Ratio Mathematica
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<p><strong>RATIO MATHEMATICA - JOURNAL OF MATHEMATICS, STATISTICS, AND APPLICATIONS</strong></p><p>Ratio Mathematica is an International, double peer-reviewed, open access journal, published every six months (June-December). This periodical has a long tradition, indeed its first issue was published in 1990. It aims to publish original research articles in the fields of Mathematics and Statistics. However, contributions with applications of Mathematics and Statistics to Social Science, Business Administration, Engineering, Programming, Economics, Management, Fuzzy Logic, and Probability, are welcome. Only English-language publications are accepted. </p><p>The main topics of interest for Ratio Mathematica are:</p><p><strong>Foundations of Mathematics:</strong> Epistemology of Mathematics, Critique of the Foundations of Mathematics, Elementary Mathematics from a higher point of view, Elementary Theory of Numbers, Foundations of Mathematics of Uncertain; Criticism of the Foundations of Computer Science.</p><p><strong>Applications of Mathematics:</strong> Applications to Engineering and Economics, Applications for Management and Business Administration, Decision making in conditions of uncertainty, Theory of Games, Fuzzy Logic and Applications, Probability, Statistics and Applications.</p><p><strong>New theories and applications:</strong> Algebraic hyperstructures and Applications, Discrete Mathematics and Applications, Fuzzy structures.</p><p><strong>New theories and practices for dissemination and communication of mathematics:</strong> Communication of History and Fundations, Communication of Discrete Mathematics, Communication of Probability and Statistics, Communication with Media.</p><p> </p><p><strong>Indexing</strong>: Ratio Mathematica is abstracted and indexed in: </p><p><a title="DOAJ" href="https://doaj.org/toc/2282-8214?source=%7B%22query%22%3A%7B%22filtered%22%3A%7B%22filter%22%3A%7B%22bool%22%3A%7B%22must%22%3A%5B%7B%22term%22%3A%7B%22index.issn.exact%22%3A%222282-8214%22%7D%7D%2C%7B%22term%22%3A%7B%22_type%22%3A%22article%22%7D%7D%5D%7D%7D%2C%22query%22%3A%7B%22match_all%22%3A%7B%7D%7D%7D%7D%2C%22sort%22%3A%5B%7B%22bibjson.year.exact%22%3A%7B%22order%22%3A%22desc%22%7D%7D%2C%7B%22bibjson.month.exact%22%3A%7B%22order%22%3A%22desc%22%7D%7D%5D%2C%22from%22%3A0%2C%22size%22%3A100%7D" target="_blank">DOAJ</a></p><p><a href="https://zbmath.org/journals/?s=0&q=ratio+mathematica">zbMATH</a></p><p><a href="http://index.pkp.sfu.ca/index.php/browse/index/1071?sortOrderId=6">PKP (Public Knowledge Project)</a></p><p><a href="https://www.worldcat.org/">OCLC WorldCat</a></p><p><a href="https://scholar.google.it/scholar?hl=it&q=+Ratio+Mathematica&btnG=&lr=">Google Scholar</a></p><p><a href="http://agriculture.academickeys.com/jour_main.php">AcademicKeys</a></p><p><a href="http://journalseek.net/cgi-bin/journalseek/journalsearch.cgi?field=issn&query=1592-7415">Genamics</a></p><p><a href="http://www.journaltocs.ac.uk/index.php?action=search&subAction=hits&journalID=37603&userQueryID=8709&high=1&ps=30&page=1&items=0&journal_filter=&journalby=">JournalTOCs</a></p><p><a href="http://acnp.unibo.it/cgi-ser/start/it/cnr/df-p.tcl?catno=2401374&libr=&person=false&B=2&proposto=NO&year_poss_from=&year_poss_to=">ANCP</a></p><p><a href="http://www.sbn.it/opacsbn/opac/iccu/free.jsp">OPAC SBN</a></p><p><a href="http://www.proquest.com/">PROQUEST</a></p><p>The printed copies of the journal are stored at the <strong>National Library of Florence</strong> and <strong>Provincial Library of Pescara, Italy</strong>.</p><p> </p><p> </p><p><strong>Publish or Perish Statistics </strong></p><p>## "Ratio Mathematica" ##</p><p>Publish or Perish 6.21.6145.6594</p><p>### Search terms ###</p><p>Publication/Journal: "Ratio Mathematica"<br />Years: all</p><p><br />### Data retrieval ###</p><p>Data source: Google Scholar<br />Query date: dom 28 gen 2018 07:52:36<br />Cache date: gio 25 gen 2018 08:03:23<br />Query result: [0] Operazione completata.</p><p><br />### Metrics ###</p><p>Publication years: 1990-2017<br />Citation years: 28 (1990-2018)<br />Papers: 276<br />Citations: 544<br />Citations/year: 19.43<br />Citations/paper: 1.97<br />Citations/author: 369.58<br />Papers/author: 192.00<br />Authors/paper: 1.73/2.0/1 (mean/median/mode)<br />Age-weighed citation rate: 61.33 (sqrt=7.83), 38.97/author<br />Hirsch h-index: 11 (a=4.50, m=0.39, 215 cites=39.5% coverage)<br />Egghe g-index: 16 (g/h=1.45, 266 cites=48.9% coverage)<br />PoP hI,norm: 9<br />PoP hI,annual: 0.32</p>en-US<p>This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:</p><ul><li>Free access for all users worldwide</li><li>Increased visibility and readership</li><li>Rapid publication</li><li>No spatial constraints</li><li>Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)</li></ul><h2>Copyright and Licensing Terms</h2><p>Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. <br />For further information visit: <a href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</a>. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards:</p><p><img id="__wp-temp-img-id" title="" src="http://www.eiris.it/ratio_numeri/ratio_accessori/cc.png" alt="Creative Commonce Licence" width="88" height="31" /></p>fabmatu@gmail.com (Fabrizio Maturo)fabmatu@gmail.com (Fabrizio Maturo)Thu, 28 Dec 2017 21:50:11 +0100OJS 2.4.8.1http://blogs.law.harvard.edu/tech/rss60On Some Applications of the Vougiouklis Hyperstructures to Probability Theory
http://eiris.it/ojs/index.php/ratiomathematica/article/view/372
Some important concepts about algebraic hyperstructures, especially from a geometric point of view, are recalled. Many applications of the Hv structures, introduced by Vougiouklis in 1990, to the de Finetti subjective probability theory are considered. We show how the wealth of probabilistic meanings of Hv-structures confirms the importance of the theoretical results obtained by Vougiouklis. Such results can be very meaningful also in many application fields, such as decision theory, highly dependent on subjective probability.Antonio Maturo, Fabrizio Maturo
Copyright (c) 2017 Antonio Maturo, Fabrizio Maturo
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/372Thu, 28 Dec 2017 21:50:10 +0100An Overview of Topological and Fuzzy Topological Hypergroupoids
http://eiris.it/ojs/index.php/ratiomathematica/article/view/389
On a hypergroup, one can define a topology such that the hyperoperation is pseudocontinuous or continuous.<br />This concepts can be extend to the fuzzy case and a connection between the classical and the fuzzy (pseudo)continuous hyperoperations can be given.<br />This paper, that is his an overview of results received by S. Hoskova-Mayerova with coauthors I. Cristea , M. Tahere and B. Davaz, gives examples of topological hypergroupoids and show that there is no relation (in general) between pseudotopological and strongly pseudotopological hypergroupoids. In particular, it shows a topological hypergroupoid that does not depend on the pseudocontinuity nor on strongly pseudocontinuity of the hyperoperation.Sarka Hosková-Mayerová
Copyright (c) 2017 Sarka Mayerova
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/389Thu, 28 Dec 2017 21:50:10 +0100Contributions in Mathematics: Hyperstructures of Professor Thomas Vougiouklis
http://eiris.it/ojs/index.php/ratiomathematica/article/view/391
After presenting some basic notions of hyperstructures and their applications, I shall point out on the contribution of Professor Thomas Vougiouklis to this field of research: algebraic hyperstructures.Violeta Leoreanu - Fotea
Copyright (c) 2017 Violeta Leoreanu - Fotea
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/391Thu, 28 Dec 2017 21:50:11 +0100A Brief Survey on the two Different Approaches of Fundamental Equivalence Relations on Hyperstructures
http://eiris.it/ojs/index.php/ratiomathematica/article/view/388
Fundamental structures are the main tools in the study of hyperstructures. Fundamental equivalence relations link hyperstructure theory to the theory of corresponding classical structures. They also introduce new hyperstructure classes.The present paper is a brief reference to the two different approaches to the notion of the fundamental relation in hyperstructures. The first one belongs to Koskas, who introduced the β ∗ - relation in hyperstructures and the second approach to Vougiouklis, who gave the name fundamental to the resulting quotient sets. The two approaches, the necessary definitions and the theorems for the introduction of the fundamental equivalence relation in hyperstructures, are presented.Nikolaos Antampoufis, Sarka Hosková-Mayerová
Copyright (c) 2017 Nikolaos Antampoufis, Sarka Mayerova
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/388Thu, 28 Dec 2017 21:50:11 +0100Some Remarks on Hyperstructures their Connections with Fuzzy Sets and Extensions to Weak Structures
http://eiris.it/ojs/index.php/ratiomathematica/article/view/384
<p>A brief excursus on the last results on Hyperstructures and their connections with Fuzzy Sets. At the end a calculation of the Fuzzy Grade of Hv-structures of order two.</p>Piergiulio Corsini
Copyright (c) 2017 Piergiulio Corsini
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/384Thu, 28 Dec 2017 21:50:11 +0100Vougiouklis Contributions in the Field of Algebraic Hyperstructures
http://eiris.it/ojs/index.php/ratiomathematica/article/view/380
Thomas Vougiouklis was born in 1948, Greece. He has many contributions to algebraic hyperstructures. $H_v$-structures are some of his main contributions. In this article, we study some of Vougiouklis ideas in the field of algebraic hyperstructures as follows: (1) Semi-direct hyperproduct of two hypergroups; (2) Representation of hypergroups; (3) Fundamental relation in hyperrings; (4) Commutative rings obtained from hyperrings; (5) $H_v$-structures; (6) The uniting elements method; (7) The e-hyperstructures;<br />(8) Helix-hyperoperations.Bijan Davvaz
Copyright (c) 2017 Bijan Davvaz
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/380Thu, 28 Dec 2017 21:50:11 +0100Special Classes of H_b-Matrices
http://eiris.it/ojs/index.php/ratiomathematica/article/view/382
<p>In the present paper we deal with constructions of 2x2 diagonal or upper-triangular or lower-triangular H<sub>b</sub>-matrices with entries either of an H<sub>b</sub>-field on ℤ<sub>2</sub> or on ℤ<sub>3</sub>. We study the kind of the hyperstructures that arise, their unit and inverse elements. Also, we focus our study on the cyclicity of these hyperstructures, their generators and the respective periods.</p>Achilles Dramalidis
Copyright (c) 2017 Achilles Dramalidis
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/382Thu, 28 Dec 2017 21:50:11 +0100On P-H_v-Structures in a Two-Dimensional Real Vector Space
http://eiris.it/ojs/index.php/ratiomathematica/article/view/381
<p>In this paper we study P-H<sub>v</sub>-structures in connection with H<sub>v</sub>-structures, arising from a specific P-hope in a two-dimensional real vector space. The visualization of these P-H<sub>v</sub>-structures is our priority, since visual thinking could be an alternative and powerful resource for people doing mathematics. Using position vectors into the plane, abstract algebraic properties of these P-H<sub>v</sub>-structures are gradually transformed into geometrical shapes, which operate, not only as a translation of the algebraic concept, but also, as a teaching process. </p>Ioanna Iliou, Achilles Dramalidis
Copyright (c) 2017 Ioanna Iliou and Achilles Dramalidis
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/381Thu, 28 Dec 2017 21:50:11 +0100Finite H_v-Fields with Strong-Inverses
http://eiris.it/ojs/index.php/ratiomathematica/article/view/373
The largest class of hyperstructures is the class of H v -structures. This is the class of hyperstructures where the equality is replaced by the non-empty intersection. This extremely large class can used to define several objects that they are not possible to be defined in the classical hypergroup theory. It is convenient, in applications, to use more axioms and conditions to restrict the research in smaller classes. In this direction, in the present paper we continue our study on H v -structures which have strong-inverse elements. More precisely we study the small finite cases.Theodora Kaplani, Thomas Vougiouklis
Copyright (c) 2017 Theodora Kaplani, Thomas Vougiouklis
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/373Thu, 28 Dec 2017 21:50:11 +0100A Fuzzy Coding Approach to Data Processing Using the Bar
http://eiris.it/ojs/index.php/ratiomathematica/article/view/387
<p>The bar is an alternative to Likert-type scale as a response format option used in closed-form questionnaires. An important advantage of using the bar is that it provides a variety of data post-processing options (i.e., ways of partitioning the values of a continuous variable into discrete groups). In this context, continuous variables are usually divided into equal-length or equalarea intervals according to a user-specified distribution (e.g. the Gaussian). However, this transition from continuous into discrete can lead to a significant loss of information. In this work, we present a fuzzy coding of the original variables which exploits linear and invertible triangular membership functions. The proposed coding scheme retains all of the information in the data and can be naturally combined with an exploratory data analysis tech<br />nique, Correspondence Analysis, in order to visually investigate both linear and non-linear variable associations. The proposed approach is illustrated with a real-world application to a student course evaluation dataset.</p>Angelos Markos
Copyright (c) 2017 Angelos Markos
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/387Thu, 28 Dec 2017 21:50:11 +0100Multiple Ways of Processing in Questionnaires
http://eiris.it/ojs/index.php/ratiomathematica/article/view/376
<p>In social sciences when questionnaires are used, there is a new tool, the bar instead of Likert scale. The bar has been suggested by Vougiouklis & Vougiouklis in 2008, who have proposed the replacement of Likert scales, usually used in questionnaires, with bar. This new tool, gives the opportunity to researchers to elaborate the questionnaires in different ways, depending on the filled questionnaires and of course on the problem. Moreover, we improve the procedure of the filling the questionnaires, using the bar instead of<br />Likert scale, on computers where we write down automatically the results, so they are ready for research. This new kind of elaboration is being applied on data obtained by a survey, studying the new results. The hyperstructure theory is being related with questionnaires and we study the obtained hyperstructures,<br />which are used as an organized device of the problem and we focus on special problems.</p>Pipina Nikolaidou
Copyright (c) 2017 Pipina Nikolaidou
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/376Thu, 28 Dec 2017 21:50:11 +0100Hyperstructures in Lie-Santilli Admissibility and Iso-Theories
http://eiris.it/ojs/index.php/ratiomathematica/article/view/374
In the quiver of hyperstructures Professor R. M. Santilli, in early 90'es, tried to find algebraic structures in order to express his pioneer Lie-Santilli's Theory. Santilli's theory on 'isotopies' and 'genotopies', born in 1960's, desperately needs 'units e' on left or right, which are nowhere singular, symmetric, real-valued, positive-defined for n-dimensional matrices based on the so called isofields.These elements can be found in hyperstructure theory, especially in $H_v$-structure theory introduced in 1990. This connection appeared first in 1996 and actually several $H_v$-fields, the e-hyperfields, can be used as isofields or genofields so as, in such way they should cover additional properties and satisfy more restrictions. Several large classes of hyperstructures as the P-hyperfields, can be used in Lie-Santilli's theory when multivalued problems appeared, either in finite or in infinite case. We review some of these topics and we present the Lie-Santilli admissibility in Hyperstructures.Maria Santilli Ruggero, Thomas Vougiouklis
Copyright (c) 2017 Maria Santilli Ruggero, Thomas Vougiouklis
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/374Thu, 28 Dec 2017 21:50:11 +0100Helix-Hopes on S-Helix Matrices
http://eiris.it/ojs/index.php/ratiomathematica/article/view/385
A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. The main characteristic of the helix-hyperoperation is that all entries of the matrices are used. Such operations<br />cannot be defined in the classical theory. Several classes of non-square matrices have results of the helix-product with small cardinality. We study the helix-hyperstructures on the representations and we extend our study up to Lie-H_v theory by using ordinary fields. We introduce and study the class of S-helix matrices.Souzana Vougioukli, Thomas Vougiouklis
Copyright (c) 2017 Souzana Vougioukli, Thomas Vougiouklis
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/385Thu, 28 Dec 2017 21:50:11 +0100H_v-Fields, h/v-Fields
http://eiris.it/ojs/index.php/ratiomathematica/article/view/386
Last decades the hyperstructures have a lot of applications in mathematics and in other sciences. These applications range from biomathematics and hadronic physics to linguistic and sociology. For applications the largest class of the hyperstructures, the H v -structures, is used, they satisfy the weak axioms where the non-empty intersection replaces the equality. The main tools in the theory of hyperstructures are the fundamental relations which connect, by quotients, the H v -structures with the corresponding classical ones. These relations are used to define hyperstructures as H v -fields, H_v-vector spaces and so on, as well. The extension of the reproduction axiom, from elements to fundamental classes, introduces the extension of H_v-structures to the class of h/v-structures. We focus our study mainly in the relation of these classes and we present some constructions on them.Thomas Vougiouklis
Copyright (c) 2017 Thomas Vougiouklis
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http://eiris.it/ojs/index.php/ratiomathematica/article/view/386Thu, 28 Dec 2017 21:50:11 +0100