syst., 390:23–47.
Farhadinia, B. and Xu, Z. (2020).A novel distance-based multiple attribute decision-making with hesitant fuzzy sets. Soft Comput., 24(7):5005–5017.
Farhadinia, B., Aickelin, U., and Khorshidi, H. A. (2020). Uncertainty measures for probabilistic hesitant fuzzy sets in multiple criteria decision making. Int. J. Intell. Syst., 35(11):1646–1679.
García-Lapresta, J. and Llamazares, B. (2001). Majority decisions based on difference of votes. Journal of Mathematical Economics, 35(3):463–481. cited By 41.
García-Lapresta, J. L. and Llamazares, B. (2010). Preference intensities and majority decisions based on difference of support between alternatives. Group Decision and Negotiation, 19(6):527–542.
Grattan-Guinness, I. (1976). Fuzzy membership mapped onto intervals and many-valued quantities. Mathematical Logic Quarterly, 22(1):149–160.
Li, C., Rodríguez, R. M., Martínez, L., Dong, Y., and Herrera, F. (2018). Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions. Knowledge-Based Systems, 145:156–165.
Lima, A. A. d. (2019).Multidimensional Fuzzy Sets. PhD thesis, Federal University of Rio Grande do Norte, Center for Exact and Earth Sciences, Department of Informatics and Applied Mathematics, Graduate Program in Systems and Computing, Natal, Rio Grande do Norte, Brazil.
Llamazares, B., Pérez-Asurmendi, P., and García-Lapresta, J. (2013). Collective transitivity in majorities based on difference in support. Fuzzy Sets and Systems, 216:3–15. cited By 9.
Matzenauer, M., Santos, H., Bedregal, B., Bustince, H., and Reiser, R. (2021b). On admissible total orders for typical hesitant fuzzy consensus measures. International Journal of Intelligent Systems, pages 1–23.
Matzenauer, M., Reiser, R., Santos, H., Bedregal, B., and Bustince, H. (2021a). Strategies on admissible total orders over typical hesitant fuzzy implications applied to decision making problems. International Journal of Intelligent Systems, pages 1–50. In press.
Miguel, L. D., Bustince, H., Fernandez, J., Induráin, E., Kolesárová, A., and Mesiar, R. (2016). Construction of admissible linear orders for interval-valued atanassov intuitionistic fuzzy sets with an application to decision making. Information Fusion,27:189 – 197.
Rezaei, K. and Rezaei, H. (2020). New distance and similarity measures for hesitant fuzzy sets and their application in hierarchical clustering. J. Intell. Fuzzy Syst.,39(3):4349–4360.
Rodríguez, R. M., Xu, Y., Martínez-López, L., and Herrera, F. (2018).Exploring consistency for hesitant preference relations in decision making: Discussing concepts, meaning and taxonomy. Multiple-Valued Logic and Soft Computing, 30(2-3):129–154.
Schneider, G. B., Moura, B. M. P., Yamin, A. C., and Reiser, R. H. S. (2020). Int-FLBCC:Model for load balancing in cloud computing using fuzzy logic type-2 and admissible orders. RITA, 27(3):102–117.
Torra, V. (2010). Hesitant fuzzy sets. Int. Journal of Intelligent Systems, 25:529–539.
Torra, V. and Narukawa, Y. (2009). On hesitant fuzzy sets and decision. In FUZZ-IEEE 2009, IEEE Int. Conference on Fuzzy Systems, Korea, 2009, Proceedings, pages1378–1382.
Unzu, J. A. and Vorsatz, M. (2011). Measuring consensus concepts, comparisons, and properties. In Consensual Processes, pages 195–211. Springer Berlin Heidelberg, Berlin, Heidelberg.
Wang, Z., Wu, J., Liu, X., and Garg, H. (2021). New framework for fcms using dual hesitant fuzzy sets with an analysis of risk factors in emergency event. Int. J. Comput. Intell. Syst., 14(1):67–78.
Xia, M. and Xu, Z. (2011). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3):395 – 407.
Zadeh, L. (1971). Quantitative fuzzy semantics.Information Sciences, 3:159 – 176.
Zadeh, L. (1975). The concept of a linguistic variable and its application to approximate reasoning – I.Information Sciences, 8(3):199 – 249.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3):338–353.
Zanotelli, R. M., Reiser, R., and Bedregal, B. R. C. (2020).n-dimensional (S,N)-implications. Int J Approx Reason, 126:1–26.
Zeng, W., Ma, R., Yin, Q., and Xu, Z. (2020).Similarity measure of hesitant fuzzy sets based on implication function and clustering analysis. IEEE Access,8:119995–120008.
Zhu, B., Xu, Z., and Xia, M. (2012). Hesitant fuzzy geometric bonferroni means. Information Sciences, 205:72 – 85
Publicado
17/11/2021
Como Citar
MATZENAUER, Mônica; REISER, Renata; SANTOS, Helida.
An approach for consensual analysis on Typical Hesitant Fuzzy Sets via extended aggregations and fuzzy implications based on admissible orders. In: WORKSHOP-ESCOLA DE INFORMÁTICA TEÓRICA (WEIT), 6. , 2021, Online.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2021
.
p. 163-170.
DOI: https://doi.org/10.5753/weit.2021.18937.
