Reviews in Mathematics and Applications

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 5249

Special Issue Editors


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Facultade de Matemáticas, Campus Vida, 15782 Santiago de Compostela, Galicia, Spain
Interests: ordinary differential equations; boundary value problems; Green's functions; comparison results; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals

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School of Computer Science and Informatics, De Montfort University, The Gateway, Leicester LE1 9BH, UK
Interests: fuzzy decision making; fuzzy preference modeling; decision support systems; consensus; recommender systems; social networks; rationality/consistency; aggregation; type-2 fuzzy logic; opinion dynamics; trust propagation
Special Issues, Collections and Topics in MDPI journals

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Special Issue Information

Dear Colleagues,

Mathematics is called the language of science because it is pervasive in almost all applied sciences, from physics and engineering to economy, biology, medicine, and even art and social studies.

This Special Issue aims to be a solid ground for attracting contributions reviewing all areas of mathematics and its applications, focusing on presenting recent advances in a systematic form. The Special Issue intends to include a series of publications that report on the latest mathematical research in a synthetic way for scientists, mathematicians, and non-mathematicians. Therefore, it is of particular importance to establish a good balance between well-known theories available in textbooks, and front-end, ongoing research with volatile, or not yet systematic, conclusions. Contributions are expected not only to include the comprehensive treatment of the fundamentals but also to have a special focus on the newest developments. Applications in present-day science are also of utmost importance, where multidisciplinary and interdisciplinary issues play a major role in gathering the synergies of distinct tools and perspectives. Cross-field review contributions with a solid mathematical background establishing bridges between different areas of knowledge are also of key relevance for supporting further progress in mathematics and its applications.

Prof. Dr. Alberto Cabada
Prof. Dr. Francisco Chiclana
Prof. Dr. Sergei Petrovskii
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • algebraic geometry
  • algebraic topology
  • analysis of PDEs
  • category theory
  • classical analysis and ODEs
  • combinatorics
  • commutative algebra
  • complex variables
  • differential geometry
  • dynamical systems
  • functional analysis
  • general mathematics
  • general topology
  • geometric topology
  • group theory
  • history and overview
  • information theory
  • K-theory and homology
  • logic
  • mathematical physics
  • metric geometry
  • number theory
  • numerical analysis
  • operator algebras
  • optimization and control
  • probability
  • quantum algebra
  • representation theory
  • rings and algebras
  • spectral theory
  • statistics theory
  • symplectic geometry
  • geometric analysis
  • variational problems
  • mathematical finance
  • harmonic analysis
  • computer science
  • quantum theory
  • mathematical and computational biology
  • fuzzy mathematic (theory and applications)
  • fuzzy logic
  • fuzzy decision making
  • mathematical ecology
  • population dynamics
  • pattern formation
  • diffusion
  • reaction waves
  • food webs and networks
  • random walks and animal movement
  • anomalous diffusion and levy flights

Published Papers (3 papers)

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Review

17 pages, 315 KiB  
Review
A Survey on the Theory of n-Hypergroups
by Bijan Davvaz, Violeta Leoreanu-Fotea and Thomas Vougiouklis
Mathematics 2023, 11(3), 551; https://doi.org/10.3390/math11030551 - 19 Jan 2023
Cited by 1 | Viewed by 1116
Abstract
This paper presents a series of important results from the theory of n-hypergroups. Connections with binary relations and with lattices are presented. Special attention is paid to the fundamental relation and to the commutative fundamental relation. In particular, join n-spaces are analyzed. Full article
(This article belongs to the Special Issue Reviews in Mathematics and Applications)
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20 pages, 419 KiB  
Review
Knowledge Gradient: Capturing Value of Information in Iterative Decisions under Uncertainty
by Donghun Lee
Mathematics 2022, 10(23), 4527; https://doi.org/10.3390/math10234527 - 30 Nov 2022
Cited by 1 | Viewed by 1867
Abstract
Many real-life problems that involve decisions under uncertainty are often sequentially repeated and can be approached iteratively. Knowledge Gradient (KG) formulates the decision-under-uncertainty problem into repeatedly estimating the value of information observed from each possible decisions and then committing to a decision with [...] Read more.
Many real-life problems that involve decisions under uncertainty are often sequentially repeated and can be approached iteratively. Knowledge Gradient (KG) formulates the decision-under-uncertainty problem into repeatedly estimating the value of information observed from each possible decisions and then committing to a decision with the highest estimated value. This paper aims to provide a multi-faceted overview of modern research on KG: firstly, on how the KG algorithm is formulated in the beginning with an example implementation of its most frequently used implementation; secondly, on how KG algorithms are related to other problems and iterative algorithms, in particular, Bayesian optimization; thirdly, on the significant trends found in modern theoretical research on KG; lastly, on the diverse examples of applications that use KG in their key decision-making step. Full article
(This article belongs to the Special Issue Reviews in Mathematics and Applications)
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17 pages, 337 KiB  
Review
Functional Representation of the Intentional Bounded Rationality of Decision-Makers: A Laboratory to Study the Decisions a Priori
by Carlos Sáenz-Royo, Francisco Chiclana and Enrique Herrera-Viedma
Mathematics 2022, 10(5), 739; https://doi.org/10.3390/math10050739 - 26 Feb 2022
Cited by 9 | Viewed by 1894
Abstract
The judgments of decision-makers are frequently the best way to process the information on complex alternatives. However, the performances of the alternatives are often not observable in their entirety, which prevents researchers from conducting controlled empirical studies. This paper justifies a functional representation [...] Read more.
The judgments of decision-makers are frequently the best way to process the information on complex alternatives. However, the performances of the alternatives are often not observable in their entirety, which prevents researchers from conducting controlled empirical studies. This paper justifies a functional representation that, due to its good predictive results, has been widely used ad hoc in studies in different branches of knowledge; it formalizes aspects of the human mental structure that influence the ability of people to decide and the intentional bounded rationality, and it subsequently analyzes how the reliability of decision-makers is affected by the difficulty of the problem and the expertise and beliefs of the decision-maker. The main research objective of this paper is to derive explicitly a general functional form that represents the behavior of a decision-maker linked to their way of thinking. This functional form allows a laboratory to be created to study a priori the performance of human decisions, i.e., the probability of choosing each of the alternatives, once the returns of the alternatives, the level of expertise, and the initial beliefs of the decision-maker are known exogenously. This laboratory will allow (1) the evaluation of decision support techniques; (2) the creation of agent-based models that anticipate group performances due to individual interactions; and (3) the development of other investigations based on statistical simulations. Full article
(This article belongs to the Special Issue Reviews in Mathematics and Applications)
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