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Mathematics
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Fuzzy and Extension of Fuzzy Theories
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Fuzzy and Extension of Fuzzy Theories

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D2: Operations Research and Fuzzy Decision Making".

Deadline for manuscript submissions: closed (30 September 2022) | Viewed by 12937

Special Issue Editors

Prof. Dr. Mihaela Colhon

E-Mail Website
Guest Editor
Department of Computer Science, University of Craiova, 200585 Craiova, Romania
Interests: artificial intelligence; natural language processing; knowledge representation
Special Issues, Collections and Topics in MDPI journals
Dr. Camelia Delcea

E-Mail Website
Guest Editor
Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, 010552 Bucharest, Romania
Interests: economic cybernetics; consumer behavior; agent-based modeling; sustainable development; gray systems theory; neutrosophic theory
Special Issues, Collections and Topics in MDPI journals
Dr. Arjab Singh Khuman

E-Mail Website
Guest Editor
Institute of Artificial Intelligence, De Montfort University, The Gateway, Leicester LE1 9BH, UK
Interests: artificial intelligence; computational intelligence; uncertainty modelling; Fuzzy LogicGrey Systems
Dr. Ioana-Alexandra Bradea

E-Mail Website
Guest Editor
Chief Department Regional Development, Projects and Tourism The North-West Regional Development Agency, Bucharest University of Economic Studies, 010374 Bucharest, Romania
Interests: optimization of financial assets; fuzzy optimization
Dr. Surapati Pramanik

E-Mail Website
Guest Editor
Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, P.O.-Narayanpur, Dist-North 24 Parganas, West Bengal, India
Interests: mathematics and math education; soft computing; operations research; grey system theory; fuzzy and neutrosophic sets
Prof. Dr. Jun Ye

E-Mail Website
Guest Editor
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
Interests: soft computing; fuzzy decision theory and method; robot intelligent control; pattern recognition and fault diagnosis; neutrosophic theory; rock mechanics; engineering modeling; optimization design
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue in the open access journal Mathematics (ISSN 2227-7390) is aimed at publishing new results in the field of fuzzy theories and the extension of fuzzy theories. Since Zadeh introduced the fuzzy sets concept, a number of new theories dealing with imprecision and uncertainty have been developed. Some of these theories are extensions of fuzzy set theory, as the extension principle is one of the most basic ideas in fuzzy set theory.

In the 1970s, Zadeh, Grattan-Guiness, Jahn and Sambuc introduced independently interval-valued fuzzy set (IVFS) in which the set membership is treated as an interval.

Later, Belnap defined four-valued logic to cope with multiple information sources.

Atanassov extended fuzzy logic to intuitionistic fuzzy sets and then, to allow a greater degree of freedom and flexibility in representing uncertainty, interval valued intuitionistic fuzzy sets were proposed.

Cuong and Kreinovich extended the concept of intuitionistic fuzzy set in picture fuzzy set, in which uncertainty can be modelled in such situations involving more answers of the types yes, abstain, and no.

In 1998, F. Smarandache proposed Neutrosophic Logic and, quite recently (in 2013), the Refined Neutrosophic Logic (which generalizes Belnap's four valued logic) to represent mathematical model of uncertainty, vagueness, ambiguity, imprecision, incompleteness, inconsistency, redundancy and contradiction.

In 2017 F. Smarandache introduced Plithogenic Logic as a generalization of all previous logics: Boolean, Fuzzy, Intuitionistic Fuzzy, Neutrosophic Logic, and all other fuzzy-extension logics. It is a MultiVariate Logic, whose truth variables may be in any type of the above logics. Aa an extension of Soft Sets, HyperSoft Set was defined in 2018 by transforming the function F into a multi-attribute function.

Therefore, for this Special Issue, authors are invited to explore new trends of fuzzy sets theory in emerging research fields of computational intelligence, data analysis and data mining, knowledge representation and reasoning, etc. We envisage new frontiers that promote a broad and up-to-date understanding of fuzzy theory-based extensions and applications. Additionally, the authors are encouraged to submit papers addressing the state of the art, or case studies featuring practical applications of fuzzy and neutrosophic theory under various conditions.

Prof. Dr. Mihaela Colhon
Prof. Dr. Camelia Delcea
Dr. Arjab Singh Khuman
Dr. Ioana-Alexandra Bradea
Dr. Surapati Pramanik
Prof. Dr. Jun Ye
Guest Editors

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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
  • extensions of fuzzy sets fuzzy sets and hybrid fuzzy sets
  • fuzzy algorithms for search, classification, approximation and learning
  • type 2 fuzzy sets
  • intuitionistic fuzzy logic
  • neutrosophic logic
  • neutrosophic portfolios
  • fuzzy refined neutrosophic logic
  • picture fuzzy logic
  • plithogenic logic
  • fuzzy sets theory-based logic
  • applications of fuzzy sets and their extensions
  • applications of neutrosophic logic

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Published Papers (5 papers)

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11 pages, 293 KiB  
Article
Linear Diophantine Fuzzy Set Theory Applied to BCK/BCI-Algebras
by Ghulam Muhiuddin, Madeline Al-Tahan, Ahsan Mahboob, Sarka Hoskova-Mayerova and Saba Al-Kaseasbeh
Mathematics 2022, 10(12), 2138; https://doi.org/10.3390/math10122138 - 19 Jun 2022
Cited by 7 | Viewed by 1903
Abstract
In this paper, we apply the concept of linear Diophantine fuzzy sets in BCK/BCI-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties [...] Read more.
In this paper, we apply the concept of linear Diophantine fuzzy sets in BCK/BCI-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained. Full article
(This article belongs to the Special Issue Fuzzy and Extension of Fuzzy Theories)
25 pages, 481 KiB  
Article
H∞ and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults
by Houssem Jerbi, Mourad Kchaou, Attia Boudjemline, Mohamed Amin Regaieg, Sondes Ben Aoun and Ahmed Lakhdar Kouzou
Mathematics 2021, 9(18), 2203; https://doi.org/10.3390/math9182203 - 8 Sep 2021
Cited by 5 | Viewed by 2158
Abstract
In this paper, the problem of reliable control design with mixed H∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less [...] Read more.
In this paper, the problem of reliable control design with mixed H∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed H∞ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature. Full article
(This article belongs to the Special Issue Fuzzy and Extension of Fuzzy Theories)
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32 pages, 8244 KiB  
Article
Stability Analysis of Systems with Fuzzy PI Controllers Applied to Electric Drives
by Constantin Voloşencu
Mathematics 2021, 9(11), 1246; https://doi.org/10.3390/math9111246 - 29 May 2021
Cited by 7 | Viewed by 2448
Abstract
This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of [...] Read more.
This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of electric drives based on fuzzy PI controllers in the context of performing stability analyses, both internal and input–output, finding solutions to stabilize these systems and provide guidance on fuzzy regulator design. The main methods of treatment applied are as follows: framing the control system in the theory of stability of multivariable non-linear systems, application of Lyapunov’s theory, performing an input–output stability analysis, and verification of the stability domain. The article presents the conditions for correcting the fuzzy controller to ensure internal and external stability, determines the limits of the stability sector, and gives indications for choosing the parameters of the controller. The considerations presented can be applied to various structures for regulating the speed of electric drives which use various PI fuzzy controllers. Full article
(This article belongs to the Special Issue Fuzzy and Extension of Fuzzy Theories)
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36 pages, 1109 KiB  
Article
Optimization of Financial Asset Neutrosophic Portfolios
by Marcel-Ioan Boloș, Ioana-Alexandra Bradea and Camelia Delcea
Mathematics 2021, 9(11), 1162; https://doi.org/10.3390/math9111162 - 21 May 2021
Cited by 5 | Viewed by 2299
Abstract
The purpose of this paper was to model, with the help of neutrosophic fuzzy numbers, the optimal financial asset portfolios, offering additional information to those investing in the capital market. The optimal neutrosophic portfolios are those categories of portfolios consisting of two or [...] Read more.
The purpose of this paper was to model, with the help of neutrosophic fuzzy numbers, the optimal financial asset portfolios, offering additional information to those investing in the capital market. The optimal neutrosophic portfolios are those categories of portfolios consisting of two or more financial assets, modeled using neutrosophic triangular numbers, that allow for the determination of financial performance indicators, respectively the neutrosophic average, the neutrosophic risk, for each financial asset, and the neutrosophic covariance as well as the determination of the portfolio return, respectively of the portfolio risk. There are two essential conditions established by rational investors on the capital market to obtain an optimal financial assets portfolio, respectively by fixing the financial return at the estimated level as well as minimizing the risk of the financial assets neutrosophic portfolio. These conditions allowed us to compute the financial assets’ share in the total value of the neutrosophic portfolios, for which the financial return reaches the level set by investors and the financial risk has the minimum value. In financial terms, the financial assets’ share answers the legitimate question of rational investors in the capital market regarding the amount of money they must invest in compliance with the optimal conditions regarding the neutrosophic return and risk. Full article
(This article belongs to the Special Issue Fuzzy and Extension of Fuzzy Theories)
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40 pages, 4568 KiB  
Article
Sectorial Fuzzy Controller Plus Feedforward for the Trajectory Tracking of Robotic Arms in Joint Space
by Andres Pizarro-Lerma, Victor Santibañez, Ramon Garcia-Hernandez and Jorge Villalobos-Chin
Mathematics 2021, 9(6), 616; https://doi.org/10.3390/math9060616 - 15 Mar 2021
Cited by 5 | Viewed by 2311
Abstract
In this paper, we propose a Sectorial Fuzzy Controller (SFC) with a feedforward compensation of the robot dynamics in joint space, evaluated at the desired angular positions, velocities, and accelerations, applied to the trajectory tracking of all revolute joints robotic arms. Global uniform [...] Read more.
In this paper, we propose a Sectorial Fuzzy Controller (SFC) with a feedforward compensation of the robot dynamics in joint space, evaluated at the desired angular positions, velocities, and accelerations, applied to the trajectory tracking of all revolute joints robotic arms. Global uniform asymptotic stability proof applying the direct Lyapunov theorem, is introduced for this new control scheme by using a strict Lyapunov function. This strict Lyapunov function is the first one within the field of fuzzy control that is applied to the trajectory control of robotic manipulators. With this strict Lyapunov function, a sensitivity analysis was also computed for this novel control scheme. Additionally, physical and simulation experimental results are given in comparison to the original control scheme, in which this new controller is inspired: the Proportional-Derivative (PD) controller plus feedforward compensation. The experimental results yielded better performance for the new fuzzy control scheme when compared to the classical structure, in both the joint position errors for similar or smaller values of applied torques, showing the expected tolerance to parametric deviations and uncertainties that all fuzzy controllers possess. Full article
(This article belongs to the Special Issue Fuzzy and Extension of Fuzzy Theories)
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