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Fuzzy Natural Logic in IFSA-EUSFLAT 2021
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Fuzzy Natural Logic in IFSA-EUSFLAT 2021

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 10149

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

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
Prof. Dr. Vilém Novák

E-Mail Website
Guest Editor
Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 702 00 Ostrava, Czech Republic
Interests: mathematical fuzzy logic and applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fuzzy natural logic (FNL) is a class of mathematical theories (theory of evaluative expressions, theory of fuzzy/linguistic IF-THEN rules and approximate reasoning based on them, theory of fuzzy generalized quantifiers and their syllogisms, models of natural human reasoning) with the goal of developing models of human thinking whose most characteristic feature is the use of natural language. 

The topics of the Special Issue include, but are not limited to:

  • development of various theories belonging to FNL,
  • fuzzy quantifiers,
  • generalized syllogisms,
  • square of opposition and its generalizations,
  • systems based on fuzzy/linguistic IF-THEN rules,
  • theory (and applications) of approximate reasoning,
  • higher-order fuzzy logics,
  • partial fuzzy logics,
  • linguistic theories of evaluative expressions and quantifiers,
  • applications of FNL in data mining, linguistics, decision making, learning, and elsewhere.

We will publish mainly extended versions of the papers presented at the IFSA-EUSFLAT 2021 conference, held in Bratislava. We expect to receive at least 50% of new content for extended conference papers. However, we will also accept submissions of topic-related papers from outside of this conference. Linguistically or philosophically oriented papers are also welcome.

Dr. Antonin Dvorak
Prof. Dr. Vilém Novák
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. 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.

Keywords

  • fuzzy natural logic
  • generalized (fuzzy) quantifiers
  • fuzzy IF-THEN rules
  • approximate reasoning
  • mathematical fuzzy logic

Published Papers (6 papers)

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Editorial

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3 pages, 173 KiB  
Editorial
Preface to the Special Issue on “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”
by Vilém Novák and Antonín Dvořák
Mathematics 2022, 10(22), 4393; https://doi.org/10.3390/math10224393 - 21 Nov 2022
Viewed by 883
Abstract
In [...] Full article
(This article belongs to the Special Issue Fuzzy Natural Logic in IFSA-EUSFLAT 2021)

Research

Jump to: Editorial

31 pages, 1877 KiB  
Article
An Evolving Fuzzy Neural Network Based on Or-Type Logic Neurons for Identifying and Extracting Knowledge in Auction Fraud
by Paulo Vitor de Campos Souza, Edwin Lughofer, Huoston Rodrigues Batista and Augusto Junio Guimaraes
Mathematics 2022, 10(20), 3872; https://doi.org/10.3390/math10203872 - 18 Oct 2022
Cited by 1 | Viewed by 1614
Abstract
The rise in online transactions for purchasing goods and services can benefit the parties involved. However, it also creates uncertainty and the possibility of fraud-related threats. This work aims to explore and extract knowledge of auction fraud by using an innovative evolving fuzzy [...] Read more.
The rise in online transactions for purchasing goods and services can benefit the parties involved. However, it also creates uncertainty and the possibility of fraud-related threats. This work aims to explore and extract knowledge of auction fraud by using an innovative evolving fuzzy neural network model based on logic neurons. This model uses a fuzzification technique based on empirical data analysis operators in an evolving way for stream samples. In order to evaluate the applied model, state-of-the-art neuro-fuzzy models were used to compare a public dataset on the topic and, simultaneously, validate the interpretability results based on a common criterion to identify the correct patterns present in the dataset. The fuzzy rules and the interpretability criteria demonstrate the model’s ability to extract knowledge. The results of the model proposed in this paper are superior to the other models evaluated (close to 98.50% accuracy) in the test. Full article
(This article belongs to the Special Issue Fuzzy Natural Logic in IFSA-EUSFLAT 2021)
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26 pages, 377 KiB  
Article
Preimage Problem Inspired by the F-Transform
by Jiří Janeček and Irina Perfilieva
Mathematics 2022, 10(17), 3209; https://doi.org/10.3390/math10173209 - 05 Sep 2022
Cited by 4 | Viewed by 1447
Abstract
In this article, we focus on discrete data processing. We propose to use the concept of closeness, which is less restrictive than a metric, to describe a certain relationship between objects. We establish a fuzzy partition of a given set of objects in [...] Read more.
In this article, we focus on discrete data processing. We propose to use the concept of closeness, which is less restrictive than a metric, to describe a certain relationship between objects. We establish a fuzzy partition of a given set of objects in a way that admits a closeness space to emerge. The fuzzy (F-) transform is a tool that maps objects with common characteristics to the same discrete image—the direct F-transform. We are interested in the inverse (preimage) problem: How can we describe the class of all functions mapped onto the same direct F-transform? In this manuscript, we focus on this preimage problem, formulated accordingly. Its solution is presented from three different points of view and shows which functions belong to the same class determined by a given image (by the direct F-transform). Conditions under which a solution to the preimage problem is given by the inverse F-transform over the same fuzzy partition, or by transforming a given image using a new system of basic functions, are formulated. The developed theory contributes to a better understanding of ill-posed problems that are typical for machine learning. The appendix contains illustrative numerical examples. Full article
(This article belongs to the Special Issue Fuzzy Natural Logic in IFSA-EUSFLAT 2021)
24 pages, 738 KiB  
Article
Describing Linguistic Vagueness of Evaluative Expressions Using Fuzzy Natural Logic and Linguistic Constraints
by Adrià Torrens-Urrutia, Vilém Novák and María Dolores Jiménez-López
Mathematics 2022, 10(15), 2760; https://doi.org/10.3390/math10152760 - 03 Aug 2022
Cited by 8 | Viewed by 1956
Abstract
In recent years, the study of evaluative linguistic expressions has crossed the field of theoretical linguistics and has aroused interest in very different research areas such as artificial intelligence, psychology or cognitive linguistics. The interest in this type of expressions may be due [...] Read more.
In recent years, the study of evaluative linguistic expressions has crossed the field of theoretical linguistics and has aroused interest in very different research areas such as artificial intelligence, psychology or cognitive linguistics. The interest in this type of expressions may be due to its relevance in applications such as opinion mining or sentiment analysis. This paper brings together Fuzzy Natural Logic and Fuzzy Property Grammars to approach evaluative expressions. Our contribution includes the marriage of mathematical and linguistic methods for providing a formalism to deal with the linguistic vagueness of evaluative expressions by describing the syntax and semantics of these structures. We contribute to the study of evaluative linguistic expressions by proposing a formal characterization of them where the concepts of semantic prime, borderline evaluative expressions and markedness are defined and where the relation between the semantic constraints of evaluations and their sentiment can be established. A proof-of-concept of how to create a lexicon of evaluative expressions for future computational applications is presented. The results demonstrate that linguistic evaluative expressions are gradient, have sentiment, and that the evaluations work as a relation of hypernym and hyponym, the hypernym being a semantic prime. Our findings provide the basis for building an ontology of evaluative expressions for future computational applications. Full article
(This article belongs to the Special Issue Fuzzy Natural Logic in IFSA-EUSFLAT 2021)
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23 pages, 694 KiB  
Article
A Fuzzy Grammar for Evaluating Universality and Complexity in Natural Language
by Adrià Torrens-Urrutia, María Dolores Jiménez-López, Antoni Brosa-Rodríguez and David Adamczyk
Mathematics 2022, 10(15), 2602; https://doi.org/10.3390/math10152602 - 26 Jul 2022
Cited by 5 | Viewed by 1519
Abstract
The paper focuses on linguistic complexity and language universals, which are two important and controversial issues in language research. A Fuzzy Property Grammar for determining the degree of universality and complexity of a natural language is introduced. In this task, the Fuzzy Property [...] Read more.
The paper focuses on linguistic complexity and language universals, which are two important and controversial issues in language research. A Fuzzy Property Grammar for determining the degree of universality and complexity of a natural language is introduced. In this task, the Fuzzy Property Grammar operated only with syntactic constraints. Fuzzy Natural Logic sets the fundamentals to express the notions of universality and complexity as evaluative expressions. The Fuzzy Property Grammar computes the constraints in terms of weights of universality and calculates relative complexity. We present a proof-of-concept in which we have generated a grammar with 42B syntactic constraints. The model classifies constraints in terms of low, medium, and high universality and complexity. Degrees of relative complexity in terms of similarity from a correlation matrix have been obtained. The results show that the architecture of a Universal Fuzzy Property Grammar is flexible, reusable, and re-trainable, and it can easily take into account new sets of languages, perfecting the degree of universality and complexity of the linguistic constraints as well as the degree of complexity between languages. Full article
(This article belongs to the Special Issue Fuzzy Natural Logic in IFSA-EUSFLAT 2021)
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27 pages, 355 KiB  
Article
A Formal Analysis of Generalized Peterson’s Syllogisms Related to Graded Peterson’s Cube
by Karel Fiala and Petra Murinová
Mathematics 2022, 10(6), 906; https://doi.org/10.3390/math10060906 - 11 Mar 2022
Cited by 1 | Viewed by 1618
Abstract
This publication builds on previous publications in which we constructed syntactic proofs of fuzzy Peterson’s syllogisms related to the graded square of opposition. The aim of the publication is to be formally able to find syntactic proofs of fuzzy Peterson’s logical syllogisms with [...] Read more.
This publication builds on previous publications in which we constructed syntactic proofs of fuzzy Peterson’s syllogisms related to the graded square of opposition. The aim of the publication is to be formally able to find syntactic proofs of fuzzy Peterson’s logical syllogisms with forms of fuzzy intermediate quantifiers that design the graded Peterson’s cube of opposition. Full article
(This article belongs to the Special Issue Fuzzy Natural Logic in IFSA-EUSFLAT 2021)
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