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Mathematics
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Modelling of Parallel Processes under Intuitionistic Fuzzy Uncertainty
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Modelling of Parallel Processes under Intuitionistic Fuzzy Uncertainty

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (1 March 2023) | Viewed by 8193

Special Issue Editor

Dr. Veselina Bureva

E-Mail Website
Guest Editor
Laboratory of Intelligent Systems, Assen Zlatarov University, 8010 Burgas, Bulgaria
Interests: artificial intelligence; big data; data mining; intuitionistic fuzzy sets; index matrices; generalized nets

Special Issue Information

Dear Colleagues,

This Special Issue aims to present the recent studies in parallel processes modelling under intuitionistic fuzzy uncertainty. The modelling tools include—but are not limited to—the apparatus of Generalized Nets (GN) introduced by Prof. Krassimir Atanassov as an extension of Petri nets. Generalized net modelling is used in many scientific fields as medicine, bioinformatics, data mining (classification, cluster analysis, association rules mining, neural networks, genetic algorithms), pattern recognition, biometrics, economic, transport, telecommunications, etc. The GN models can use intuitionistic fuzzy logic to overcome the challenges related to uncertainty. In these models, the intuitionistic fuzzy evaluations estimate the degrees of membership, non-membership and uncertainty. Intuitionistic fuzzy sets (IFS) theory was introduced by Prof. Krassimir Atanassov in 1983 as an extension of fuzzy sets. The intuitionistic fuzzy sets and their extensions (interval-valued intuitionistic fuzzy sets, temporal intuitionistic fuzzy sets, etc.) are applied successfully in the area of decision making. IFS are a tool that is used in a new decision making method, “InterCriteria Analysis (ICA)”, which provides the opportunity for decision making estimation of multiple objects by multiple criteria. The application of ICA can be found in the fields of medicine, chemistry, university rankings, economics, etc.

Subject areas covered are listed, but not limited, to those below:

  • Generalized nets and their extensions (IFGN);
  • Intuitionistic fuzzy logic;
  • Intuitionistic fuzzy sets and their extensions—theory and applications;
  • Intuitionistic fuzzy estimations;
  • Modelling of parallel processes under intuitionistic fuzzy uncertainty in data mining, artificial intelligence, optimization methods, bioinformatics, decision making methods, pattern recognition, etc.;
  • Decision theory and optimization methods under intuitionistic fuzzy uncertainty;
  • InterCriteria analysis and its extensions (InterCriteria analysis over intuitionistic fuzzy data, Three-Dimensional ICA, ICA with triples, Interval-Valued ICA).

For this Special Issue, the authors are invited to publish their new theories, concepts or applications related to the modelling of parallel processes under intuitionistic fuzzy uncertainty. The studies can present new research works in the area of generalized nets, intuitionistic fuzzy sets and other concepts related to them.

Dr. Veselina Bureva
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. 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

  • Generalized nets (Intuitionistic Fuzzy Generalized Nets)
  • Intuitionistic fuzzy logic
  • Intuitionistic fuzzy sets
  • Interval-valued intuitionistic fuzzy sets
  • Intuitionistic fuzzy estimations
  • Modelling of parallel processes under intuitionistic fuzzy uncertainty
  • InterCriteria Analysis

Published Papers (6 papers)

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Research

13 pages, 361 KiB  
Article
Two Approaches to the Traffic Quality Intuitionistic Fuzzy Estimation of Service Compositions
by Stoyan Poryazov, Velin Andonov, Emiliya Saranova and Krassimir Atanassov
Mathematics 2022, 10(23), 4439; https://doi.org/10.3390/math10234439 - 24 Nov 2022
Cited by 11 | Viewed by 948
Abstract
Recently, intuitionistic fuzzy pairs have been used as uncertainty estimations of the request services in service systems. In the present paper, three intuitionistic fuzzy characterizations of virtual service devices are specified: intuitionistic fuzzy traffic estimation, intuitionistic fuzzy flow estimation and intuitionistic fuzzy estimation [...] Read more.
Recently, intuitionistic fuzzy pairs have been used as uncertainty estimations of the request services in service systems. In the present paper, three intuitionistic fuzzy characterizations of virtual service devices are specified: intuitionistic fuzzy traffic estimation, intuitionistic fuzzy flow estimation and intuitionistic fuzzy estimation about probability. Discussed herein are two approaches to the intuitionistic fuzzy estimation of the uncertainty of compositions of services. One of the approaches is based on the definitions of the intuitionistic fuzzy pairs for one service device. The other approach is based on the aggregation operators over intuitionistic fuzzy pairs. A total of six intuitionistic fuzzy estimations of the uncertainty of comprise service device are proposed. The proposed uncertainty estimations allow for the definition of new Quality of Service (QoS) indicators and can be used to determine the quality of service compositions across a wide range of service systems. Full article
(This article belongs to the Special Issue Modelling of Parallel Processes under Intuitionistic Fuzzy Uncertainty)
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17 pages, 2558 KiB  
Article
Application of InterCriteria Analysis to Assess the Performance of Scoring Functions in Molecular Docking Software Packages
by Dessislava Jereva, Petko Alov, Ivanka Tsakovska, Maria Angelova, Vassia Atanassova, Peter Vassilev, Nikolay Ikonomov, Krassimir Atanassov, Ilza Pajeva and Tania Pencheva
Mathematics 2022, 10(15), 2549; https://doi.org/10.3390/math10152549 - 22 Jul 2022
Cited by 5 | Viewed by 1504
Abstract
(1) Background: In silico approaches to rational drug design are among the fastest evolving ones. Depending on the available structural information for the biomacromolecule and the small molecule, the in silico methods are classified as ligand- and structure-based. The latter predict ligand–receptor binding [...] Read more.
(1) Background: In silico approaches to rational drug design are among the fastest evolving ones. Depending on the available structural information for the biomacromolecule and the small molecule, the in silico methods are classified as ligand- and structure-based. The latter predict ligand–receptor binding using 3D structures of both molecules, whose computational simulation is referred to as molecular docking. It aims at estimating the binding affinity (approximated by scoring function) and the ligand binding pose in the receptor’s active site, which postulates a key role of the scoring functions in molecular docking algorithms. This study focuses on the performance of different types of scoring functions implemented in molecular modelling software packages. (2) Methods: An InterCriteria analysis (ICrA) was applied to assess the performance of the scoring functions available in MOE, GOLD, SeeSAR, and AutoDock Vina software platforms. The InterCriteria analysis was developed to distinguish possible relations between pairs of criteria when multiple objects are considered. All 12 investigated scoring functions were tested by docking a set of protease inhibitors in the binding sites of two protein targets. The dataset consisted of 88 benzamidine-type compounds with experimentally measured inhibitory constants for thrombin and trypsin, which allows for the objective assessment of the scoring functions performance. The results generated by the molecular docking were subjected to ICrA in order to analyze both docking energies as approximations of the binding affinities and RMSDs (root-mean-square deviation) as measures of the experimental binding pose proximity between the compounds and the co-crystalized ligand, based on the atoms in the common scaffold. (3) Results: The results obtained for the best poses, the average of the best 5 or 30 poses retained after docking, were analyzed. A comparison with the experimentally observed inhibitory effects was also performed. The InterCriteria analysis application confirms that the performance of the scoring functions for the same dataset of ligands depends on the studied protein. The analysis reveals that none of the studied scoring functions is a good predictor of the compounds’ binding affinities for the considered protein targets. (4) Conclusion: In terms of this analysis, the investigated scoring functions do not produce equivalent results, which suggests the necessity for their combined use in consensus docking studies. Full article
(This article belongs to the Special Issue Modelling of Parallel Processes under Intuitionistic Fuzzy Uncertainty)
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8 pages, 262 KiB  
Article
InterCriteria Analysis Applied on Air Pollution Influence on Morbidity
by Stefka Fidanova, Petar Zhivkov and Olympia Roeva
Mathematics 2022, 10(7), 1195; https://doi.org/10.3390/math10071195 - 6 Apr 2022
Cited by 5 | Viewed by 1515
Abstract
Human health is reflected in all spheres of life and the economy. One of the main causes of morbidity and early mortality is polluted air. Ambient air pollution is a serious source of disease and mortality across the world. Cities are notorious for [...] Read more.
Human health is reflected in all spheres of life and the economy. One of the main causes of morbidity and early mortality is polluted air. Ambient air pollution is a serious source of disease and mortality across the world. Cities are notorious for their high levels of air pollution and sickness. However, the precise degree of the health impacts of air pollution at the municipal level are still largely unclear. One of the main reasons for increased morbidity is the presence of particulate matter. The aim of our study is to show the relationship between elevated levels of particulate matter in the air and certain diseases. In this paper, we apply InterCriteria Analysis (ICrA) to find the correlation between the level of air pollution and the number of people seeking medical help. This is a new approach for the problem. The results show the affect of air pollution on certain diseases with a short exposure on polluted air and when the exposure is prolonged. We observed that some diseases are exacerbated by brief exposure to polluted air, while in others, exacerbation occurs after prolonged exposure. Full article
(This article belongs to the Special Issue Modelling of Parallel Processes under Intuitionistic Fuzzy Uncertainty)
9 pages, 225 KiB  
Article
A Generalized Net Model of the Prostate Gland’s Functioning
by Martin Lubich, Velimir Papazov, Elenko Popov, Radostina Georgieva, Dmitrii Dmitrenko, Borislav Bojkov, Chavdar Slavov, Peter Vassilev, Vassia Atanassova, Lyudmila Todorova and Krassimir T. Atanassov
Mathematics 2022, 10(3), 479; https://doi.org/10.3390/math10030479 - 2 Feb 2022
Viewed by 1187
Abstract
Over the last 20 years, many Generalized Net (GN) models of the ways of functioning of the different systems and organs in the human body and models related to the description of biomedical processes in living organisms have been constructed. In this paper, [...] Read more.
Over the last 20 years, many Generalized Net (GN) models of the ways of functioning of the different systems and organs in the human body and models related to the description of biomedical processes in living organisms have been constructed. In this paper, a GN model of the prostate gland’s functioning was developed, as a continuation of the previous research. The model provides the possibility to trace the logical relations of the interactions of the prostate gland and various individual organs in the human body. The model shows the possibility for the existence of currently unknown feedback loops. Full article
(This article belongs to the Special Issue Modelling of Parallel Processes under Intuitionistic Fuzzy Uncertainty)
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10 pages, 320 KiB  
Article
Generalized Net Model of Forest Zone Monitoring by UAVs
by Krassimir T. Atanassov, Peter Vassilev, Vassia Atanassova, Olympia Roeva, Rosen Iliev, Dafina Zoteva, Veselina Bureva, Deyan Mavrov and Alexander Alexandrov
Mathematics 2021, 9(22), 2874; https://doi.org/10.3390/math9222874 - 12 Nov 2021
Cited by 3 | Viewed by 1437
Abstract
The paper presents a generalized net (GN) model of the process of terrain observation with the help of unmanned aerial vehicles (UAVs) for the prevention and rapid detection of wildfires. Using a GN, the process of monitoring a zone (through a UAV, which [...] Read more.
The paper presents a generalized net (GN) model of the process of terrain observation with the help of unmanned aerial vehicles (UAVs) for the prevention and rapid detection of wildfires. Using a GN, the process of monitoring a zone (through a UAV, which is further called a reconnaissance drone) and the localization of forest fires is described. For a more indepth study of the terrain, the reconnaissance drone needs to coordinate with a second UAV, called a specialized drone, so that video and sensory information is provided to the supervising fire command operational center. The proposed GN model was developed to assist in the decision-making process related to the coordination of the operation of both UAVs under dynamically changing terrain circumstances, such as those related to preventing or quickly containing wildfires. It describes the stages (transitions), logical determinants (transition predicate matrices), and directions of information flow (token characteristics) within the process of localization of fires using the pair of reconnaissance and specialized drones. Full article
(This article belongs to the Special Issue Modelling of Parallel Processes under Intuitionistic Fuzzy Uncertainty)
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10 pages, 360 KiB  
Article
Modelling the Process of Production of Diesel Fuels by the Use of Generalized Nets
by Danail Dichev Stratiev, Dicho Stratiev and Krassimir Atanassov
Mathematics 2021, 9(19), 2351; https://doi.org/10.3390/math9192351 - 22 Sep 2021
Cited by 5 | Viewed by 1200
Abstract
The process of commodity diesel fuel production in a refinery has been modelled by the use of the Generalized Net (GN) apparatus. GNs are extensions of Petri nets and of all their modifications and extensions. The model accounts for the orders of different [...] Read more.
The process of commodity diesel fuel production in a refinery has been modelled by the use of the Generalized Net (GN) apparatus. GNs are extensions of Petri nets and of all their modifications and extensions. The model accounts for the orders of different grades of diesel fuel and the available amounts of the different diesel fuel components. It can be used for the synchronization and optimization of these processes. Full article
(This article belongs to the Special Issue Modelling of Parallel Processes under Intuitionistic Fuzzy Uncertainty)
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