Logical Entropy of Fuzzy Dynamical Systems

被引：23
作者：
Markechova, Dagmar [1 ]
Riecan, Beloslav [2 ,3 ]
机构：
[1] Constantine Philosopher Univ Nitra, Fac Nat Sci, Dept Math, A Hlinku 1, SK-94901 Nitra, Slovakia
[2] Matej Bel Univ, Fac Nat Sci, Dept Math, Tajovskeho 40, SK-97401 Banska Bystrica, Slovakia
[3] Slovak Acad Sci, Math Inst, Stefanikova 49, SK-81473 Bratislava, Slovakia
来源：
ENTROPY | 2016年 / 18卷 / 04期
关键词：
fuzzy probability space; fuzzy partition; logical entropy; logical mutual information; fuzzy dynamical system; PROBABILITY; EQUIVALENCE; PARTITIONS;
D O I：
10.3390/e18040157
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Recently the logical entropy was suggested by D. Ellerman (2013) as a new information measure. The present paper deals with studying logical entropy and logical mutual information and their properties in a fuzzy probability space. In particular, chain rules for logical entropy and for logical mutual information of fuzzy partitions are established. Using the concept of logical entropy of fuzzy partition we define the logical entropy of fuzzy dynamical systems. Finally, it is proved that the logical entropy of fuzzy dynamical systems is invariant under isomorphism of fuzzy dynamical systems.
引用
收藏
页数：14
相关论文
共 35 条
[1]   A REVIEW OF FUZZY SET AGGREGATION CONNECTIVES [J].
DUBOIS, D ;
PRADE, H .
INFORMATION SCIENCES, 1985, 36 (1-2) :85-121
[2]   FUZZY MEASURES AND THE ENTROPY OF FUZZY PARTITIONS [J].
DUMITRESCU, D .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 176 (02) :359-373
[3]   ENTROPY OF A FUZZY PROCESS [J].
DUMITRESCU, D .
FUZZY SETS AND SYSTEMS, 1993, 55 (02) :169-177
[4]   ENTROPY OF FUZZY DYNAMICAL-SYSTEMS [J].
DUMITRESCU, D .
FUZZY SETS AND SYSTEMS, 1995, 70 (01) :45-57
[5]   FUZZY QUANTUM MODELS [J].
DVURECENSKIJ, A ;
RIECAN, B .
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 1991, 20 (01) :39-54
[6]   ON JOINT DISTRIBUTION OF OBSERVABLES FOR F-QUANTUM SPACES [J].
DVURECENSKIJ, A ;
RIECAN, B .
FUZZY SETS AND SYSTEMS, 1991, 39 (01) :65-73
[7]   FUZZY QUANTUM SPACES AND COMPATIBILITY [J].
DVURECENSKIJ, A ;
CHOVANEC, F .
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 1988, 27 (09) :1069-1082
[8]   THE RADON-NIKODYM THEOREM FOR FUZZY PROBABILITY SPACES [J].
DVURECENSKIJ, A .
FUZZY SETS AND SYSTEMS, 1992, 45 (01) :69-78
[9]   AN INTRODUCTION TO LOGICAL ENTROPY AND ITS RELATION TO SHANNON ENTROPY [J].
Ellerman, David .
INTERNATIONAL JOURNAL OF SEMANTIC COMPUTING, 2013, 7 (02) :121-145
[10]  
Gray R. M., 2009, ENTROPY INFORM THEOR
1234