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Algorithms
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Fuzzy Sets and Fuzzy Logic. A Commemorative Special Issue in...
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Fuzzy Sets and Fuzzy Logic. A Commemorative Special Issue in Honor of 100th Anniversary of the Birth of Professor Lotfi A. Zadeh, Creator of Fuzzy Sets and Fuzzy Logic

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (15 February 2023) | Viewed by 5023

Special Issue Editors

Prof. Dr. Eugene Levner

E-Mail Website
Guest Editor
Department of Computer Science, Holon Institute of Technology, Holon 5810201, Israel
Interests: design and analysis of computer algorithms; artificial-intelligence-based algorithms; green supply chains; cybersecurity algorithms in networks
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Milan Vlach

E-Mail Website
Guest Editor
1. Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 2/25, 11800 Prague, Czech Republic
2. Kyoto College of Graduate Studies for Informatics, 7, Monzen-cho, Tanaka, Sakyo-ku, Kyoto 606 8225, Japan
Interests: game theory, social choice, decision making under uncertainty, fuzzy sets and systems, rough sets

Special Issue Information

Dear Colleagues,

This Special Issue celebrates the 100th anniversary of the birth of Lotfi A. Zadeh, an eminent scientist of our time and a legendary “father” of fuzzy sets, fuzzy logic, and fuzzy systems.

In his seminal paper (1965) on objects with a continuum of grades of membership, Prof. Zadeh gave an outline of the mathematics of fuzzy set theory. Later he widened his vision and proposed fuzzy logic, an extension of the classic many-valued logic. Since then, many authors have developed the theory of fuzzy sets and fuzzy logic, and applied them in various areas of theory and practice.

The current theory of fuzzy sets and systems allows us to investigate and solve various optimization and decision-making problems under uncertainty in a purely mathematical way. Today this theory has a fascinatingly broad range of applications—in artificial intelligence, computer science, robotics, quantum physics, control theory, engineering, digital medicine, economics, ecology, and many more—practically in all areas of science and technology.

Concluding our brief introduction to this Special Issue, we would like to recall the words of Prof. Zadeh, which he declared repeatedly in his articles and keynote lectures and which he repeated to us personally during our unforgettable meetings with him: 

"To begin with, fuzzy logic is not fuzzy. Fuzzy logic is precise"

We invite everyone to submit their recent results on fuzzy sets, fuzzy logic, fuzzy systems, and their applications to this Commemorative Special Issue. 

Prof. Dr. Eugene Levner
Prof. Dr. Milan Vlach
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. Algorithms 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 1600 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

  • mathematical background of fuzzy systems and fuzzy logic
  • fuzzy systems in industry, economics, communications and commercial products
  • fuzzy sets in approximate reasoning
  • fuzzy sets in artificial intelligence
  • fuzzy algorithms and soft computing
  • fuzzy sets in decision sciences
  • classical relations and logic vs. fuzzy relations and logic
  • fuzzy numbers and zadeh’s operations over them
  • s-norms and t-norms and their properties
  • fuzzy arithmetic
  • membership function design
  • zadeh’s extension principle and its variations
  • linguistic variables and hedges
  • basic principles of inference in fuzzy logic and fuzzy IF–THEN rules
  • fuzzy inference engines
  • fuzzification and defuzzification in fuzzy expert systems
  • fuzzy events and fuzzy measures
  • possibility distributions as fuzzy sets, possibility vs. probability

Published Papers (3 papers)

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Research

12 pages, 2556 KiB  
Article
Defuzzify Imprecise Numbers Using the Mellin Transform and the Trade-Off between the Mean and Spread
by Chin-Yi Chen and Jih-Jeng Huang
Algorithms 2022, 15(10), 355; https://doi.org/10.3390/a15100355 - 28 Sep 2022
Viewed by 1237
Abstract
Uncertainty or vagueness is usually used to reflect the limitations of human subjective judgment on practical problems. Conventionally, imprecise numbers, e.g., fuzzy and interval numbers, are used to cope with such issues. However, these imprecise numbers are hard for decision-makers to make decisions, [...] Read more.
Uncertainty or vagueness is usually used to reflect the limitations of human subjective judgment on practical problems. Conventionally, imprecise numbers, e.g., fuzzy and interval numbers, are used to cope with such issues. However, these imprecise numbers are hard for decision-makers to make decisions, and, therefore, many defuzzification methods have been proposed. In this paper, the information of the mean and spread/variance of imprecise data are used to defuzzify imprecise data via Mellin transform. We illustrate four numerical examples to demonstrate the proposed methods, and extend the method to the simple additive weighting (SAW) method. According to the results, our method can solve the problem of the inconsistency between the mean and spread, compared with the center of area (CoA) and bisector of area (BoA), and is easy and efficient for further applications. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Logic. A Commemorative Special Issue in Honor of 100th Anniversary of the Birth of Professor Lotfi A. Zadeh, Creator of Fuzzy Sets and Fuzzy Logic)
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32 pages, 1318 KiB  
Article
A Vibration Based Automatic Fault Detection Scheme for Drilling Process Using Type-2 Fuzzy Logic
by Satyam Paul, Rob Turnbull, Davood Khodadad and Magnus Löfstrand
Algorithms 2022, 15(8), 284; https://doi.org/10.3390/a15080284 - 12 Aug 2022
Cited by 7 | Viewed by 1562
Abstract
The fault detection system using automated concepts is a crucial aspect of the industrial process. The automated system can contribute efficiently in minimizing equipment downtime therefore improving the production process cost. This paper highlights a novel model based fault detection (FD) approach combined [...] Read more.
The fault detection system using automated concepts is a crucial aspect of the industrial process. The automated system can contribute efficiently in minimizing equipment downtime therefore improving the production process cost. This paper highlights a novel model based fault detection (FD) approach combined with an interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy system for fault detection in the drilling process. The system uncertainty is considered prevailing during the process, and type-2 fuzzy methodology is utilized to deal with these uncertainties in an effective way. Two theorems are developed; Theorem 1, which proves the stability of the fuzzy modeling, and Theorem 2, which establishes the fault detector algorithm stability. A Lyapunov stabilty analysis is implemented for validating the stability criterion for Theorem 1 and Theorem 2. In order to validate the effective implementation of the complex theoretical approach, a numerical analysis is carried out at the end. The proposed methodology can be implemented in real time to detect faults in the drilling tool maintaining the stability of the proposed fault detection estimator. This is critical for increasing the productivity and quality of the machining process, and it also helps improve the surface finish of the work piece satisfying the customer needs and expectations. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Logic. A Commemorative Special Issue in Honor of 100th Anniversary of the Birth of Professor Lotfi A. Zadeh, Creator of Fuzzy Sets and Fuzzy Logic)
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13 pages, 546 KiB  
Article
Intuitionistic and Interval-Valued Fuzzy Set Representations for Data Mining
by Fred Petry and Ronald Yager
Algorithms 2022, 15(7), 249; https://doi.org/10.3390/a15070249 - 19 Jul 2022
Cited by 2 | Viewed by 1395
Abstract
Data mining refers to a variety of techniques in the fields of databases, machine learning and pattern recognition. The intent is to obtain useful patterns and associations from a large collection of data. In this paper we describe extensions to the attribute generalization [...] Read more.
Data mining refers to a variety of techniques in the fields of databases, machine learning and pattern recognition. The intent is to obtain useful patterns and associations from a large collection of data. In this paper we describe extensions to the attribute generalization process to deal with interval and intuitionistic fuzzy information. Specifically, we consider extensions for using interval-valued fuzzy representations in both data and the generalization hierarchy. Moreover, preliminary representations using intuitionistic fuzzy information for attribute generalization are described. Finally, we consider how to use fuzzy hierarchies for the generalization of interval-valued fuzzy representations. Full article
(This article belongs to the Special Issue Fuzzy Sets and Fuzzy Logic. A Commemorative Special Issue in Honor of 100th Anniversary of the Birth of Professor Lotfi A. Zadeh, Creator of Fuzzy Sets and Fuzzy Logic)
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