Article
Computer Science, Artificial Intelligence
Vilem Novak, Petra Murinova, Petr Ferbas
Summary: This paper investigates generalized Peterson's syllogisms with intermediate quantifiers and presents two types of results. Firstly, it shows that all the valid syllogisms can be derived from two inequalities and one equality at the semantic level. Secondly, the paper formalizes Peterson's rules and demonstrates that all the valid syllogisms with intermediate quantifiers indeed satisfy these rules.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2022)
Article
Computer Science, Theory & Methods
Nicolas Madrid, Manuel Ojeda-Aciego
Summary: This paper continues the research on the properties of the f-indexes of inclusion and contradiction, and specifically demonstrates the relationship between the two concepts through the reformulated Aristotelian square of opposition.
FUZZY SETS AND SYSTEMS
(2024)
Article
Mathematics, Applied
Hans Smessaert, Lorenz Demey
Summary: In this paper, we investigate the interaction between the square of opposition for Aristotelian quantifiers and the square of opposition generated by the proportional quantifier 'most'. We first analyze the squares independently using bitstring semantics, where 'most' yields a tripartition while the degenerate square for 'all' in FOL yields a quadripartition. Then, we combine these two squares to form an unattested octagon of opposition in logical geometry. Finally, by switching to a logical system with existential import, we reduce the bitstring semantics of the octagon to a pentapartition.
Article
Computer Science, Artificial Intelligence
Stefania Boffa, Petra Murinova, Vilem Novak
Summary: This article focuses on the application of quantifier-based operators in fuzzy concept lattices and Aristotle's square, highlighting the new connections between evaluative linguistic expressions, fuzzy formal concept analysis, and Aristotle's square studies.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2021)
Article
Computer Science, Artificial Intelligence
Vilem Novak, Petra Murinova
Summary: This paper continues the previous work on analyzing Peterson's rules for checking the validity of classical syllogisms and their extension for syllogisms with intermediate quantifiers. It formalizes the rules and proves that only four rules are sufficient. It also proves that a syllogism is valid if and only if it satisfies all four (and consequently all six) extended Peterson's rules.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2023)
Article
Computer Science, Artificial Intelligence
Stefania Boffa, Petra Murinova, Vilem Novak, Petr Ferbas
Summary: This article introduces a method of constructing extended fuzzy concept lattices and opposition forms using special fuzzy quantifier-based operators, and extends this method by organizing more general structures of opposition.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2022)
Article
Computer Science, Theory & Methods
Lingqiang Li, Qiu Jin
Summary: In this paper, a lattice-valued category TNG (TTNG) of (topological) T-neighborhood groups is presented, where the object is a group equipped with a (topological) T-neighborhood space such that the group operations are continuous with respect to the (topological) T-neighborhood space. The category TNG is studied to obtain results regarding its properties, structure, and embedding into other categories.
FUZZY SETS AND SYSTEMS
(2022)
Article
Mathematics, Applied
Stef Frijters, Lorenz Demey
Summary: In this paper, the authors introduce and study AD-logic, a system of modal logic used for reasoning about Aristotelian diagrams. They establish a sound and complete axiomatization for AD-logic and show a bijection between finite Aristotelian diagrams and finite AD-frames. Furthermore, they demonstrate how AD-logic can express various insights about Aristotelian diagrams and generate new and interesting diagrams.
Article
Logic
Alexander De Klerck, Leander Vignero, Lorenz Demey
Summary: In this paper, the study of Aristotelian diagrams in logical geometry is formalized using category theory. Different categories are built and evaluated based on their ability to generalize previous work and their category-theoretical properties. The most promising category is identified, which can significantly enhance further research effectiveness in logical geometry.
LOGICA UNIVERSALIS
(2023)
Article
Mathematics
Karel Fiala, Petra Murinova
Summary: This publication presents syntactic proofs of fuzzy Peterson's logical syllogisms related to the graded square of opposition, and aims to formally find these proofs using fuzzy intermediate quantifiers to design the graded Peterson's cube of opposition.
Article
Computer Science, Artificial Intelligence
Ahmad Nor Kasruddin Nasir, Ahmad Azwan Abdul Razak
Summary: This paper presents two variants of the Opposition-based Spiral Dynamic Algorithm (ObSDA) and applies them to optimize a type-2 fuzzy logic controller for an inverted pendulum system. The results show that the ObSDA variants outperform the original SDA in locating the theoretical optima solution and improving the accuracy in the control problem.
EXPERT SYSTEMS WITH APPLICATIONS
(2022)
Article
Computer Science, Artificial Intelligence
Yinsheng Zhang
Summary: The paper uncovers three unsolved problems with Aristotelian categorical propositions and offers solutions through reforming the form of propositions. These efforts aim to incorporate modern logic into traditional proposition and predicate logic, enabling more accurate and ubiquitous representation and computation of the reformed propositions.
JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING
(2022)
Article
Computer Science, Artificial Intelligence
Angelo Gaeta
Summary: The paper proposes using set-theoretic measures to define and adopt structures of opposition and evaluate emotional dynamics in conversations on social media. A graded hexagon of opposition is used to compare emotional profiles, with set-theoretic measures constructing the hexagon and analyzing the conversation's tendency towards empathy or lack thereof. These results are important for social media providers to receive early warnings about emotional dynamics that may lead to information disorder, and have been evaluated using conversations from the Empathetic Dialogue dataset.
Article
Mathematics, Applied
Lorenz Demey
Summary: This paper examines Aristotelian diagrams for non-normal systems of modal logic and discusses the phenomenon of logic-sensitivity, providing examples of different types of logic-sensitivity in the realm of normal modal logic. Subtle examples of Aristotelian diagrams are also discussed, which exhibit high logic-sensitivity in non-normal systems of modal logic despite being insensitive in normal modal logics.
Article
Mathematics, Applied
Oscar Castillo, Juan R. Castro, Patricia Melin
Summary: This article presents an intelligent system that uses type-3 fuzzy logic for automated image quality tuning in televisions. By utilizing interval type-3 fuzzy logic, the system automates the tuning process on production lines and achieves the best image quality.
Article
Computer Science, Theory & Methods
Irina Perfilieva, Shokrollah Ziari, Rahele Nuraei, Thi Minh Tam Pham
Summary: The proposed approach uses the F-transform to construct an operational matrix for solving the Volterra integral equation. The transformed form of the equation reduces to a system of linear equations with a triangular matrix, making the numerical method efficient and low computational. The paper provides proofs of convergence, estimation of computational complexity, and compares the results with other methods using test cases.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Yongliang Yang, Guilong Liu, Qing Li, Choon Ki Ahn
Summary: This paper proposes a novel type of Nussbaum function to handle the feedback control design problem with multiple unknown time-varying control coefficients. By separately compensating the unknown control coefficients and combining with the fixed-time stability theory, the issue of mutual cancellation is resolved and Lyapunov stability analysis becomes feasible. The theoretical discussions and simulation experiments demonstrate the effectiveness of the presented design for continuous-time stochastic nonlinear dynamical systems.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Yingfang Li, Xingxing He, Dan Meng, Keyun Qin
Summary: This paper presents an improved method for estimating the similarity between LR-type fuzzy numbers and compares it with existing methods. The proposed method overcomes the shortcomings of existing methods by considering the shape of LR-type fuzzy numbers.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Tong Kang, Leifan Yan, Long Ye, Jun Li
Summary: This note solves an open problem proposed in the paper Kang et al. (2023) [9] by demonstrating the linearity of set-valued pan-integrals based on a fuzzy measure and the operations pair (+, center dot) through the subadditivity of the fuzzy measure. It also provides an example to show the necessity of the subadditivity condition for the linearity of set-valued pan-integrals. Furthermore, it introduces the pan-integral of set-valued functions based on a fuzzy measure and pan-operations pair (circle plus, circle times).
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Marzieh Shamsizadeh, Mohammad Mehdi Zahedi, Mohamad Javad Agheli Goki
Summary: In this paper, we study a new generalization for the notion of fuzzy automata, called hesitant L-fuzzy automaton (HLFA). The mathematics framework for the theory of HLFA is presented. Moreover, the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA are introduced. Additionally, a minimal complete accessible deterministic hesitant L-fuzzy automaton is presented for recognizing any hesitant L-fuzzy language, and an algorithm is proposed to determine the states of the minimal hesitant L-fuzzy automaton along with its time complexity.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
S. O. Mashchenko
Summary: This paper investigates a fuzzy matrix game with fuzzy sets of player strategies and proposes a method to construct a game value using Zadeh's extension principle and the approach to fuzzy matrix games. It is proved that the fuzzy sets of players strategies in a fuzzy matrix game generate a game value in the form of a type-2 fuzzy set on the real line.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Gustave Bainier, Benoit Marx, Jean-Christophe Ponsart
Summary: The Nonlinear Sector Approach (NLSA) is a method to construct Takagi-Sugeno (T-S) models that precisely represent nonlinear systems with bounded nonlinearities. This paper generalizes the NLSA to polytopic and smooth convex bounding sets, providing new ways to reduce the conservatism of TS representations with interdependent scheduling parameters. Various Linear Matrix Inequalities (LMI) criteria are also provided for stability analysis of these models.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Mi Zhou, Ya-Jing Zhou, Jian-Bo Yang, Jian Wu
Summary: This study proposes a new dissimilarity measure for basic probability assignments (BPAs) in the Dempster-Shafer evidence structure, considering both distance measure and conflict belief. Comparative analysis demonstrates the applicability and validity of the proposed measure, which is further applied to multi-source data fusion and large-scale group decision making.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Nicolas Madrid, Manuel Ojeda-Aciego
Summary: This paper continues the research on the properties of the f-indexes of inclusion and contradiction, and specifically demonstrates the relationship between the two concepts through the reformulated Aristotelian square of opposition.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Hanbiao Yang, Zhongqiang Yang, Taihe Fan, Lin Yang
Summary: This paper discusses the topological structures on fuzzy numbers and their related sets, and investigates the continuity of weighted mean maps with respect to these structures. An application of the results is provided, demonstrating their practical significance.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Narayan Choudhary, S. P. Tiwari, Shailendra Singh
Summary: This paper studies different compositions of (L-fuzzy) automata using category theory and introduces four different categories for the study. It shows that each category has specific properties and advances the existing categories in the field. The monoidal description of these categories enriches the fuzzy automata theory.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Lifeng Li, Qinjun Luo
Summary: In this study, we investigate monotone comparative statics under interval uncertainty. We introduce interval-valued supermodular functions and interval-valued quasisupermodular functions with respect to a partial order relation on intervals. Moreover, we derive some sufficient conditions for monotone comparative statics under interval uncertainty. We also apply these results to analyze the monotone comparative statics of interval games with strategic complements.
FUZZY SETS AND SYSTEMS
(2024)
