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2018 | OriginalPaper | Buchkapitel

On the Problem of Comparing Ordered Ordinary Fuzzy Multisets

verfasst von : Ángel Riesgo, Pedro Alonso, Irene Díaz, Vladimír Janiš, Vladimír Kobza, Susana Montes

Erschienen in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Verlag: Springer International Publishing

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Abstract

In this work we deal with a particular type of hesitant fuzzy set, in the case where membership values can appear multiple times and are ordered. They are called ordered ordinary fuzzy multisets. Some operations between them are introduced by means of an extension principle. In particular, the divergence measures between two of these multisets are defined and we have studied in detail the local family of divergences. Finally, these measures are related to the ones given for ordinary fuzzy sets.

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Literatur
1.
2.
Zurück zum Zitat Bouchon-Meunier, B., Rifqi, M., Bothorel, S.: Towards general measures of comparison of objects. Fuzzy Sets Syst. 84, 143–153 (1996)MathSciNetCrossRef Bouchon-Meunier, B., Rifqi, M., Bothorel, S.: Towards general measures of comparison of objects. Fuzzy Sets Syst. 84, 143–153 (1996)MathSciNetCrossRef
4.
Zurück zum Zitat Couso, I., Garrido, L., Sánchez, L.: Similarity and dissimilarity measures between fuzzy sets: a formal relational study. Inf. Sci. 229, 122–141 (2013)MathSciNetCrossRef Couso, I., Garrido, L., Sánchez, L.: Similarity and dissimilarity measures between fuzzy sets: a formal relational study. Inf. Sci. 229, 122–141 (2013)MathSciNetCrossRef
5.
Zurück zum Zitat Dubois, D., Prade, H.: Fundamentals of Fuzzy Sets. Kluwer Academic Publishers, Massachusetts (2000)CrossRef Dubois, D., Prade, H.: Fundamentals of Fuzzy Sets. Kluwer Academic Publishers, Massachusetts (2000)CrossRef
6.
Zurück zum Zitat Grattan-Guinness, I.: Fuzzy membership mapped onto intervals and many-valued quantities. Math. Logic Q. 22–1, 149–160 (1976)MathSciNetCrossRef Grattan-Guinness, I.: Fuzzy membership mapped onto intervals and many-valued quantities. Math. Logic Q. 22–1, 149–160 (1976)MathSciNetCrossRef
8.
Zurück zum Zitat Klir, G.J., Folger, T.A.: Fuzzy Sets Uncertainty and Information. Prentice-Hall, Englewood Cliffs (1988)MATH Klir, G.J., Folger, T.A.: Fuzzy Sets Uncertainty and Information. Prentice-Hall, Englewood Cliffs (1988)MATH
9.
Zurück zum Zitat Kobza, V., Janiš, V., Montes, S.: Generalizated local divergence measures. J. Intell. Fuzzy Syst. 33, 337–350 (2017)CrossRef Kobza, V., Janiš, V., Montes, S.: Generalizated local divergence measures. J. Intell. Fuzzy Syst. 33, 337–350 (2017)CrossRef
10.
Zurück zum Zitat Li, Y., Qin, K., He, X.: Some new approaches to constructing similarity measures. Fuzzy Sets Syst. 234(1), 46–60 (2014)MathSciNetCrossRef Li, Y., Qin, K., He, X.: Some new approaches to constructing similarity measures. Fuzzy Sets Syst. 234(1), 46–60 (2014)MathSciNetCrossRef
11.
Zurück zum Zitat Lui, X.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52, 305–318 (1992)MathSciNetCrossRef Lui, X.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52, 305–318 (1992)MathSciNetCrossRef
12.
Zurück zum Zitat Montes, I., Pal, N.R., Janiš, V., Montes, S.: Divergence measures for intuitionistic fuzzy sets. IEEE Trans. Fuzzy Syst. 23(2), 444–456 (2015)CrossRef Montes, I., Pal, N.R., Janiš, V., Montes, S.: Divergence measures for intuitionistic fuzzy sets. IEEE Trans. Fuzzy Syst. 23(2), 444–456 (2015)CrossRef
14.
Zurück zum Zitat Montes, S., Couso, I., Gil, P., Bertoluzza, C.: Divergence measure between fuzzy sets. Int. J. Approx. Reason. 30, 91–105 (2002)MathSciNetCrossRef Montes, S., Couso, I., Gil, P., Bertoluzza, C.: Divergence measure between fuzzy sets. Int. J. Approx. Reason. 30, 91–105 (2002)MathSciNetCrossRef
15.
Zurück zum Zitat Rodríguez, R.M., Bedregal, B., Bustince, H., Dong, Y.C., Farhadinia, B., Kahraman, C., Martínez, L., Torra, V., Xu, Y.J., Xu, Z.S., Herrera, F.: A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf. Fusion 29, 89–97 (2016)CrossRef Rodríguez, R.M., Bedregal, B., Bustince, H., Dong, Y.C., Farhadinia, B., Kahraman, C., Martínez, L., Torra, V., Xu, Y.J., Xu, Z.S., Herrera, F.: A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf. Fusion 29, 89–97 (2016)CrossRef
16.
Zurück zum Zitat Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25–6, 529–539 (2010)MATH Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25–6, 529–539 (2010)MATH
17.
Zurück zum Zitat Valverde, L., Ovchinnikov, S.: Representations of T-similarity relations. Fuzzy Sets Syst. 159(17), 2211–2220 (2008)MathSciNetCrossRef Valverde, L., Ovchinnikov, S.: Representations of T-similarity relations. Fuzzy Sets Syst. 159(17), 2211–2220 (2008)MathSciNetCrossRef
18.
Zurück zum Zitat Wilbik, A., Keller, J.M.: A fuzzy measure similarity between sets of linguistic summaries. IEEE Trans. Fuzzy Syst. 21(1), 183–189 (2013)CrossRef Wilbik, A., Keller, J.M.: A fuzzy measure similarity between sets of linguistic summaries. IEEE Trans. Fuzzy Syst. 21(1), 183–189 (2013)CrossRef
20.
21.
Zurück zum Zitat Zadeh, L.A.: A note on similarity-based definitions of possibility and probability. Inf. Sci. 267, 334–336 (2014)MathSciNetCrossRef Zadeh, L.A.: A note on similarity-based definitions of possibility and probability. Inf. Sci. 267, 334–336 (2014)MathSciNetCrossRef
22.
Zurück zum Zitat Zhang, C., Fu, H.: Similarity measures on three kinds of fuzzy sets. Pattern Recogn. Lett. 27(12), 1307–1317 (2006)CrossRef Zhang, C., Fu, H.: Similarity measures on three kinds of fuzzy sets. Pattern Recogn. Lett. 27(12), 1307–1317 (2006)CrossRef
Metadaten
Titel
On the Problem of Comparing Ordered Ordinary Fuzzy Multisets
verfasst von
Ángel Riesgo
Pedro Alonso
Irene Díaz
Vladimír Janiš
Vladimír Kobza
Susana Montes
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-91476-3_29