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

共 50 条

[41] A NOTE ON BRONDSTED'S FIXED POINT THEOREM
Zubelevich, Oleg
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2023,
[42] On Krasnoselskii's Cone Fixed Point Theorem
Man Kam Kwong
[J]. Fixed Point Theory and Applications, 2008
[43] Handel's fixed point theorem revisited
Xavier, Juliana
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2013, 33 : 1584 - 1610
[44] On the Fixed Point Method and Bloch's Theorem
Cortissoz, Jean C.
[J]. MICHIGAN MATHEMATICAL JOURNAL, 2022, 71 (03) : 553 - 578
[45] A Generalization of Kannan's Fixed Point Theorem
Yusuke Enjouji
Masato Nakanishi
Tomonari Suzuki
[J]. Fixed Point Theory and Applications, 2009
[46] Tarski’s Theorem and the Extensionality of Truth
Stewart Shapiro
[J]. Erkenntnis, 2013, 78 : 1197 - 1204
[47] A Note On The Constructive Proof Of Kakutani's Fixed Point Theorem With Uniformly Locally At Most One Fixed Point Without Countable Choice
Tanaka, Yasuhito
[J]. APPLIED MATHEMATICS E-NOTES, 2013, 13 : 8 - 16
[48] CONSTRUCTIVE VERSIONS OF TARSKI FIXED-POINT THEOREMS
COUSOT, P
COUSOT, R
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1979, 82 (01) : 43 - 57
[49] A companion preorder to G-majorization and a Tarski type fixed-point theorem section: convex analysis
Marek Niezgoda
[J]. Journal of Fixed Point Theory and Applications, 2023, 25
[50] A companion preorder to G-majorization and a Tarski type fixed-point theorem section: convex analysis
Niezgoda, Marek
[J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2023, 25 (02)

← 1 2 3 4 5 →