On fuzzification of Tarski's fixed point theorem without transitivity

被引：3

作者：

Vcelar, Frantisek ^{[1
]}

Patikova, Zuzane ^{[1
]}

机构：

[1] Tomas Bata Univ Zlin, Fac Appl Informat, Dept Math, Nad Stranemi 4511, Zlin 76005, Czech Republic

来源：

FUZZY SETS AND SYSTEMS | 2017年 / 320卷

关键词：

Fuzzy relation; Fixed point; Residuated lattice; L-ordered set; L-fuzzy monotone map; Transitivity; FUZZY; LATTICES;

D O I：

10.1016/j.fss.2016.06.016

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The aim of this paper is to present a fuzzification of Tarski's fixed point theorem without the assumption of transitivity. For this purpose a new structure - the so called L-complete propelattice, which generalizes complete lattices and completely lattice L-ordered sets, is introduced. Our results show that for L-fuzzy isotone maps on L-complete propelattices a variant of Tarski's fixed point theorem holds. Especially, the set of fixed points is nonempty and of a certain structure. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：93 / 113

页数：21

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