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Symmetry
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Recent Advances in Mathematical Modeling
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Recent Advances in Mathematical Modeling

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (28 February 2022)

Special Issue Editor

Prof. Dr. Basil K. Papadopoulos

E-Mail Website
Guest Editor
Section of Mathematics, Programming and General Courses, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Xanthi, Greece
Interests: engineering models; fuzzy logic; topology; fuzzy artificial intelligence; decision making

Special Issue Information

Dear Colleagues,

Phenomena can be regarded as either random or deterministic ones. Deterministic phenomena can be expressed or approached by mathematical models as differential equations or difference equations, etc. or using numerical analysis methods or fuzzy logic methods.   

We believe that in the topic of engineering modeling, the randomness approach is not the most appropriate. For example, it is not correct to consider the compressive strength of a concrete type as a random variable. We believe that this compressive strength depends on the percentage of water, of cement, of aggregates, etc., to make a certain volume of concrete.

Thus, in such cases as the above, we believe that randomness should be replaced by experience in many cases.

The purpose of this Special Issue of the journal Symmetry is to present some recent developments, as well as possible future directions in mathematical modeling. Special emphasis will be given in engineering modeling using statistical and fuzzy tools.

Papers represented by a mathematical model which could be described by a (fuzzy) difference equation or a (fuzzy) differential equation are also welcome.

Prof. Basil Papadopoulos
Guest Editor

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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • Engineering mathematical modeling
  • Mathematical models using fuzzy logic
  • Models using statistical and probability theory
  • Fuzziness versus probability
  • Hybrid models (probabilistic and fuzzy ones)
  • Fuzzy t-norms
  • fuzzy t-conorms fuzzy implications
  • (Fuzzy) difference equations
  • (fuzzy) differential equations

Published Papers (3 papers)

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Research

16 pages, 687 KiB  
Article
Parametric Fuzzy Implications Produced via Fuzzy Negations with a Case Study in Environmental Variables
by Stefanos Makariadis, Georgios Souliotis and Basil Papadopoulos
Symmetry 2021, 13(3), 509; https://doi.org/10.3390/sym13030509 - 20 Mar 2021
Cited by 7 | Viewed by 1749
Abstract
In this paper, we present a new Fuzzy Implication Generator via Fuzzy Negations which was generated via conical sections, in combination with the well-known Fuzzy Conjunction. The new Fuzzy Implication Generator takes its final forms after being configured by the fuzzy strong negations [...] Read more.
In this paper, we present a new Fuzzy Implication Generator via Fuzzy Negations which was generated via conical sections, in combination with the well-known Fuzzy Conjunction. The new Fuzzy Implication Generator takes its final forms after being configured by the fuzzy strong negations and combined with the most well-known fuzzy conjunctions TM, TP, TLK, TD, and TnM. The final implications that emerge, given that they are configured with the appropriate code, select the best value of the parameter and the best combination of the fuzzy conjunctions. This choice is made after comparing them with the Empiristic implication, which was created with the help of real temperature and humidity data from the Hellenic Meteorological Service. The use of the Empiristic implication is based on real data, and it also reduces the volume of the data without canceling them. Finally, the MATLAB code, which was used in the programming part of the paper, uses the new Fuzzy Implication Generator and approaches the Empiristic implication satisfactorily which is our final goal. Full article
(This article belongs to the Special Issue Recent Advances in Mathematical Modeling)
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21 pages, 336 KiB  
Article
Decision Making for Project Appraisal in Uncertain Environments: A Fuzzy-Possibilistic Approach of the Expanded NPV Method
by Konstantinos A. Chrysafis and Basil K. Papadopoulos
Symmetry 2021, 13(1), 27; https://doi.org/10.3390/sym13010027 - 25 Dec 2020
Cited by 10 | Viewed by 3368
Abstract
The major drawback of the classic approaches for project appraisal is the lack of the possibility to handle change requests during the project’s life cycle. This fact incorporates the concept of uncertainty in the estimation of this investment’s worth. To resolve this issue, [...] Read more.
The major drawback of the classic approaches for project appraisal is the lack of the possibility to handle change requests during the project’s life cycle. This fact incorporates the concept of uncertainty in the estimation of this investment’s worth. To resolve this issue, the authors use fuzzy numbers, possibilistic moments of fuzzy numbers and the hybrid (fuzzy statistic) fuzzy estimators’ method in order to introduce a fuzzy possibilistic version of the expanded net present value method (FPeNPV). This approach consists of two factors: the fuzzy possibilistic NPV and the fuzzy option premium. For the estimation of the fuzzy NPV, some basic assumptions are taken into consideration: (1) the opportunity cost of capital, used as the present value interest factor calculated through the weighted average cost of capital (WACC), (2) the equity cost, determined through the possibilistic set-up of the capital asset pricing model CAPM, and (3) the inflation factor, also included in the estimation of the NPV. The fuzzy estimators’ method is used for the computation of the fuzzy option premium. An algorithm of nine major steps leads to the computation of the FPeNPV. This gives the administration the opportunity to adapt to potential changes in the company’s internal and external environments. In this way, the symmetry between the planning and execution phase of a project can be reinstated. The results validate the statement that fuzzy and intelligent methods remain valuable tools to express uncertainty in various scientific areas. Finally, an illustrative example aims at a thorough comprehension of this new approach of the expanded NPV method. Full article
(This article belongs to the Special Issue Recent Advances in Mathematical Modeling)
11 pages, 1138 KiB  
Article
The Use of Fuzzy Linear Regression and ANFIS Methods to Predict the Compressive Strength of Cement
by Fani Gkountakou and Basil Papadopoulos
Symmetry 2020, 12(8), 1295; https://doi.org/10.3390/sym12081295 - 04 Aug 2020
Cited by 18 | Viewed by 3255
Abstract
In this paper, the prediction of compressive cement strength using the fuzzy linear regression (FLR) and adaptive neuro-fuzzy inference system (ANFIS) methods was studied. Specifically, an accurate prediction method is needed as the modeling of cement strength is a difficult task, which is [...] Read more.
In this paper, the prediction of compressive cement strength using the fuzzy linear regression (FLR) and adaptive neuro-fuzzy inference system (ANFIS) methods was studied. Specifically, an accurate prediction method is needed as the modeling of cement strength is a difficult task, which is based on its composite nature. However, many approaches are widely implemented in strength-predicting problems, such as the artificial neural network (ANN), Mamdani fuzzy rules in MATLAB, FLR and ANFIS models. Applying these methods and comparing the results with the corresponding observed ones, we concluded that the ANFIS method successfully decreased the level of uncertainty in predicting cement strength, as the average percentage error level was extremely low. Although the FLR method had the highest average percentage error level compared with the other methods, it provides a standard equation to estimate the output values by using symmetric triangular fuzzy numbers and determines the most important factor in increasing compressive strength, in contrast to ANFIS and ANN, which are black box models, and to the fuzzy method, which uses rules without providing the specific way by which the results come out. Thus, ANFIS and FLR are appropriate methods for dealing with engineering mathematical models by using fuzzy logic. Full article
(This article belongs to the Special Issue Recent Advances in Mathematical Modeling)
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