A Residuated Lattice of L-Fuzzy Subalgebras of a Mono-Unary Algebra

2019 ◽  
Vol 15 (03) ◽  
pp. 539-551 ◽  
Author(s):  
S. V. Tchoffo Foka ◽  
Marcel Tonga
Keyword(s):  
Boolean Algebra ◽  
Residuated Lattice ◽  
Heyting Algebra ◽  
Unary Algebra ◽  
Complete Residuated Lattice ◽  
Fuzzy Subsets

Given a complete residuated lattice [Formula: see text] and a mono-unary algebra [Formula: see text], it is well known that [Formula: see text] and the residuated lattice [Formula: see text] of [Formula: see text]-fuzzy subsets of [Formula: see text] satisfy the same residuated lattice identities. In this paper, we show that [Formula: see text] and the residuated lattice [Formula: see text] of [Formula: see text]-fuzzy subalgebras of [Formula: see text] satisfy the same residuated lattice identities if and only if the Heyting algebra [Formula: see text] of subuniverses of [Formula: see text] is a Boolean algebra. We also show that [Formula: see text] is a Boolean algebra (respectively, an [Formula: see text]-algebra) if and only if [Formula: see text] is a Boolean algebra (respectively, an [Formula: see text]-algebra) and [Formula: see text] is a Boolean algebra.

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

scholarly journals Essential extensions of filters in residuated lattices

2021 ◽  
Author(s):  
Masoud Haveshki
Keyword(s):  
Boolean Algebra ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Essential Extension ◽  
Mv Algebra ◽  
Essential Extensions

Abstract We define the essential extension of a filter in the residuated lattice A associated to an ideal of L(A) and investigate its related properties. We prove the residuated lattice A is a Boolean algebra, G(RL)-algebra or MV -algebra if and only if the essential extension of {1} associated to A \ P is a Boolean filter, G-filter or MV -filter (for all P ∈ SpecA), respectively. Also, some properties of lattice of essential extensions are studied.

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.

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