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Symmetry
Special Issues
Mathematical Fuzzy Logic and Fuzzy Set Theory
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Mathematical Fuzzy Logic and Fuzzy Set Theory

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 March 2019) | Viewed by 6380

Special Issue Editors

Prof. Dr. Erich Peter Klement

E-Mail Website
Guest Editor
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University Linz Altenberger Straße 694040 Linz, Austria
Interests: foundations of fuzzy logic and fuzzy control; triangular norms; measure and integration theory; applications to probability and game theory
Dr. Tommaso Flaminio

E-Mail Website
Guest Editor
Artificial Intelligence Research Institute, Spanish National Research Council Campus de la Universidad Autònoma de Barcelona s/n 08193 Bellaterra, Spain
Interests: mathematical logic; uncertain reasoning; many-valued logic; coherence

Special Issue Information

Dear Colleagues,

Fuzzy set theory (FST) started with L. A. Zadeh’s 1965 paper where he suggested the unit interval as a set of truth values instead of the classical binary Boolean algebra. This was followed by J. Goguen’s generalization (1967), replacing the unit interval by an abstract set L (which mostly is assumed to be a bounded lattice). Since then, fuzzy sets and some generalizations thereof (such as L-fuzzy sets or type-2 fuzzy sets) have been considered in a variety of fields, ranging from algebra, topology and category theory to measures, integrals, probability and statistics, and to decision making.

Zadeh’s paper on fuzzy sets also inspired the development of a discipline which today is known as Mathematical Fuzzy Logic (MFL). MFL moved its first steps at the beginning of the 1990’s when logical systems having the real unit interval as standard domain for truth-values, started to be systematically studied. These foundational issues are collected in two volumes which constitute the backbone of MFL: P. Hájek, "Metamathematics of Fuzzy Logic" (1998) and S. Gottwald, "A Treatise on Many-Valued Logics" (2001). Nowadays, MFL reaches other areas of pure and applied logic: proof theory, modal logics, first order logics and generalized quantifiers, game theory, and foundational issues.

The solid mathematical ground on which both FST and MFL are based, directly reveals that symmetry is a guiding inspiration for all researchers which are working on and contributing to the growth and the development of these areas. This Special Issue aims at collecting profound papers where the methods and inspiration are deeply related to the notion of symmetry.

Prof. Erich Peter Klement
Dr. Tommaso Flaminio
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. Symmetry 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 2400 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

  • Algebraic analysis
  • Abstract algebraic logic
  • Computational complexity
  • First-order and higher-order logics
  • Foundational aspects
  • Game semantics
  • Generalizations of fuzzy sets
  • Generalized measures and integrals
  • Modal logics
  • Probability and uncertainty theories
  • Proof theory
  • Quantales and categorical aspects of fuzzy sets

Published Papers (3 papers)

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Research

20 pages, 258 KiB  
Article
Some Results in Weak Pseudo-Quasi-Wajsberg Algebras
by Wenjun Liu and Wenjuan Chen
Symmetry 2019, 11(4), 447; https://doi.org/10.3390/sym11040447 - 29 Mar 2019
Cited by 1 | Viewed by 1767
Abstract
In this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak [...] Read more.
In this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak filters and right weak filters of a weak PQW-algebra and study related properties of them. We also discuss the relation between normal filters and filter congruences on a weak PQW-algebra. Finally, we characterize the relationship between weak PQW-algebras and some bounded residuated quasi-ordered monoids with supplementary conditions. Full article
(This article belongs to the Special Issue Mathematical Fuzzy Logic and Fuzzy Set Theory)
13 pages, 424 KiB  
Article
The Logic of Pseudo-Uninorms and Their Residua
by SanMin Wang
Symmetry 2019, 11(3), 368; https://doi.org/10.3390/sym11030368 - 12 Mar 2019
Cited by 2 | Viewed by 1996
Abstract
Our method for density elimination is generalized to the non-commutative substructural logic GpsUL * . Then, the standard completeness of HpsUL * follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that HpsUL * is the [...] Read more.
Our method for density elimination is generalized to the non-commutative substructural logic GpsUL * . Then, the standard completeness of HpsUL * follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that HpsUL * is the logic of pseudo-uninorms and their residua and answered the question posed by Prof. Metcalfe, Olivetti, Gabbay and Tsinakis. Full article
(This article belongs to the Special Issue Mathematical Fuzzy Logic and Fuzzy Set Theory)
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7 pages, 245 KiB  
Article
Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics
by Sanmin Wang
Symmetry 2018, 10(12), 755; https://doi.org/10.3390/sym10120755 - 15 Dec 2018
Viewed by 2197
Abstract
Semilinear substructural logics UL ω and IUL ω are logics for finite UL and IUL -algebras, respectively. In this paper, the standard completeness of UL ω and IUL ω is proven by the method developed by Jenei, Montagna, Esteva, Gispert, Godo, and Wang. [...] Read more.
Semilinear substructural logics UL ω and IUL ω are logics for finite UL and IUL -algebras, respectively. In this paper, the standard completeness of UL ω and IUL ω is proven by the method developed by Jenei, Montagna, Esteva, Gispert, Godo, and Wang. This shows that UL ω and IUL ω are substructural fuzzy logics. Full article
(This article belongs to the Special Issue Mathematical Fuzzy Logic and Fuzzy Set Theory)
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