Lattice-Valued Kripke Structures Based on Complete Residuated Lattice

2012 ◽  
Author(s):  
Haiyu Pan ◽  
Min Zhang ◽  
Yixiang Chen
Keyword(s):  
Residuated Lattice ◽  
Kripke Structures ◽  
Complete Residuated Lattice

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

2010 ◽  
Vol 20 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Yunqiang Yin ◽  
Jianming Zhan ◽  
P. Corsini
Keyword(s):  
Residuated Lattice ◽  
Complete Residuated Lattice

l-Valued multiset automata and l-valued multiset languages

2020 ◽  
pp. 1-15
Author(s):  
Vinay Gautam
Keyword(s):  
Finite Automaton ◽  
Residuated Lattice ◽  
Regular Languages ◽  
Automata Theory ◽  
Necessary And Sufficient Condition ◽  
Zero Divisors ◽  
Complete Residuated Lattice ◽  
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.

State hyperstructures of tree automata based on lattice-valued logic

2018 ◽  
Vol 52 (1) ◽  
pp. 23-42 ◽  
Author(s):  
Maryam Ghorani
Keyword(s):  
Residuated Lattice ◽  
Residuated Lattices ◽  
The Other ◽  
Equivalence Relations ◽  
Tree Automaton ◽  
Tree Automata ◽  
Other Hand ◽  
Complete Residuated Lattice ◽  
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.

scholarly journals The Relations between Residuated Frames and Residuated Connections

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 295
Author(s):  
Yong Chan Kim ◽  
Ju-Mok Oh
Keyword(s):  
Fuzzy Logic ◽  
Complete Lattice ◽  
Rough Sets ◽  
Residuated Lattice ◽  
Macneille Completion ◽  
Relational Semantics ◽  
Fuzzy Rough Sets ◽  
Complete Residuated Lattice

We introduce the notion of (dual) residuated frames as a viewpoint of relational semantics for a fuzzy logic. We investigate the relations between (dual) residuated frames and (dual) residuated connections as a topological viewpoint of fuzzy rough sets in a complete residuated lattice. As a result, we show that the Alexandrov topology induced by fuzzy posets is a fuzzy complete lattice with residuated connections. From this result, we obtain fuzzy rough sets on the Alexandrov topology. Moreover, as a generalization of the Dedekind–MacNeille completion, we introduce R-R (resp. D R - D R ) embedding maps and R-R (resp. D R - D R ) frame embedding maps.

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