Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

Fuzzy Logic Is Not Fuzzy: World-renowned Computer Scientist Lotfi A. Zadeh

In 1965 Lotfi A. Zadeh published "Fuzzy Sets", his pioneering and controversial paper, that now reaches almost 100,000 citations. All Zadeh’s papers were cited over 185,000 times. Starting from the ideas presented in that paper, Zadeh founded later the Fuzzy Logic theory, that proved to have useful applications, from consumer to industrial intelligent products. We are presenting general aspects of Zadeh’s contributions to the development of Soft Computing(SC) and Artificial Intelligence(AI), and also his important and early influence in the world and in Romania. Several early contributions in fuzzy sets theory were published by Romanian scientists, such as: Grigore C. Moisil (1968), Constantin V. Negoita & Dan A. Ralescu (1974), Dan Butnariu (1978). In this review we refer the papers published in "From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence" (2008, Eds.: L.A. Zadeh, D. Tufis, F.G. Filip, I. Dzitac), and also from the two special issues (SI) of the International Journal of Computers Communications & Control (IJCCC, founded in 2006 by I. Dzitac, F.G. Filip & M.J. Manolescu; L.A. Zadeh joined in 2008 to editorial board). In these two SI, dedicated to the 90th birthday of Lotfi A. Zadeh (2011), and to the 50th anniversary of "Fuzzy Sets" (2015), were published some papers authored by scientists from Algeria, Belgium, Canada, Chile, China, Hungary, Greece, Germany, Japan, Lithuania, Mexico, Pakistan, Romania, Saudi Arabia, Serbia, Spain, Taiwan, UK and USA

A technique for fuzzifying metric spaces via metric preserving mappings

[EN] In this paper we develop a new technique for constructing fuzzy metric spaces, in the sense of George and Veeramani, from metric spaces and by means of the Lukasievicz t-norm. In particular such a technique is based on the use of metric preserving functions in the sense of J. Dobos. Besides, the new generated fuzzy metric spaces are strong and completable, and if we add an extra condition, they are principal. Appropriate examples of such fuzzy metric spaces are given in order to illustrate the exposed technique.Valentín Gregori acknowledges the support of the Spanish Ministry of Economy and Competitiveness under Grant MTM2015-64373-P (MINECO/FEDER, UE). Oscar Valero acknowledges the support of the Spanish Ministry of Economy and Competitiveness under Grants TIN2014-56381-REDT (LODISCO), TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE funds.Gregori Gregori, V.; Miñana, J.; Valero Sierra, Ó. (2018). A technique for fuzzifying metric spaces via metric preserving mappings. Fuzzy Sets and Systems. 330:1-15. https://doi.org/10.1016/j.fss.2017.07.022S11533

Representations for Morphological Image Operators and Analogies with Linear Operators

1.1 Why a representation theory?...............................