**About the Editors**

### **Sorin N ˘ad ˘aban**

Sorin Nad˘ aban is a professor in the Department of Mathematics and Computer Science of Aurel ˘ Vlaicu University of Arad. He received his bachelor's in Mathematics (1991) and PhD in Mathematics (2000) from the Western University of Timis¸oara, Romania. His research interests are in the areas of fuzzy mathematics and operator theory. He is the Editor-in-Chief of the journal Theory and Applications of Mathematics & Computer Science and a reviewer of the American Mathematical Society.

## **Preface to "Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh"**

In 1965, Lotfi A. Zadeh published "Fuzzy Sets", his pioneering and controversial paper, which has now had over 115,000 citations. Altogether, Zadeh's papers have been cited over 248,000 times. Starting from the ideas presented in that paper, Zadeh later founded the Fuzzy Logic Theory, which has useful applications from consumer to industrial intelligent products. In accordance with Zadeh's definition, soft computing (SC) consists of computational techniques in computer science, machine learning, and some engineering disciplines to study, model, and analyze very complex reality, for which more traditional methods have been either unusable or inefficient. SC uses soft techniques, contrasting it with classical artificial intelligence hard computing (HC) techniques, and includes fuzzy logic, neural computing, evolutionary computation, machine learning, and probabilistic reasoning. HC is bound by a computer science (CS) concept called NP-complete, which stipulates that there is a direct connection between the size of a problem and the amount of resources needed to solve it, called the "grand challenge problem". SC helps to surmount NP-complete problems by using inexact methods to give useful but inexact answers to intractable problems. SC became a formal CS area of study in the early 1990s. Earlier computational approaches could only model and precisely analyze relatively simple systems. More complex systems arising in biology, medicine, the humanities, managemen<sup>t</sup> sciences, and similar fields often remained intractable to HC. It should be pointed out that the simplicity and complexity of systems are relative, and many conventional mathematical models have been both challenging and very productive. SC techniques resemble biological processes more closely than traditional techniques, which are largely based on formal logical systems, such as Boolean logic, or rely heavily on computer-aided numerical analysis techniques (such as finite element analysis). SC techniques are intended to complement HC techniques. Unlike HC schemes, which strive for exactness and full truth, SC techniques exploit the given tolerance of imprecision, partial truth, and uncertainty for a particular problem. Inductive reasoning plays a larger role in SC than in HC. SC and HC can be used together in certain fusion techniques. SC can deal with ambiguous or noisy data, and it is tolerant of imprecision, uncertainty, partial truth, and approximation. In effect, the role model for SC is the human mind. Artificial intelligence and computational intelligence based on SC provide the background for the development of smart managemen<sup>t</sup> systems and decisions in the case of ill-posed problems.

The present book contains 14 articles accepted for publication among the 40 manuscripts in total that were submitted to the Special Issue of the MDPI Mathematics journal entitled "Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017)". These articles have been published in Volume 9 (2021) of the journal and cover a wide variety of topics related to fuzzy logic and soft computing. We hope that this book will be useful for those who work in the domains of fuzzy logic and soft computing or for those who want to familiarize themselves with the most advanced knowledge in the field of fuzzy mathematics.

As the Guest Editor of this Special Issue, I am grateful to the authors of the papers for their high-quality contributions, to the reviewers for their valuable comments towards the improvement of the articles submitted, and to the administrative staff of the MDPI publications for their support in completing this project. Special thanks are due to the Managing Editor of the Special Issue, Mr. Claude Zhang, for his excellent collaboration and valuable assistance.

**Ioan Dzitac and Sorin Nadaban** *Editors*

#### *Editorial* **Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)**

**Sorin N ˘ad ˘aban**

> Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Dr ˘agoi 2, RO-310330 Arad, Romania; snadaban@gmail.com
