Algebraic analysis of fuzzy systems

被引：59
作者：
Di Nola, Antonio
Lettieri, Ada
Perfilieva, Irina
Novak, Vilem
机构：
[1] Univ Ostrava, Inst Res & Applicat Fuzzy Modeling, Ostrava 70103 1, Czech Republic
[2] Univ Salerno, Fac Sci, Dipartimento Matemat & Informat, I-84081 Baronissi, Italy
[3] Univ Naples Federico 2, Dipt Costruzioni & Metodi Matemat Architettura, I-80134 Naples, Italy
来源：
FUZZY SETS AND SYSTEMS | 2007年 / 158卷 / 01期
关键词：
fuzzy logic; MV-algebra; semimodule; semilinear space; semiring; fuzzy systems;
D O I：
10.1016/j.fss.2006.09.003
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, we have developed an algebraic theory, suitable for the analysis of fuzzy systems. We have used the notions of semiring and semimodule, introduced the notion of semilinear space, have given numerous examples of them and defined also the notions of linear dependence and independence. We have shown that the composition operation, which plays an essential role in the analysis of fuzzy systems because of its role in the compositional rule of inference, can be interpreted as a homomorphism between special semimodules. Consequently, this operation is, in a certain sense, a linear operation. This property formally explains why fuzzy systems are attractive for applications. (C) 2006 Elsevier B.V. All rights reserved.
引用
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页码：1 / 22
页数：22
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