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Riesgo, Á., Alonso, P., Díaz, I., Montes, S.. (1399). General definitions for the union and intersection of ordered fuzzy multisets. نشریه علمی دانشگاه سیستان و بلوچستان, 17(4), 41-54. doi: 10.22111/ijfs.2020.5405
Á. Riesgo; P. Alonso; I. Díaz; S. Montes. "General definitions for the union and intersection of ordered fuzzy multisets". نشریه علمی دانشگاه سیستان و بلوچستان, 17, 4, 1399, 41-54. doi: 10.22111/ijfs.2020.5405
Riesgo, Á., Alonso, P., Díaz, I., Montes, S.. (1399). 'General definitions for the union and intersection of ordered fuzzy multisets', نشریه علمی دانشگاه سیستان و بلوچستان, 17(4), pp. 41-54. doi: 10.22111/ijfs.2020.5405
Riesgo, Á., Alonso, P., Díaz, I., Montes, S.. General definitions for the union and intersection of ordered fuzzy multisets. نشریه علمی دانشگاه سیستان و بلوچستان, 1399; 17(4): 41-54. doi: 10.22111/ijfs.2020.5405

General definitions for the union and intersection of ordered fuzzy multisets

Iranian Journal of Fuzzy Systems
دوره 17، شماره 4، مهر و آبان 2020، صفحه 41-54    اصل مقاله (507.84 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2020.5405
نویسندگان
Á. Riesgo* 1؛ P. Alonso2؛ I. Díaz3؛ S. Montes1
1Department of Statistics and O. R., University of Oviedo, Spain
2Department of Mathematics, University of Oviedo, Spain
3Department of Computer Science, University of Oviedo, Spain
چکیده
Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membership, the key difference being that the fuzzy multisets allow for repeated membership values whereas the hesitant fuzzy sets do not. But in neither case are these collections of values ordered, as they are simply represented through multisets or sets. In this paper, we study ordered fuzzy multisets, where the membership value can be an ordered $n$-tuple of values, thus accounting for both order and repetition. We present some basic definitions and results and explore the relation between these ordered fuzzy multisets and the fuzzy multisets and hesitant fuzzy sets.
کلیدواژه‌ها
Fuzzy sets؛ fuzzy multisets؛ ordered fuzzy multisets
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