Axioms

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by Ümit Budak, Yanhui Guo, Abdulkadir Şengür and Florentin Smarandache

Axioms 2017, 6(4), 35; https://doi.org/10.3390/axioms6040035 - 18 Dec 2017

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Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image [...] Read more.

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its shape detection performance, in this paper, we proposed neutrosophic Hough transform (NHT). As it was proved earlier, neutrosophy theory based image processing applications were successful in noisy environments. To this end, the Hough space is initially transferred into the NS domain by calculating the NS membership triples (T, I, and F). An indeterminacy filtering is constructed where the neighborhood information is used in order to remove the indeterminacy in the spatial neighborhood of neutrosophic Hough space. The potential peaks are detected based on thresholding on the neutrosophic Hough space, and these peak locations are then used to detect the lines in the image domain. Extensive experiments on noisy and noise-free images are performed in order to show the efficiency of the proposed NHT algorithm. We also compared our proposed NHT with traditional HT and fuzzy HT methods on variety of images. The obtained results showed the efficiency of the proposed NHT on noisy images. Full article

(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making)

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303 KiB

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On Indistinguishability Operators, Fuzzy Metrics and Modular Metrics

by Juan-José Miñana and Oscar Valero

Axioms 2017, 6(4), 34; https://doi.org/10.3390/axioms6040034 - 15 Dec 2017

Cited by 10 | Viewed by 3099

Abstract

The notion of indistinguishability operator was introduced by Trillas, E. in 1982, with the aim of fuzzifying the crisp notion of equivalence relation. Such operators allow for measuring the similarity between objects when there is a limitation on the accuracy of the performed [...] Read more.

The notion of indistinguishability operator was introduced by Trillas, E. in 1982, with the aim of fuzzifying the crisp notion of equivalence relation. Such operators allow for measuring the similarity between objects when there is a limitation on the accuracy of the performed measurement or a certain degree of similarity can be only determined between the objects being compared. Since Trillas introduced such kind of operators, many authors have studied their properties and applications. In particular, an intensive research line is focused on the metric behavior of indistinguishability operators. Specifically, the existence of a duality between metrics and indistinguishability operators has been explored. In this direction, a technique to generate metrics from indistinguishability operators, and vice versa, has been developed by several authors in the literature. Nowadays, such a measurement of similarity is provided by the so-called fuzzy metrics when the degree of similarity between objects is measured relative to a parameter. The main purpose of this paper is to extend the notion of indistinguishability operator in such a way that the measurements of similarity are relative to a parameter and, thus, classical indistinguishability operators and fuzzy metrics can be retrieved as a particular case. Moreover, we discuss the relationship between the new operators and metrics. Concretely, we prove the existence of a duality between them and the so-called modular metrics, which provide a dissimilarity measurement between objects relative to a parameter. The new duality relationship allows us, on the one hand, to introduce a technique for generating the new indistinguishability operators from modular metrics and vice versa and, on the other hand, to derive, as a consequence, a technique for generating fuzzy metrics from modular metrics and vice versa. Furthermore, we yield examples that illustrate the new results. Full article

(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)

275 KiB

Open AccessArticle

Universal Enveloping Commutative Rota–Baxter Algebras of Pre- and Post-Commutative Algebras

by Vsevolod Gubarev

Axioms 2017, 6(4), 33; https://doi.org/10.3390/axioms6040033 - 07 Dec 2017

Cited by 2 | Viewed by 3083

Abstract

Universal enveloping commutative Rota–Baxter algebras of pre- and post-commutative algebras are constructed. The pair of varieties (RB_λCom, postCom) is proved to be a Poincaré–Birkhoff–Witt-pair (PBW)-pair and the pair (RBCom, preCom) is proven not to be. Full article

(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang–Baxter Equations 2017)

506 KiB

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Factorization of Graded Traces on Nichols Algebras

by Simon Lentner and Andreas Lochmann

Axioms 2017, 6(4), 32; https://doi.org/10.3390/axioms6040032 - 04 Dec 2017

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Abstract

A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of the existence of a root system [...] Read more.

A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of the existence of a root system and a Poincare-Birkhoff-Witt (PBW) basis basis, but, for nondiagonal examples (e.g., Fomin–Kirillov algebras), this is an ongoing surprise. In this article, we discuss this phenomenon and observe that it continues to hold for the graded character of the involved group and for automorphisms. First, we discuss thoroughly the diagonal case. Then, we prove factorization for a large class of nondiagonal Nichols algebras obtained by the folding construction. We conclude empirically by listing all remaining examples, which were in size accessible to the computer algebra system GAP and find that again all graded characters factorize. Full article

(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang–Baxter Equations 2017)

232 KiB

Open AccessArticle

Mild Solutions to the Cauchy Problem for Some Fractional Differential Equations with Delay

by Jin Liang and Yunyi Mu

Axioms 2017, 6(4), 30; https://doi.org/10.3390/axioms6040030 - 20 Nov 2017

Cited by 4 | Viewed by 3381

Abstract

In this paper, we present new existence theorems of mild solutions to Cauchy problem for some fractional differential equations with delay. Our main tools to obtain our results are the theory of analytic semigroups and compact semigroups, the Kuratowski measure of non-compactness, and [...] Read more.

In this paper, we present new existence theorems of mild solutions to Cauchy problem for some fractional differential equations with delay. Our main tools to obtain our results are the theory of analytic semigroups and compact semigroups, the Kuratowski measure of non-compactness, and fixed point theorems, with the help of some estimations. Examples are also given to illustrate the applicability of our results. Full article

(This article belongs to the Special Issue Fractional Differential Equations)

1765 KiB

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A Dynamic Ticket Pricing Approach for Soccer Games

by Mehmet Şahin and Rızvan Erol

Axioms 2017, 6(4), 31; https://doi.org/10.3390/axioms6040031 - 19 Nov 2017

Cited by 6 | Viewed by 8494

Abstract

This study proposes a mathematical model of dynamic pricing for soccer game tickets. The logic behind the dynamic ticket pricing model is price change based on multipliers which reflect the effects of time and inventory. Functions are formed for the time and inventory [...] Read more.

This study proposes a mathematical model of dynamic pricing for soccer game tickets. The logic behind the dynamic ticket pricing model is price change based on multipliers which reflect the effects of time and inventory. Functions are formed for the time and inventory multipliers. The optimization algorithm attempts to find optimal values of these multipliers in order to maximize revenue. By multiplying the mean season ticket price (used as the reference price) by the multipliers, dynamic ticket prices are obtained. Demand rates at different prices are needed for the model, and they are provided by a unique fuzzy logic model. The results of this model are compared with real data to test the model’s effectiveness. According to the results of the dynamic pricing model, the total revenue generated is increased by 8.95% and 0.76% compared with the static pricing strategy in the first and second cases, respectively. The results of the fuzzy logic model are also found to be competitive and effective. This is the first time a fuzzy logic model has been designed to forecast the attendance of soccer games. It is also the first time this type of mathematical model of dynamic pricing for soccer game tickets has been designed. Full article

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262 KiB

Open AccessArticle

Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness

by Paolo Bevilacqua, Gianni Bosi and Magalì Zuanon

Axioms 2017, 6(4), 29; https://doi.org/10.3390/axioms6040029 - 28 Oct 2017

Cited by 4 | Viewed by 3325

Abstract

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy [...] Read more.

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space. Full article

(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)

324 KiB

Open AccessArticle

Large Sets in Boolean and Non-Boolean Groups and Topology

by Ol’ga V. Sipacheva

Axioms 2017, 6(4), 28; https://doi.org/10.3390/axioms6040028 - 24 Oct 2017

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Abstract

Various notions of large sets in groups, including the classical notions of thick, syndetic, and piecewise syndetic sets and the new notion of vast sets in groups, are studied with emphasis on the interplay between such sets in Boolean groups. Natural topologies closely [...] Read more.

Various notions of large sets in groups, including the classical notions of thick, syndetic, and piecewise syndetic sets and the new notion of vast sets in groups, are studied with emphasis on the interplay between such sets in Boolean groups. Natural topologies closely related to vast sets are considered; as a byproduct, interesting relations between vast sets and ultrafilters are revealed. Full article

(This article belongs to the Collection Topological Groups)

299 KiB

Open AccessArticle

Computing the Scale of an Endomorphism of a totally Disconnected Locally Compact Group

by George A. Willis

Axioms 2017, 6(4), 27; https://doi.org/10.3390/axioms6040027 - 20 Oct 2017

Cited by 1 | Viewed by 4584

Abstract

The scale of an endomorphism of a totally disconnected, locally compact group G is defined and an example is presented which shows that the scale function is not always continuous with respect to the Braconnier topology on the automorphism group of G. [...] Read more.

The scale of an endomorphism of a totally disconnected, locally compact group G is defined and an example is presented which shows that the scale function is not always continuous with respect to the Braconnier topology on the automorphism group of G. Methods for computing the scale, which is a positive integer, are surveyed and illustrated by applying them in diverse cases, including when G is compact; an automorphism group of a tree; Neretin’s group of almost automorphisms of a tree; and a p-adic Lie group. The information required to compute the scale is reviewed from the perspective of the, as yet incomplete, general theory of totally disconnected, locally compact groups. Full article

(This article belongs to the Collection Topological Groups)

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Axioms, Volume 6, Issue 4 (December 2017) – 9 articles

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