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Axioms
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Fuzzy Logic as the Foundation for Theories of Fuzzy Mathematical...
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Fuzzy Logic as the Foundation for Theories of Fuzzy Mathematical Structures

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: closed (10 August 2022) | Viewed by 10167
Please contact the Guest Editor or the Journal Editor for any queries about the scope, discount, submission procedure and publication process.

Special Issue Editors

Dr. Alexander Šostak

E-Mail Website
Guest Editor
1. Department of Mathematics, University of Latvia, LV-1004 Riga, Latvia
2. Institute of Mathematics and CS, University of Latvia, LV-1459 Riga, Latvia
Interests: general topology (cardinal invariants of topological spaces, extension of continuous mappings, theory of retracts and extensors, shapes, generalised metric spaces, compactness type properties); category theory; L-valued topological and algebraic structures; fuzzy sets; applications of fuzzy sets and fuzzy structures; many-valued logics
Dr. Michal Holcapek

E-Mail Website
Guest Editor
Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic
Interests: statistics; fuzzy modelling; algebra; theory of fuzzy sets; measure theory
Dr. Antonin Dvorak

E-Mail Website
Guest Editor
Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 701 03 Ostrava, Czech Republic
Interests: mathematical fuzzy logic; fuzzy inference systems; generalized and fuzzy quantifiers; aggregation operators on ordered structures
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fuzzy logic, initiated in 1965 by L.A. Zadeh, serves now as the basis for a broad field of modern science that can be unified as the theory and applications of fuzzy mathematical structures. In turn, now, more than 55 years after Zadeh's pioneering paper, fuzzy logic has evolved into a deep field of mathematics that has numerous applications in both theoretical mathematics and other fields of science. This Special Issue is dedicated to the 70th birthday and approximate 45th anniversary of the research activity in this field of the outstanding scientist Prof. Vilém Novák, whose contribution to fuzzy logic, both in the narrow and broad sense, is fundamental. The Guest Editors of this issue invite high-quality papers on fuzzy logic, both theoretical and applied, as well as papers on the various fields of fuzzy mathematical structures, where ideas, methods, and results of fuzzy logic are manifested.

Dr. Alexander Šostak
Dr. Michal Holcapek
Dr. Antonin Dvorak
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. Axioms 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

  • fuzzy logic
  • fuzzy topological and algebraic structures
  • fuzzy relations and fuzzy relational equations
  • fuzzy metrics
  • fuzzy categories
  • fuzzy transform and its applications
  • natural language processing methods using fuzzy logic

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Published Papers (4 papers)

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Research

9 pages, 369 KiB  
Article
Homogeneity of Complex Fuzzy Operations
by Bo Hu, Wei Wu and Songsong Dai
Axioms 2022, 11(6), 274; https://doi.org/10.3390/axioms11060274 - 6 Jun 2022
Viewed by 1798
Abstract
The homogeneity of binary functions on the unit interval [0, 1] is a very useful property in many real practical applications. This paper studies the homogeneity of binary functions on the unit circle of the complex plane. The homogeneity is a generalization of [...] Read more.
The homogeneity of binary functions on the unit interval [0, 1] is a very useful property in many real practical applications. This paper studies the homogeneity of binary functions on the unit circle of the complex plane. The homogeneity is a generalization of both rotational invariance and ratio scale invariance for complex fuzzy operations. We show that a binary function is homogeneous if and only if it is both rotationally invariant and ratio scale invariant. Moreover, we consider the simplification of the homogeneity for complex fuzzy binary operators. Full article
(This article belongs to the Special Issue Fuzzy Logic as the Foundation for Theories of Fuzzy Mathematical Structures)
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18 pages, 737 KiB  
Article
Generalization of Fuzzy Connectives
by Stefanos Makariadis and Basil Papadopoulos
Axioms 2022, 11(3), 130; https://doi.org/10.3390/axioms11030130 - 12 Mar 2022
Cited by 2 | Viewed by 2955
Abstract
This paper is centered around the creation of new fuzzy connectives using automorphism functions. The fuzzy connectives theory has been implemented in many problems and fields. In particular, the N-negations, t-norms, S-conorms and I-implications concepts played crucial roles in forming the theory and [...] Read more.
This paper is centered around the creation of new fuzzy connectives using automorphism functions. The fuzzy connectives theory has been implemented in many problems and fields. In particular, the N-negations, t-norms, S-conorms and I-implications concepts played crucial roles in forming the theory and applications of the fuzzy sets. Thus far, there are multiple strategies for producing fuzzy connectives. The purpose of this paper is to provide a new strategy that is more flexible and fast in comparison with the rest. In order to create this method, automorphism and additive generator functions were utilized. The general formulas created with this method can provide new fuzzy connectives. The main conclusion is that new fuzzy connectives can be created faster and with more flexibility with our strategy. Full article
(This article belongs to the Special Issue Fuzzy Logic as the Foundation for Theories of Fuzzy Mathematical Structures)
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15 pages, 806 KiB  
Article
Generalized Rough Sets via Quantum Implications on Quantum Logic
by Songsong Dai
Axioms 2022, 11(1), 2; https://doi.org/10.3390/axioms11010002 - 22 Dec 2021
Viewed by 2395
Abstract
This paper introduces some new concepts of rough approximations via five quantum implications satisfying Birkhoff–von Neumann condition. We first establish rough approximations via Sasaki implication and show the equivalence between distributivity of multiplication over join and some properties of rough approximations. We further [...] Read more.
This paper introduces some new concepts of rough approximations via five quantum implications satisfying Birkhoff–von Neumann condition. We first establish rough approximations via Sasaki implication and show the equivalence between distributivity of multiplication over join and some properties of rough approximations. We further establish rough approximations via other four quantum implication and examine their properties. Full article
(This article belongs to the Special Issue Fuzzy Logic as the Foundation for Theories of Fuzzy Mathematical Structures)
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16 pages, 353 KiB  
Article
Characterization of Transitivity in L-Tolerance Spaces by Convergence and Closure
by Gunther Jäger and T. M. G. Ahsanullah
Axioms 2021, 10(4), 268; https://doi.org/10.3390/axioms10040268 - 21 Oct 2021
Viewed by 1677
Abstract
We show that the category of quantale-valued tolerance spaces is isomorphic to a category of quantale-valued convergence spaces. We define suitable quantale-valued closure functions and use them to characterize transitivity axioms. Furthermore, transitivity is characterized by convergence and diagonal axioms. Quantale-valued tolerance relations [...] Read more.
We show that the category of quantale-valued tolerance spaces is isomorphic to a category of quantale-valued convergence spaces. We define suitable quantale-valued closure functions and use them to characterize transitivity axioms. Furthermore, transitivity is characterized by convergence and diagonal axioms. Quantale-valued tolerance relations compatible with group structures are also characterized by convergence and it is shown that they are transitive. Full article
(This article belongs to the Special Issue Fuzzy Logic as the Foundation for Theories of Fuzzy Mathematical Structures)
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