Generalized Metrics and Fuzzy Similarities: Theory and Applications

Dear Colleagues,

Distances and the topologies they induce are fundamental tools for quantifying dissimilarity when information is assumed to be precise. However, the rigid axiomatic framework of traditional metrics limits their applicability in many relevant contexts, motivating an intense scientific activity focused on more general notions of dissimilarity and the types of topologies they induce.

Among these generalized approaches are quasi-pseudo-metrics, partial metrics, relaxed metrics, and modular metrics. Furthermore, when dissimilarity assessments involve uncertainty, fuzzy sets and similarity relations become indispensable, with fuzzy (modular) binary relations constituting a particularly powerful and versatile framework.

The aim of this Special Issue is to gather high-quality mathematical contributions showcasing the most recent advances in the theory and applications of generalized metrics, fuzzy similarities, and related topics. The scope encompasses both theoretical and applied developments, including topics such as generalized metrics (specifically quasi-pseudo-metrics, partial metrics, relaxed metrics, modular metrics), as well as fuzzy sets and their extensions (intuitionistic, picture, Pythagorean, spherical, 2-type, and interval-valued models). It also includes fuzzy metrics, fuzzy relations, and fuzzy modular relations, as well as duality principles between fuzzy relations and generalized metric spaces. Contributions concerning aggregation methods in their broadest sense are equally welcome, including generalizations of aggregation functions, aggregation operators for extended fuzzy sets, aggregation of fuzzy and modular fuzzy relations, and aggregation of generalized metrics, among others. From an applied perspective, relevant areas include approximate reasoning, image processing, model identification and parametrization, diagnostics and prognostics, data mining, decision-making, clustering under uncertainty, multiagent systems, robotics, machine learning, pattern recognition, swarm intelligence, and business and financial analysis.

Prof. Dr. Jesús López
Prof. Dr. Óscar Valero Sierra
Prof. Dr. Halis Aygün
Dr. Olga Grigorenko
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 250 words) can be sent to the Editorial Office for assessment.

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.