scholarly journals Generalized fuzzy hypergraphs and hypergroupoids

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2375-2387 ◽  
Author(s):  
Mahdi Farshi ◽  
Bijan Davvaz
Keyword(s):  
Equivalence Relation ◽  
Higher Order ◽  
Regular Equivalence ◽  
Fuzzy Hypergraphs

This article first generalizes the ordinary fuzzy hypergraphs to generalized fuzzy hypergraphs and it makes a connection between generalized fuzzy hypergraphs and fuzzy hyperstructures. We construct a partial fuzzy hypergroupoid associated with it, giving some properties of the associated fuzzy hyperstructure. Moreover, we construct higher order fuzzy hypergroupoids and study their properties. Finally, by considering a regular equivalence relation on a (g-f)p-hypergroupoid, we define a quotient (g-f)phypergroupoid and we investigate some relationships between diagonal product of hypergroupoids and p-product of (g-f)-hypergraphs.

scholarly journals Transitivity of the εm-relation on (m-idempotent) hyperrings

2018 ◽  
Vol 16 (1) ◽  
pp. 1012-1021 ◽  
Author(s):  
Morteza Norouzi ◽  
Irina Cristea
Keyword(s):  
Equivalence Relation ◽  
Transitive Closure ◽  
Fundamental Relation ◽  
Strongly Regular ◽  
Regular Equivalence ◽  
Quotient Set ◽  
Classical Ring

AbstractOn a general hyperring, there is a fundamental relation, denoted γ*, such that the quotient set is a classical ring. In a previous paper, the authors defined the relation εm on general hyperrings, proving that its transitive closure $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is a strongly regular equivalence relation smaller than the γ*-relation on some classes of hyperrings, such that the associated quotient structure modulo $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is an ordinary ring. Thus, on such hyperrings, $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is a fundamental relation. In this paper, we discuss the transitivity conditions of the εm-relation on hyperrings and m-idempotent hyperrings.

scholarly journals A further study on ordered regular equivalence relations in ordered semihypergroups

2018 ◽  
Vol 16 (1) ◽  
pp. 168-184 ◽  
Author(s):  
Jian Tang ◽  
Xinyang Feng ◽  
Bijan Davvaz ◽  
Xiang-Yun Xie
Keyword(s):  
Equivalence Relation ◽  
Open Problem ◽  
Equivalence Relations ◽  
Ordered Semigroups ◽  
Regular Equivalence

AbstractIn this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208–217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.

Γ∗-Relation on Fuzzy Hyperrings and Fundamental Ring

2021 ◽  
pp. 1-11
Author(s):  
N. Firouzkouhi ◽  
B. Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Fundamental Relation ◽  
Complete Part ◽  
Strongly Regular ◽  
Regular Equivalence ◽  
Fundamental Ring ◽  
Algebraic Hyperstructure

Fundamental relation performs an important role on fuzzy algebraic hyperstructure and is considered as the smallest equivalence relation such that the quotient is a universal algebra. In this paper, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings such that the set of the quotient is a ring that is non-commutative. Also, we introduce the concept of a complete part of a fuzzy hyperring and study its principal traits. At last, we convey the relevance between the fundamental relation and complete parts of a fuzzy hyperring.

An application of PER models to program extraction

1993 ◽  
Vol 3 (3) ◽  
pp. 309-331 ◽  
Author(s):  
Stefano Berardi
Keyword(s):  
Equivalence Relation ◽  
Type Theory ◽  
Lambda Calculus ◽  
Higher Order ◽  
Constructive Proof ◽  
Program Extraction ◽  
Relation Model

Type theory allows us to extract from a constructive proof that a specification is satisfiable a program that satisfies the specification. Algorithms for optimization of such programs are currently the object of research.In this paper we consider one such algorithm, which was described in Beeson (1985) and which we will call ‘Harrop’. This algorithm greatly simplifies programs extracted from proofs in the Pure Construction Calculus. We use a Partial Equivalence Relation model for higher order lambda calculus, to check that t and Harrop(t) return the same outputs from the same inputs, i.e. that they are extensionally equal.As a corollary, we show that it is correct (and, of course, useful) to replace a program t with Harrop(t). Such a correctness result has already been proved by Möhring (Möhring 1989a, 1989b) using realizability semantics, but we obtain it as a corollary of a new result, the extensional equality between t and Harrop(t). Also the semantic method we use is interesting in its own right.

scholarly journals Labelled seeds and the mutation group

2016 ◽  
Vol 163 (2) ◽  
pp. 193-217
Author(s):  
ALASTAIR KING ◽  
MATTHEW PRESSLAND
Keyword(s):  
Automorphism Group ◽  
Homogeneous Space ◽  
Equivalence Relation ◽  
Cluster Algebra ◽  
Equivalence Relations ◽  
Connected Components ◽  
Model Field ◽  
Regular Equivalence ◽  
Mutation Group

AbstractWe study the set${\mathcal{S}}$of labelled seeds of a cluster algebra of rankninside a field${\mathcal{F}}$as a homogeneous space for the groupMnof (globally defined) mutations and relabellings. Regular equivalence relations on${\mathcal{S}}$are associated to subgroupsWof AutMn(${\mathcal{S}}$), and we thus obtain groupoidsW\${\mathcal{S}}$. We show that for two natural choices of equivalence relation, the corresponding groupsWcandW+act on${\mathcal{F}}$, and the groupoidsWc\${\mathcal{S}}$andW+\${\mathcal{S}}$act on the model field${\mathcal{K}}$=ℚ(x1,. . .,xn). The groupoidW+\${\mathcal{S}}$is equivalent to Fock–Goncharov's cluster modular groupoid. Moreover,Wcis isomorphic to the group of cluster automorphisms, andW+to the subgroup of direct cluster automorphisms, in the sense of Assem–Schiffler–Shramchenko.We also prove that, for mutation classes whose seeds have mutation finite quivers, the stabiliser of a labelled seed underMndetermines the quiver of the seed up to ‘similarity’, meaning up to taking opposites of some of the connected components. Consequently, the subgroupWcis the entire automorphism group of${\mathcal{S}}$in these cases.

scholarly journals A Comparison of Complete Parts on m-Idempotent Hyperrings

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 554
Author(s):  
Azam Adineh Zadeh ◽  
Morteza Norouzi ◽  
Irina Cristea
Keyword(s):  
Equivalence Relation ◽  
Quotient Ring ◽  
Transitivity Property ◽  
Strongly Regular ◽  
Regular Equivalence ◽  
Symmetrical Group

On a particular class of m-idempotent hyperrings, the relation ξ m * is the smallest strongly regular equivalence such that the related quotient ring is commutative. Thus, on such hyperrings, ξ m * is a new representation for the α * -relation. In this paper, the ξ m -parts on hyperrings are defined and compared with complete parts, α -parts, and m-complete parts, as generalizations of complete parts in hyperrings. It is also shown how the ξ m -parts help us to study the transitivity property of the ξ m -relation. Finally, ξ m -complete hyperrings are introduced and studied, stressing on the fact that they can be characterized by ξ m -parts. The symmetry plays a fundamental role in this study, since the protagonist is an equivalence relation, defined using also the symmetrical group of permutations of order n.

scholarly journals Cyclic Groups Obtained as Quotient Hypergroups

2015 ◽  
Vol 61 (1) ◽  
pp. 109-122
Author(s):  
S.Sh. Mousavi ◽  
V. Leoreanu-Fotea ◽  
M. Jafarpour
Keyword(s):  
Cyclic Group ◽  
Equivalence Relation ◽  
Cyclic Groups ◽  
Strongly Regular ◽  
Regular Equivalence ◽  
Transitivity Condition

Abstract We introduce a strongly regular equivalence relation ρ*A on the hypergroup H, such that in a particular case the quotient is a cyclic group. Then by using the notion of ρ*A-parts, we investigate the transitivity condition of ρA. Finally, a characterization of the derived hypergroup Dc(H) has been considered.

scholarly journals Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 496 ◽  
Author(s):  
Anam Luqman ◽  
Muhammad Akram ◽  
Ali N. A. Koam
Keyword(s):  
Hierarchical Structure ◽  
Equivalence Relation ◽  
Quotient Space ◽  
Space Structures ◽  
Comparison Analysis ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Fuzzy Hypergraphs ◽  
Different Levels

In this paper, we define q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q-rung picture fuzzy equivalence relation and q-rung picture fuzzy hierarchical quotient space structures. In particular, a q-rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q-rung picture fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of the universal set is more efficient through q-rung picture fuzzy hypergraphs and the q-rung picture fuzzy equivalence relation. We also present an arithmetic example and comparison analysis to signify the superiority and validity of our proposed model.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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