Fuzzy Galois connections on Alexandrov L-topologies

In this paper, we introduce the notion of Galois and dual Galois connections as a topological viewpoint of concept lattices in a complete residuated lattice. Under various relations, we investigate the Galois and dual Galois connections on Alexandrov L-topologies. Moreover, their properties and examples are investigated.

Pumping lemma in automata theory based on complete residuated lattice-valued logic: A note

Fuzzy Sets and Systems ◽

10.1016/j.fss.2006.03.014 ◽

2006 ◽

Vol 157 (15) ◽

pp. 2128-2138 ◽

Cited By ~ 52

Author(s):

Daowen Qiu

Keyword(s):

Residuated Lattice ◽

Automata Theory ◽

Pumping Lemma

2012 IEEE Sixth International Conference on Software Security and Reliability Companion ◽

Lattice-Valued Kripke Structures Based on Complete Residuated Lattice

10.1109/sere-c.2012.29 ◽

2012 ◽

Author(s):

Haiyu Pan ◽

Min Zhang ◽

Yixiang Chen

Keyword(s):

Residuated Lattice ◽

Kripke Structures ◽

Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice

Neural Computing and Applications ◽

10.1007/s00521-010-0465-6 ◽

2010 ◽

Vol 20 (1) ◽

pp. 41-57 ◽

Cited By ~ 12

Author(s):

Yunqiang Yin ◽

Jianming Zhan ◽

P. Corsini

Keyword(s):

Residuated Lattice ◽

l-Valued multiset automata and l-valued multiset languages

New Mathematics and Natural Computation ◽

10.1142/s1793005721500095 ◽

2020 ◽

pp. 1-15

Author(s):

Vinay Gautam

Keyword(s):

Finite Automaton ◽

Residuated Lattice ◽

Regular Languages ◽

Automata Theory ◽

Necessary And Sufficient Condition ◽

Zero Divisors ◽

Pumping Lemma ◽

Deterministic Formula ◽

Necessary And Sufficient

The reason for this work is to present and study deterministic multiset automata, multiset automata and their languages with membership values in complete residuated lattice without zero divisors. We build up the comparability of deterministic [Formula: see text]-valued multiset finite automaton and [Formula: see text]-valued multiset finite automaton in sense of recognizability of a [Formula: see text]-valued multiset language. Then, we relate multiset regular languages to a given [Formula: see text]-valued multiset regular languages and vice versa. At last, we present the concept of pumping lemma for [Formula: see text]-valued multiset automata theory, which we utilize to give a necessary and sufficient condition for a [Formula: see text]-valued multiset language to be non-constant.

Intuitionistic fuzzy automata based on complete residuated lattice-valued logic

International Journal of Materials and Product Technology ◽

10.1504/ijmpt.2012.051346 ◽

2012 ◽

Vol 45 (1/2/3/4) ◽

pp. 108 ◽

Cited By ~ 3

Author(s):

Qiansheng Zhang ◽

Yirong Huang

Keyword(s):

Residuated Lattice ◽

Intuitionistic Fuzzy ◽

Fuzzy Automata

L-Almost separation axioms in L-fuzzifying-bitopologies via complete residuated lattice-valued logic

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-018-0575-x ◽

2018 ◽

Vol 5 (1) ◽

Author(s):

Mohammed M. Khalaf ◽

A. A. Abd El-Latif

Keyword(s):

Residuated Lattice ◽

Separation Axioms ◽

State hyperstructures of tree automata based on lattice-valued logic

RAIRO - Theoretical Informatics and Applications ◽

10.1051/ita/2018004 ◽

2018 ◽

Vol 52 (1) ◽

pp. 23-42 ◽

Cited By ~ 2

Author(s):

Maryam Ghorani

Keyword(s):

Residuated Lattice ◽

Residuated Lattices ◽

The Other ◽

Equivalence Relations ◽

Tree Automaton ◽

Tree Automata ◽

Other Hand ◽

The Creation ◽

The Given

In this paper, an association is organized between the theory of tree automata on one hand and the hyperstructures on the other hand, over complete residuated lattices. To this end, the concept of order of the states of a complete residuated lattice-valued tree automaton (simply L-valued tree automaton) is introduced along with several equivalence relations in the set of the states of an L-valued tree automaton. We obtain two main results from this study: one of the relations can lead to the creation of Kleene’s theorem for L-valued tree automata, and the other one leads to the creation of a minimal v-valued tree automaton that accepts the same language as the given one.