Functional equations related to fuzzy sets and representable orderings

被引：2
|
作者：
Jesus Campion, Maria [1 ,2 ]
Catalan, Raquel G. [1 ,2 ]
Garay, Jose [3 ]
Indurain, Esteban [1 ,2 ]
机构：
[1] Univ Publ Navarra, INAMAT, E-31006 Pamplona, Spain
[2] Univ Publ Navarra, Dept Matemat, E-31006 Pamplona, Spain
[3] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain
来源：
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS | 2015年 / 29卷 / 03期
关键词：
Functional equations in two variables; fuzzy sets; representable total preorders; interval orders and semiorders; separability functional equation; INTERVAL ORDERS; NUMERICAL REPRESENTABILITY; TOTAL PREORDERS; SEMIORDERS; AGGREGATION;
D O I：
10.3233/IFS-151720
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The original definition of a fuzzy set hides several additional structures related to functional equations. In the present paper, we analyze the separability functional equation and some of its variants, proving that the solutions of those equations can be described in terms of pairs of linked fuzzy sets on the same universe. In addition, we show that representable total preorders, interval orders and semiorders on a universe can also be analyzed throughout separability functional equations and, consequently, by means of fuzzy sets. Other functional equations related to fuzzy sets, as well as some relationship between this setting and other approaches as the construction of quasi-metrics on a universe are also pointed out as a by-product.
引用
收藏
页码：1065 / 1077
页数：13
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