Convex structures in a new kind of ordered fuzzy group1

By means of a fuzzy binary operation defined on partially ordered sets, a new kind of ordered fuzzy group is proposed in this paper. Some properties of this ordered fuzzy group are studied. Following that, its substructures, such as subgroup and convex subgroup, as well as its homomorphisms, along with their properties are explored. It is shown that each family of these substructures forms a convex structure, where the convex hull of a subset is exactly the (convex) subgroup generated by itself, and the homomorphisms between two ordered fuzzy groups are convexity-preserving mappings between the corresponding convex spaces. In addition, when these substructures are extended to fuzzy setting, several L-convex structures are constructed and investigated.

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Quadratic Gröbner bases arising from partially ordered sets

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-26246 ◽

2017 ◽

Vol 121 (1) ◽

pp. 19 ◽

Cited By ~ 4

Author(s):

Takayuki Hibi ◽

Kazunori Matsuda ◽

Akiyoshi Tsuchiya

Keyword(s):

Convex Hull ◽

Ordered Set ◽

Convex Polytope ◽

Partially Ordered Sets ◽

Ordered Sets ◽

Toric Ideals ◽

Partially Ordered ◽

Initial Ideals ◽

Order Polytope ◽

Fano Polytope

The order polytope $\mathcal {O}(P)$ and the chain polytope $\mathcal {C}(P)$ associated to a partially ordered set $P$ are studied. In this paper, we introduce the convex polytope $\Gamma (\mathcal {O}(P), -\mathcal {C}(Q))$ which is the convex hull of $\mathcal {O}(P) \cup (-\mathcal {C}(Q))$, where both $P$ and $Q$ are partially ordered sets with $|P|=|Q|=d$. It will be shown that $\Gamma (\mathcal {O}(P), -\mathcal {C}(Q))$ is a normal and Gorenstein Fano polytope by using the theory of reverse lexicographic squarefree initial ideals of toric ideals.

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To the spectral theory of partially ordered sets

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2019.60.308 ◽

2018 ◽

Vol 60 (3) ◽

pp. 578-598

Author(s):

Yu. L. Ershov ◽

M. V. Schwidefsky

Keyword(s):

Spectral Theory ◽

Partially Ordered Sets ◽

Ordered Sets ◽

Partially Ordered

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Modelling Nondeterministic Concurrent Processes with Event Structures

Fundamenta Informaticae ◽

10.3233/fi-1991-14103 ◽

1991 ◽

Vol 14 (1) ◽

pp. 39-73

Author(s):

Rita Loogen ◽

Ursula Goltz

Keyword(s):

Dynamic Behaviour ◽

Partially Ordered Sets ◽

Parallel Composition ◽

Ordered Sets ◽

Communicating Sequential Processes ◽

Partially Ordered ◽

Event Structures ◽

Transition Relation ◽

Concurrent Processes ◽

Sequential Processes

We present a non-interleaving model for non deterministic concurrent processes that is based on labelled event structures. We define operators on labelled event structures like parallel composition, nondeterministic combination, choice, prefixing and hiding. These operators correspond to the operations of the “Theory of Communicating Sequential Processes” (TCSP). Infinite processes are defined using the metric approach. The dynamic behaviour of event structures is defined by a transition relation which describes the execution of partially ordered sets of actions, abstracting from internal events.

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Estimating the area under a receiver operating characteristic curve using partially ordered sets

The International Journal of Biostatistics ◽

10.1515/ijb-2019-0127 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Ehsan Zamanzade ◽

Xinlei Wang

Keyword(s):

Roc Curve ◽

Characteristic Curve ◽

Partially Ordered Sets ◽

Sampling Technique ◽

Real Data ◽

Cost Effective ◽

Ordered Sets ◽

Operating Characteristics ◽

Partially Ordered ◽

Receiver Operating

AbstractRanked set sampling (RSS), known as a cost-effective sampling technique, requires that the ranker gives a complete ranking of the units in each set. Frey (2012) proposed a modification of RSS based on partially ordered sets, referred to as RSS-t in this paper, to allow the ranker to declare ties as much as he/she wishes. We consider the problem of estimating the area under a receiver operating characteristics (ROC) curve using RSS-t samples. The area under the ROC curve (AUC) is commonly used as a measure for the effectiveness of diagnostic markers. We develop six nonparametric estimators of the AUC with/without utilizing tie information based on different approaches. We then compare the estimators using a Monte Carlo simulation and an empirical study with real data from the National Health and Nutrition Examination Survey. The results show that utilizing tie information increases the efficiency of estimating the AUC. Suggestions about when to choose which estimator are also made available to practitioners.

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