Similarity measures, penalty functions, and fuzzy entropy from new fuzzy subsethood measures

被引：11
作者：
Santos, Helida [1 ]
Couso, Ines [2 ]
Bedregal, Benjamin [3 ]
Takac, Zdenko [4 ]
Minarova, Maria [5 ]
Asiain, Alfredo [6 ]
Barrenechea, Edurne [7 ]
Bustince, Humberto [7 ,8 ]
机构：
[1] Univ Fed Rio Grande, Ctr Ciencias Computacionais, Rio Grande, Brazil
[2] Univ Oviedo, Dept Estadist & IO & DM, Gijon, Spain
[3] Univ Fed Rio Grande do Norte, Dept Informat & Matemat Aplicada, Natal, RN, Brazil
[4] Slovak Univ Technol Bratislava, Inst Informat Engn Automat & Math, Bratislava, Slovakia
[5] Slovak Univ Technol Bratislava, Dept Math & Descript Geometry, Bratislava, Slovakia
[6] Univ Publ Navarra, Dept Filol & Didact Lengua, Pamplona, Spain
[7] Univ Publ Navarra, Dept Stat Comp Sci & Math, Inst Smart Cities, Pamplona 31006, Spain
[8] KAU, Fac Comp & Informat Technol, Jeddah, Saudi Arabia
来源：
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS | 2019年 / 34卷 / 06期
关键词：
fuzzy entropy; fuzzy sets; penalty functions; similarity measures; subsethood measure; AGGREGATION FUNCTIONS; INCLUSION MEASURE; SETS; CONSTRUCTION; EQUIVALENCE; DEFINITION; DISTANCE; SCALE;
D O I：
10.1002/int.22096
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this study, we discuss a new class of fuzzy subsethood measures between fuzzy sets. We propose a new definition of fuzzy subsethood measure as an intersection of other axiomatizations and provide two construction methods to obtain them. The advantage of this new approach is that we can construct fuzzy subsethood measures by aggregating fuzzy implication operators which may satisfy some properties widely studied in literature. We also obtain some of the classical measures such as the one defined by Goguen. The relationships with fuzzy distances, penalty functions, and similarity measures are also investigated. Finally, we provide an illustrative example which makes use of a fuzzy entropy defined by means of our fuzzy subsethood measures for choosing the best fuzzy technique for a specific problem.
引用
收藏
页码：1281 / 1302
页数：22
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