Algebras of fuzzy sets

被引：13

作者：

Bosnjak, I. ^{[1
]}

Madarasz, R. ^{[1
]}

Vojvodic, G. ^{[1
]}

机构：

[1] Univ Novi Sad, Dept Math & Informat, Novi Sad 21000, Serbia

来源：

FUZZY SETS AND SYSTEMS | 2009年 / 160卷 / 20期

关键词：

Algebra; Fuzzy set; Zadeh's extension principle; Residuated lattice; Homomorphism; Subalgebra; Direct product; PROPOSITIONAL CALCULI; RESIDUATED LATTICES; UNIVERSAL ALGEBRA; LOGIC; SUBALGEBRAS;

D O I：

10.1016/j.fss.2009.04.005

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we investigate two kinds of algebras of fuzzy sets, which are obtained by using Zadeh's extension principle. We give conditions under which a homomorphism between two algebras induces a homomorphism between corresponding algebras of fuzzy sets. We prove that if the structure of truth values is a complete residuated lattice, the induced algebra of a subalgebra of an algebra A can be embedded into the induced algebra of fuzzy sets of A. For direct products we give conditions under which the direct product of algebras of fuzzy sets could be embedded into the algebra of fuzzy sets of the direct product. In the case of homomorphisms and direct products, the two kinds of algebras of fuzzy sets behave in different ways. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：2979 / 2988

页数：10

共 50 条

[21] Soft rough fuzzy sets and soft fuzzy rough sets [J].

Meng, Dan ;

Zhang, Xiaohong ;

Qin, Keyun .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (12) :4635-4645

[22] FUZZY TOPOLOGICAL ALGEBRAS AND LOCALLY MULTIPLICATIVELY CONVEX FUZZY TOPOLOGICAL ALGEBRAS [J].

吴从炘 ;

马明 .

ScienceBulletin, 1985, (02) :277-277

[23] A novel approach to neutrosophic sets in UP-algebras [J].

Songsaeng, Metawee ;

Iampan, Aiyared .

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2020, 21 (01) :78-98

[24] Fuzzy rough sets are intuitionistic L-fuzzy sets [J].

Coker, D .

FUZZY SETS AND SYSTEMS, 1998, 96 (03) :381-383

[25] FUZZY-SETS AS NAMED SETS [J].

BURGIN, M ;

KUZNETSOV, V .

FUZZY SETS AND SYSTEMS, 1992, 46 (02) :189-192

[26] Shadowed sets of dynamic fuzzy sets [J].

Cai M. ;

Li Q. ;

Lang G. .

Granular Computing, 2017, 2 (2) :85-94

[27] Algebras with fuzzy equalities [J].

Belohlávek, R ;

Vychodil, V .

FUZZY SETS AND SYSTEMS, 2006, 157 (02) :161-201

[28] Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets [J].

Burillo, P ;

Bustince, H .

FUZZY SETS AND SYSTEMS, 1996, 78 (03) :305-316

[29] Granular fuzzy sets and three-way approximations of fuzzy sets [J].

Yao, Yiyu ;

Yang, Jilin .

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2023, 161

[30] Rough and T-Rough Sets Arising from Intuitionistic Fuzzy Ideals in BCK-Algebras [J].

Alsager, Kholood M. ;

El-Deeb, Sheza M. .

MATHEMATICS, 2024, 12 (18)

← 1 2 3 4 5 →