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Mathematics
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Fuzzy Logic and Its Applications
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Fuzzy Logic and Its Applications

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 (20 September 2022) | Viewed by 16456

Special Issue Editor

Dr. Krystian Jobczyk

E-Mail Website
Guest Editor
Department of Applied Computer Science, AGH University of Science and Technology, 30-059 Krakow, Poland
Interests: fuzzy logic; fuzzy category theory; metalogic; artificial intelligence

Special Issue Information

Dear Colleagues,

This Special Issue calls for the newest advancements under the banner "fuzzy logic and its applications" to create a common communication platform for both theoreticians and practitioners working on fuzzy logic in the area of its application to fuzzy systems, soft computing, and related areas. It will provide a platform for exchanging ideas among scientists: mathematicians, logicians, computer scientists, specialists in AI and knowledge engineering, experts in soft computing, etc.

From the historical perspective, the conceptual provenance of fuzzy logic may be inferred from the early works of Łukasiewicz, Wajsberg, Post, and Goedel on different aspects of multi-valency. However, Zadeh's and Pavelka's achievements in the 1970s gave an essential impulse for its development—not only in the theoretic framework of logic and mathematics. A multi-dimensional development in research on fuzzy logic and its applications in the 1980s and 1990s is a merit of many communities and researchers such as P. Hajek, L. Godo, H. Prade, P. Klement, D. Mundici, and many others.

Fuzzy logic may be currently seen as a broad spectrum of logical systems, which allow the statements to take truth values from the whole continuum between truth and falsehood. Indeed, fuzzy logic may be currently understood from mutually different epistemic perspectives, which elucidate the nature of fuzzy logic itself and a broad variety of different ways in which fuzzy logic lives in engineering practice and applications. Logicians can see fuzzy logic as a branch of mathematical logic and foundations of formal sciences. Mathematicians may tend to consider fuzzy logic as interesting research on MV-algebras and other close-related structures. Finally, experts in soft computing, AI, and knowledge representation may rather see fuzzy logic as machinery for dealing with approximate reference, uncertainty and vagueness in practice. 

Dr. Krystian Jobczyk
Guest Editor

Manuscript Submission Information

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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

  • Fuzzy logic in algebraic treatment
  • Fuzzy logic and analytic structures
  • Fuzzy logic and fuzzy mathematics
  • Fuzzy logic versus multi-valued logic
  • Fuzzy logic in its interaction with modal logic
  • Fuzzy logic in approximate reasoning
  • Fuzzy logic in system modeling, control, and automation
  • Fuzzy logic for decision support systems
  • Fuzzy logic for security
  • Fuzzy logic and machine learning/deep learning
  • Fuzzy computing
  • Fuzzy logic economy and industry

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Published Papers (8 papers)

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Research

18 pages, 4634 KiB  
Article
Fast Method Based on Fuzzy Logic for Gaussian-Impulsive Noise Reduction in CT Medical Images
by Josep Arnal and Luis Súcar
Mathematics 2022, 10(19), 3652; https://doi.org/10.3390/math10193652 - 5 Oct 2022
Cited by 5 | Viewed by 2381
Abstract
To remove Gaussian-impulsive mixed noise in CT medical images, a parallel filter based on fuzzy logic is applied. The used methodology is structured in two steps. A method based on a fuzzy metric is applied to remove the impulsive noise at the first [...] Read more.
To remove Gaussian-impulsive mixed noise in CT medical images, a parallel filter based on fuzzy logic is applied. The used methodology is structured in two steps. A method based on a fuzzy metric is applied to remove the impulsive noise at the first step. To reduce Gaussian noise, at the second step, a fuzzy peer group filter is used on the filtered image obtained at the first step. A comparative analysis with state-of-the-art methods is performed on CT medical images using qualitative and quantitative measures evidencing the effectiveness of the proposed algorithm. The parallel method is parallelized on shared memory multiprocessors. After applying parallel computing strategies, the obtained computing times indicate that the introduced filter enables to reduce Gaussian-impulse mixed noise on CT medical images in real-time. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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17 pages, 6197 KiB  
Article
Interval-Type 3 Fuzzy Differential Evolution for Designing an Interval-Type 3 Fuzzy Controller of a Unicycle Mobile Robot
by Cinthia Peraza, Patricia Ochoa, Oscar Castillo and Zong Woo Geem
Mathematics 2022, 10(19), 3533; https://doi.org/10.3390/math10193533 - 28 Sep 2022
Cited by 17 | Viewed by 1577
Abstract
Recently, interval-type 3 fuzzy systems have begun to appear in different research areas. This article outlines a methodology for the parameterization of interval type-3 membership functions using vertical cuts applied to the dynamic parameter adaptation of the differential evolution algorithm and implemented in [...] Read more.
Recently, interval-type 3 fuzzy systems have begun to appear in different research areas. This article outlines a methodology for the parameterization of interval type-3 membership functions using vertical cuts applied to the dynamic parameter adaptation of the differential evolution algorithm and implemented in an interval-type 3 Sugeno controller. This methodology was applied to the dynamic adaptation of the F (mutation) parameter in differential evolution to improve the performance of this method as the generations occur. To test the type-3 fuzzy differential evolution algorithm, the optimal design of a type-3 Sugeno controller was considered. In this case, the parameterization of the type-3 membership functions of this Sugeno fuzzy controller was performed. The experimentation is based on the application of three different noise levels for validation of the efficacy of the method and performing a comparison study with respect to other articles in the literature. The main idea is to implement the parameterization of interval type-3 membership functions to enhance the ability of differential evolution in designing an optimal interval type-3 system to control a unicycle mobile robot. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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27 pages, 13487 KiB  
Article
A Fuzzy Implication-Based Approach for Validating Climatic Teleconnections
by Stefanos Makariadis and Basil Papadopoulos
Mathematics 2022, 10(15), 2692; https://doi.org/10.3390/math10152692 - 29 Jul 2022
Cited by 2 | Viewed by 1771
Abstract
Fuzzy logic, during recent decades, has evolved into one of the most influential scientific fields. To an extent, this is due to its applications which have a profound impact on the daily life of people worldwide. The goal of this paper is to [...] Read more.
Fuzzy logic, during recent decades, has evolved into one of the most influential scientific fields. To an extent, this is due to its applications which have a profound impact on the daily life of people worldwide. The goal of this paper is to focus on the applications of fuzzy logic to the study of our climate, and especially if fuzzy implications can validate the climatic teleconnections observed on climatic data. To achieve this goal, a real world case study is provided which focuses on the relationship between temperature anomalies observed at different European cities. The results of this case study are that, indeed, fuzzy implications can validate the climatic teleconnections observed on climatic data. The conclusions drawn are that fuzzy logic can assist to the definitive proof of phenomena which, till now, could only be researched experimentally. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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16 pages, 347 KiB  
Article
Regular Partial Residuated Lattices and Their Filters
by Nan Sheng and Xiaohong Zhang
Mathematics 2022, 10(14), 2429; https://doi.org/10.3390/math10142429 - 12 Jul 2022
Cited by 11 | Viewed by 1319
Abstract
To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. [...] Read more.
To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied partial residuated implications (PRIs) and proposed the concept of partial residuated lattices (PRLs). In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. Second, we define regular partial residuated lattices (rPRLs) and study their corresponding properties. Third, we study the relations among commutative quasi-residuated lattices, commutative Q-residuated lattices, partial residuated lattices, and regular partial residuated lattices. Last, in order to obtain the filter theory of regular partial residuated lattices, we restrict certain conditions and then propose special regular partial residuated lattices (srPRLs) in order to finally construct the quotient structure of regular partial residuated lattices. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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19 pages, 7558 KiB  
Article
Fuzzy Fusion of Stereo Vision, Odometer, and GPS for Tracking Land Vehicles
by Marcos J. Villaseñor-Aguilar, José E. Peralta-López, David Lázaro-Mata, Carlos E. García-Alcalá, José A. Padilla-Medina, Francisco J. Perez-Pinal, José A. Vázquez-López and Alejandro I. Barranco-Gutiérrez
Mathematics 2022, 10(12), 2052; https://doi.org/10.3390/math10122052 - 14 Jun 2022
Cited by 5 | Viewed by 1981
Abstract
The incorporation of high precision vehicle positioning systems has been demanded by the autonomous electric vehicle (AEV) industry. For this reason, research on visual odometry (VO) and Artificial Intelligence (AI) to reduce positioning errors automatically has become essential in this field. In this [...] Read more.
The incorporation of high precision vehicle positioning systems has been demanded by the autonomous electric vehicle (AEV) industry. For this reason, research on visual odometry (VO) and Artificial Intelligence (AI) to reduce positioning errors automatically has become essential in this field. In this work, a new method to reduce the error in the absolute location of AEV using fuzzy logic (FL) is presented. The cooperative data fusion of GPS, odometer, and stereo camera signals is then performed to improve the estimation of AEV localization. Although the most important challenge of this work focuses on the reduction in the odometry error in the vehicle, the defiance of synchrony and the information fusion of sources of different nature is solved. This research is integrated by three phases: data acquisition, data fusion, and statistical evaluation. The first one is data acquisition by using an odometer, a GPS, and a ZED camera in AVE’s trajectories. The second one is the data analysis and fuzzy fusion design using the MatLab 2019® fuzzy logic toolbox. The last is the statistical evaluation of the positioning error of the different sensors. According to the obtained results, the proposed model with the lowest error is that which uses all sensors as input (stereo camera, odometer, and GPS). It can be highlighted that the best proposed model manages to reduce the positioning mean absolute error (MAE) up to 25% with respect to the state of the art. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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21 pages, 2219 KiB  
Article
Are Citizens Credentialist or Post-Nationalists? A Fuzzy-Eco Apostle Model Applied to National Identity
by Alessandro Indelicato and Juan Carlos Martín
Mathematics 2022, 10(12), 1978; https://doi.org/10.3390/math10121978 - 8 Jun 2022
Cited by 2 | Viewed by 2147
Abstract
The debate on national identity has been receiving more attention from academics, social planners, and the public in recent years. This study aims to analyse citizens’ different national identity typologies using data from the International Social Survey Program (ISSP) in two waves: 2003 [...] Read more.
The debate on national identity has been receiving more attention from academics, social planners, and the public in recent years. This study aims to analyse citizens’ different national identity typologies using data from the International Social Survey Program (ISSP) in two waves: 2003 and 2013. The study is based on 10 countries for which the dimensions of the national identity construct are first examined through multi-group confirmatory factor analysis (MGCFA). Then, a fuzzy hybrid approach is used to obtain two synthetic indicators for each dimension of national identity, namely ethnic and civic orientations. Then, a fuzzy clustering analysis is used to extend the Classical Apostle Model, obtaining 16 different national identity categories that expand the four Apostle categories denominated as credentialists, post-nationalists, ethnic-oriented and civic-oriented. The study ends by applying the Binary Probit Model to analyse whether some socioeconomic characteristics can partly explain the four pure national identity categories. Our results show that people seem to be increasingly credentialists. Furthermore, the civic–ethnic dichotomy of France–Germany is no longer confirmed, as Germans appear to be included in the civic-oriented national identity group. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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17 pages, 2815 KiB  
Article
Attitude Control of a Flexible Spacecraft via Fuzzy Optimal Variance Technique
by Chokri Sendi
Mathematics 2022, 10(2), 179; https://doi.org/10.3390/math10020179 - 7 Jan 2022
Cited by 3 | Viewed by 1826
Abstract
This paper investigates the performance of a fuzzy optimal variance control technique for attitude stability and vibration attenuation with regard to a spacecraft made of a rigid platform and multiple flexible appendages that can be retargeted to the line of sight. The proposed [...] Read more.
This paper investigates the performance of a fuzzy optimal variance control technique for attitude stability and vibration attenuation with regard to a spacecraft made of a rigid platform and multiple flexible appendages that can be retargeted to the line of sight. The proposed technique addresses the problem of actuators’ amplitude and rate constraints. The fuzzy model of the spacecraft is developed based on the Takagi-Sugeno(T-S) fuzzy model with disturbances, and the control input is designed using the Parallel Distributed Compensation technique (PDC). The problem is presented as an optimization problem in the form of Linear Matrix Inequalities (LMIs). The performance and the stability of the proposed controller are investigated through numerical simulation. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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15 pages, 576 KiB  
Article
Pointwise k-Pseudo Metric Space
by Yu Zhong, Alexander Šostak and Fu-Gui Shi
Mathematics 2021, 9(19), 2505; https://doi.org/10.3390/math9192505 - 6 Oct 2021
Cited by 2 | Viewed by 1972
Abstract
In this paper, the concept of a k-(quasi) pseudo metric is generalized to the L-fuzzy case, called a pointwise k-(quasi) pseudo metric, which is considered to be a map [...] Read more.
In this paper, the concept of a k-(quasi) pseudo metric is generalized to the L-fuzzy case, called a pointwise k-(quasi) pseudo metric, which is considered to be a map d:J(LX)×J(LX)⟶[0,∞) satisfying some conditions. What is more, it is proved that the category of pointwise k-pseudo metric spaces is isomorphic to the category of symmetric pointwise k-remote neighborhood ball spaces. Besides, some L-topological structures induced by a pointwise k-quasi-pseudo metric are obtained, including an L-quasi neighborhood system, an L-topology, an L-closure operator, an L-interior operator, and a pointwise quasi-uniformity. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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