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

[21] A generalization of Matkowski's fixed point theorem and Istratescu's fixed point theorem concerning convex contractions
Miculescu, Radu
Mihail, Alexandru
[J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2017, 19 (02) : 1525 - 1533
[22] Browder's Theorem through Brouwer's Fixed Point Theorem
Solan, Eilon
Solan, Omri N. N.
[J]. AMERICAN MATHEMATICAL MONTHLY, 2023, 130 (04): : 370 - 374
[23] A generalization of Matkowski’s fixed point theorem and Istrăţescu’s fixed point theorem concerning convex contractions
Radu Miculescu
Alexandru Mihail
[J]. Journal of Fixed Point Theory and Applications, 2017, 19 : 1525 - 1533
[24] The Complexity of Determining the Uniqueness of Tarski's Fixed Point under the Lexicographic Ordering
Dang, Chuangyin
Ye, Yinyu
[J]. INTERNET AND NETWORK ECONOMICS, 2010, 6484 : 455 - +
[25] On the complexity of an expanded Tarski's fixed point problem under the componentwise ordering
Dang, Chuangyin
Ye, Yinyu
[J]. THEORETICAL COMPUTER SCIENCE, 2018, 732 : 26 - 45
[26] The Sandwich theorem via Pataraia’s fixed point theorem
Massimiliano Amarante
[J]. Positivity, 2019, 23 : 97 - 100
[27] The Sandwich theorem via Pataraia's fixed point theorem
Amarante, Massimiliano
[J]. POSITIVITY, 2019, 23 (01) : 97 - 100
[28] Tarski's Theorem and the Extensionality of Truth
Shapiro, Stewart
[J]. ERKENNTNIS, 2013, 78 (05) : 1197 - 1204
[29] ON A CONVERSE TO BANACH'S FIXED POINT THEOREM
Marton Elekes
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (09) : 3139 - 3146
[30] Remark on Krasnoselskii's fixed point theorem
Vladimirescu, Cristian
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (3-4) : 876 - 880

← 1 2 3 4 5 →