http://eiris.it/ojs/index.php/ratiomathematica/issue/feedRatio Mathematica2017-12-29T10:59:15+01:00Fabrizio Maturofabmatu@gmail.comOpen Journal Systems<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>http://eiris.it/ojs/index.php/ratiomathematica/article/view/372On Some Applications of the Vougiouklis Hyperstructures to Probability Theory2017-12-29T10:59:15+01:00Antonio Maturoantomato75@gmail.comFabrizio Maturof.maturo@unich.itSome 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.2017-12-28T21:50:10+01:00Copyright (c) 2017 Antonio Maturo, Fabrizio Maturohttp://eiris.it/ojs/index.php/ratiomathematica/article/view/389An Overview of Topological and Fuzzy Topological Hypergroupoids2017-12-28T23:05:57+01:00Sarka Hosková-Mayerovásarka.mayerova@seznam.czOn 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.2017-12-28T21:50:10+01:00Copyright (c) 2017 Sarka Mayerovahttp://eiris.it/ojs/index.php/ratiomathematica/article/view/391Contributions in Mathematics: Hyperstructures of Professor Thomas Vougiouklis2017-12-28T22:57:02+01:00Violeta Leoreanu - Foteafoteavioleta@gmail.comAfter 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.2017-12-28T21:50:11+01:00Copyright (c) 2017 Violeta Leoreanu - Foteahttp://eiris.it/ojs/index.php/ratiomathematica/article/view/388A Brief Survey on the two Different Approaches of Fundamental Equivalence Relations on Hyperstructures2017-12-28T22:52:42+01:00Nikolaos Antampoufisantanik@otenet.grSarka Hosková-Mayerovásarka.mayerova@seznam.czFundamental 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.2017-12-28T21:50:11+01:00Copyright (c) 2017 Nikolaos Antampoufis, Sarka Mayerovahttp://eiris.it/ojs/index.php/ratiomathematica/article/view/384Some Remarks on Hyperstructures their Connections with Fuzzy Sets and Extensions to Weak Structures2017-12-28T23:08:37+01:00Piergiulio Corsinipiergiuliocorsini@gmail.com<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>2017-12-28T21:50:11+01:00Copyright (c) 2017 Piergiulio Corsinihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/380Vougiouklis Contributions in the Field of Algebraic Hyperstructures2017-12-28T23:10:29+01:00Bijan Davvazdavvaz@yazd.ac.irThomas 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.2017-12-28T21:50:11+01:00Copyright (c) 2017 Bijan Davvazhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/382Special Classes of H_b-Matrices2017-12-28T21:51:19+01:00Achilles Dramalidisadramali@psed.duth.gr<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>2017-12-28T21:50:11+01:00Copyright (c) 2017 Achilles Dramalidishttp://eiris.it/ojs/index.php/ratiomathematica/article/view/381On P-H_v-Structures in a Two-Dimensional Real Vector Space2017-12-28T21:51:18+01:00Ioanna Iliouiiliou@eled.duth.grAchilles Dramalidisadramali@psed.duth.gr<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>2017-12-28T21:50:11+01:00Copyright (c) 2017 Ioanna Iliou and Achilles Dramalidishttp://eiris.it/ojs/index.php/ratiomathematica/article/view/373Finite H_v-Fields with Strong-Inverses2017-12-28T22:57:30+01:00Theodora Kaplanidorakikaplani@gmail.comThomas Vougiouklistvougiou@eled.duth.grThe 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.2017-12-28T21:50:11+01:00Copyright (c) 2017 Theodora Kaplani, Thomas Vougiouklishttp://eiris.it/ojs/index.php/ratiomathematica/article/view/387A Fuzzy Coding Approach to Data Processing Using the Bar2017-12-28T22:57:37+01:00Angelos Markosamarkos@eled.duth.gr<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>2017-12-28T21:50:11+01:00Copyright (c) 2017 Angelos Markoshttp://eiris.it/ojs/index.php/ratiomathematica/article/view/376Multiple Ways of Processing in Questionnaires2017-12-28T21:51:19+01:00Pipina Nikolaidoupnikolai@eled.duth.gr<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>2017-12-28T21:50:11+01:00Copyright (c) 2017 Pipina Nikolaidouhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/374Hyperstructures in Lie-Santilli Admissibility and Iso-Theories2017-12-28T23:12:36+01:00Maria Santilli Ruggeroresearch@i-b-r.orgThomas Vougiouklistvougiou@eled.duth.grIn 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.2017-12-28T21:50:11+01:00Copyright (c) 2017 Maria Santilli Ruggero, Thomas Vougiouklishttp://eiris.it/ojs/index.php/ratiomathematica/article/view/385Helix-Hopes on S-Helix Matrices2017-12-28T21:51:19+01:00Souzana Vougiouklielsouvou@gmail.comThomas Vougiouklistvougiou@eled.duth.grA 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.2017-12-28T21:50:11+01:00Copyright (c) 2017 Souzana Vougioukli, Thomas Vougiouklishttp://eiris.it/ojs/index.php/ratiomathematica/article/view/386H_v-Fields, h/v-Fields2017-12-28T22:58:15+01:00Thomas Vougiouklistvougiou@eled.duth.grLast 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.2017-12-28T21:50:11+01:00Copyright (c) 2017 Thomas Vougiouklis