Constructing interval-valued fuzzy material implication functions derived from general interval-valued grouping functions

Grouping functions and their dual counterpart, overlap functions, have drawn the attention of many authors, mainly because they constitute a richer class of operators compared to other types of aggregation functions. Grouping functions are a useful theoretical tool to be applied in various problems, like decision making based on fuzzy preference relations. In pairwise comparisons, for instance, those functions allow one to convey the measure of the amount of evidence in favor of either of two given alternatives. Recently, some generalizations of grouping functions were proposed, such as (i) the n-dimensional grouping functions and the more flexible general grouping functions, which allowed their application in n-dimensional problems, and (ii) n-dimensional and general interval-valued grouping functions, in order to handle uncertainty on the definition of the membership functions in real-life problems. Taking into account the importance of interval-valued fuzzy implication functions in several application problems under uncertainty, such as fuzzy inference mechanisms, this paper aims at introducing a new class of interval-valued fuzzy material implication functions. We study their properties, characterizations, construction methods and provide examples.upported by CNPq (301618/2019-4, 311429/2020-3), FAPERGS (19/2551-0001660-3), UFERSA, the Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019-108392GB I00 (MCIN/AEI/10.13039/501100011033)) and Navarra de Servicios y Tecnologías, S.A. (NASERTIC)

Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences

Mathematical fuzzy logic (MFL) specifically targets many-valued logic and has significantly contributed to the logical foundations of fuzzy set theory (FST). It explores the computational and philosophical rationale behind the uncertainty due to imprecision in the backdrop of traditional mathematical logic. Since uncertainty is present in almost every real-world application, it is essential to develop novel approaches and tools for efficient processing. This book is the collection of the publications in the Special Issue “Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences”, which aims to cover theoretical and practical aspects of MFL and FST. Specifically, this book addresses several problems, such as:- Industrial optimization problems- Multi-criteria decision-making- Financial forecasting problems- Image processing- Educational data mining- Explainable artificial intelligence, etc

Generalization of QL-operators based on general overlap and general grouping functions

Firstly, this work discusses the main conditions guarantying that general overlap (grouping) functions can be obtained from n-dimensional overlap (grouping) functions. Focusing on QL-implications, which are usually generated by strong negations together with t-norms and t-conorms, we consider a non-restrictive construction, by relaxing not only the associativity and the corresponding neutral elements (NE) but also the reverse construction of other properties. Thus, the main properties of the QL-implication class are studied, considering a tuple (G,N,O) generated from grouping and overlap functions together with the greatest fuzzy negation. In addition, in order to provide more flexibility, we define a subclass of QL-implications generated from general overlap and general grouping functions. Some examples are introduced, illustrating the constructive methods to generate such operators.This work was partially supported by CAPES, UFERSA, PQ/CNPq (309160/2019-7; 311429/2020-3), PqG/FAPERGS (21/2551-0002057-1) and FAPERGS/CNPq PRONEX (16/2551-0000488-9)