Relating De Morgan triples with Atanassov's intuitionistic De Morgan triples via automorphisms

被引：35

作者：

da Costa, Claudilene Gomes ^{[1
]}

Bedregal, Benjamin Callejas ^{[2
]}

Doria Neto, Adriao Duarte ^{[3
]}

机构：

[1] Fed Univ Paraiba UFPB, Dept Exact Sci DCE, BR-58297000 Rio Tinto, PB, Brazil

[2] Univ Fed Rio Grande do Norte, DIMAp, Grp Log Language Informat Theory & Applicat LoLIT, BR-59072970 Natal, RN, Brazil

[3] Univ Fed Rio Grande do Norte, Dept Comp Engn & Automat DCA, BR-59090530 Natal, RN, Brazil

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2011年 / 52卷 / 04期

关键词：

Atanassov's intuitionistic fuzzy sets; De Morgan triples; Automorphism; Atanassov's operators; INTERVAL-VALUED FUZZY; T-NORMS; REPRESENTATION; OPERATORS; NEGATIONS; SETS;

D O I：

10.1016/j.ijar.2010.11.004

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper the relation between De Morgan triples on the unit interval and Atanassov's intuitionistic De Morgan triples is presented, showing how to obtain, in a canonical way, Atanassov's intuitionistic De Morgan triples from De Morgan triples. Moreover, we also show that the automorphisms on the unit interval and on L* (the intuitionistic value lattice) are in one-to-one correspondence and how automorphisms on L* act on Atanassov's intuitionistic De Morgan triples. It is also proved that the action of automorphisms and the canonical construction of De Morgan triples on L* commutes. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：473 / 487

页数：15

共 46 条

[31] Lipschitzian De Morgan triplets of fuzzy connectives
Kolesarova, Anna
Mesiar, Radko
[J]. INFORMATION SCIENCES, 2010, 180 (18) : 3488 - 3496
[32] A bipolar model of assertability and belief
Lawry, Jonathan
Gonzalez-Rodriguez, Ines
[J]. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2011, 52 (01) : 76 - 91
[33] Lowen R., 1996, FUZZY SET THEORY BAS
[34] DIVISIBLE, RECIPROCAL AUTOMORPHISMS OF THE UNIT INTERVAL
Maes, Koen C.
De Baets, Bernard
[J]. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 2009, 17 (02) : 221 - 235
[35] Mayor G., 2005, LOGICAL ALGEBRAIC AN
[36] Statistical metrics
Menger, K
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1942, 28 : 535 - 537
[37] Characterization of measures based on strict triangular norms
Navara, M
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 236 (02) : 370 - 383
[38] Nguyen HungT., 2000, 1 COURSE FUZZY LOGIC
[39] Ozturk M., 2006, PREFERENCES SPECIFIC
[40] REISER RHS, 2008, TEMA-TEND MAT APL CO, V9, P143

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