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Explicit formulas for t-conorms constructed by the sum of ranges of discrete additive generators of t-conorms Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-04-08 Peter Viceník
Explicit formulas for t-conorms constructed by the sum of ranges of discrete additive generators of t-conorms are introduced.
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Updating information based on generalized credal sets. Part 2: General case Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-04-08 Andrey G. Bronevich, Igor N. Rozenberg
In the first part of this paper, we have considered: a) generalized credal sets on the powerset of a finite set ; b) their general definition allowing a generalized credal set to be not convex; c) the justification of basic aggregation rules on generalized credal sets; d) ways of updating information. The second part is devoted to the solutions of the above problems for the general case, when generalized
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Model checking fuzzy computation tree logic of multi-agent systems based on fuzzy interpreted systems Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-04-08 Zhanyou Ma, Xia Li, Ziyuan Liu, Ruiqi Huang, Nana He
Effective communication among autonomous agents is crucial for coordination and solving complex tasks within multi-agent systems. To formalize interactions between agents, social accessibility relations are often utilized. Current research employs model checking algorithms to verificate social commitment properties in multi-agent systems. In fuzzy multi-agent systems, direct quantification and computation
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A unified framework of fuzzy implications and coimplications Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-29 Yifan Zhao, Hua-Wen Liu
Fuzzy implications and coimplications play important roles in both theoretic and applied communities of fuzzy set theory. In this paper, we provide a unified framework for fuzzy implications and coimplications. Specifically, firstly, we introduce the concept of uni-implications, which is the unification of fuzzy implications and coimplications, and describe the structure of uni-implications. Secondly
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Pseudo-moment generating functions: Application to pseudo-Schur constant random vectors Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-29 Sabrina Mulinacci, Massimo Ricci
In this note we show that pseudo-analysis tools can be effective in obtaining results in a distorted probability framework. More precisely, we introduce the notion of pseudo-independence and that of pseudo-moment generating function, the latter representing a generalization of the pseudo-Laplace transform, and both aiming at extending the corresponding notions in the usual probabilistic context. We
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The Craig interpolation property in first-order Gödel logic Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-28 N.R. Tavana, M. Pourmahdian, S.M.A. Khatami
In this article, a model-theoretic approach is proposed to prove that the first-order Gödel logic, , as well as its extension associated with first-order relational languages enjoy the Craig interpolation property. These results partially provide an affirmative answer to a question posed in .
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Two dimensional fuzzy context-free languages and tiling patterns Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-28 A. John Kaspar, D.K. Sheena Christy, V. Masilamani, D.G. Thomas
Fuzzy context-free languages are powerful compared to fuzzy regular languages as they are generated by fuzzy context-free grammars and fuzzy pushdown automata, which follow an enhanced computational mechanism. A two dimensional language (picture language) is a collection of two dimensional words, which are a rectangular array of symbols made up of finite alphabets. Two dimensional automata can recognize
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On state monadic MV-algebras Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-28 Pengfei He, Ya Wei, Juntao Wang
Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. In this paper, we extend monadic MV-algebras with a state operator that describes algebraic properties of states. The resulting variety of algebras will be called state monadic MV-algebras. First, we introduce state monadic MV-algebras and
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Approximate weak simulations and bisimulations for fuzzy automata over the product structure Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-28 Ivana Micić, Miroslav Ćirić, Jelena Matejić, Stefan Stanimirović, Linh Anh Nguyen
In this article, we modify the product structure and turn it into the so-called -truncated product structure , for any . The new structure keeps the property of being a complete residuated lattice, and additionally, its semiring reduct is locally finite. We convert each fuzzy automaton over the product structure into a fuzzy automaton over , and accordingly, we turn the problems of testing the existence
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A special fuzzy star-shaped number space with the sendograph metric Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-24 Wenjuan Liu, Dongming Liu
As a natural generalization of fuzzy numbers, fuzzy star-shaped numbers play a crucial role in fuzzy mathematics. Let be a non-degenerate compact convex subset of the -dimensional Euclidean space, and let be the family consisting of all fuzzy star-shaped numbers with respect to whose supports contained in . Using methods from infinite-dimensional topology, we mainly show that the space with the topology
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Distorted copulas Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-21 Roberto Ghiselli Ricci
In this paper, we deal with the problem of preserving the copula property by means of a transformation called distortion where automorphisms of the real unit interval are involved. A new methodological approach is followed by resorting to a special branch of group theory. The crucial role of absolute continuity of one-dimensional sections of a distorted copula is illustrated. Some necessary and sufficient
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Construction of fuzzy classification systems by fitness sharing based genetic search and boosting based ensemble Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-20 Jidong Li, Xuejie Zhang
This paper concentrates on the development of precise fuzzy rule-based classification systems for high-dimensional and multi-class problems. The approach begins with the extraction on potential fuzzy if-then rules using fitness sharing based genetic algorithms, this ensures effective searching for productive niches, thereby evolving and maintaining a diverse, cooperative population. Subsequently, for
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Generating methods of some classes of fuzzy implications obtained by unary functions and algebraic structures Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-20 Isabel Aguiló, Vikash Kumar Gupta, Balasubramaniam Jayaram, Sebastia Massanet, Juan Vicente Riera, Nageswara Rao Vemuri
The existing generating methods of fuzzy implications are closed in the set of all fuzzy implications, but not when applied to some families of these operators. In this paper, some binary operations are defined on some well-established families of fuzzy implications. Namely, the families of -implications with continuous t-conorms, -implications obtained from continuous t-norms, Yager's - and -generated
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Onion lattices and an answer to an open problem on convolution lattices Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-18 Xufeng Zhang, Aiping Wang
We develop a new class of lattices called Onion lattices, analyse the properties of Onion lattices and further prove that the set of idempotent lattice functions on a bounded lattice is closed under convolution operations if and only if is an Onion lattice. This solves the second open problem posed by De Miguel, Bustince and De Baets (2018) . Furthermore, we study in depth the lattice function algebraic
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Separable programming problem with bipolar max-T fuzzy relation equation constraints Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-18 Ali Abbasi Molai
One of the most important classes of nonlinear programming problems is separable programming problem due to its applications in theory and practice. This paper studies this class of the problems subject to a system of bipolar fuzzy relation equations using the max-T composition operator, where T is a continuous and Archimedean t-norm. Its feasible solution set structure is determined by two vectors
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Existence of solutions to a class of interval-valued differential equation with impulses relative to length constraints Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-18 Hongzhou Wang, Rosana Rodríguez-López, Alireza Khastan
This paper provides a new model framework to study interval-valued dynamical systems with length constraints. We use impulses instead of switching points to control the length of solutions to interval-valued differential equation under -differentiability. Firstly, we consider a class of interval-valued differential equation with impulses. Then, we study interval-valued differential equation with impulses
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Closure operators constructed by logical operations on bounded lattices Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-16 M. Nesibe Kesicioğlu, Ece Kürkçü Çakar
In this paper, closure operators obtained from functions having some properties on bounded lattices are defined. By this way, it is aimed to generalize the notions and -closure operators obtained from t-norms and uninorms, respectively. The relationships between the closure operators obtained from functions and their conjugacies (dual functions) are determined. In special cases, the closure operators
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Stochastic monotone wing property: A new dependence structure for copulas Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-16 Rosy Oh, Jae Youn Ahn
In this study, we introduce a novel concept of a copula dependence structure termed the stochastic monotone wing property and investigate its associated properties. This concept is closely related to the monotone conditional variance property, which describes the behavior of the conditional variance of given as either an increasing or a decreasing function of for a given random vector with a certain
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Wasserstein distance for OWA operators Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-16 István Á. Harmati, Lucian Coroianu, Robert Fullér
We suggest a distance measure for OWA operators. First we associate an OWA operator with a unique regular increasing monotone quantifier and then define the distance between two OWA operators as the Wasserstein-1 distance between their associated quantifiers.
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New results on synchronization control of memristor-based quaternion-valued fuzzy neural networks with delayed impulses Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-15 Ningning Zhao, Yuanhua Qiao, Chuanqing Xu
A model of memristor-based quaternion-valued fuzzy neural networks (MQVFNNs) with delayed impulses and time-varying delays is established, and the synchronization issue is investigated in this paper. Firstly, to avoid non-commutativity, the MQVFNNs are decomposed into real-valued delayed impulsive neural networks. Secondly, a novel lemma for delayed impulsive system is introduced based on Halanay differential
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Linear optimization over the approximate solutions of a system of max-min equations Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-15 Pingke Li
When a system of max-min equations is inconsistent, which is frequently encountered in modelling with fuzzy relations, the approximate solutions may be considered instead within an admissible error bound. This paper tackles the linear optimization problem over the approximate solutions with respect to the and the residual error, respectively. It demonstrates that such an optimization problem can be
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n-roots on MV-algebras Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-13 A. Dvurečenskij, O. Zahiri, M. Shenavaei, R.A. Borzooei
We introduce and investigate -roots in the context of MV-algebras as a generalization of square roots introduced in . We outline their main properties and establish that the class of MV-algebras with -roots, , forms a variety. Next, we introduce the concept of strict -roots and demonstrate an equivalence between and the class of -divisible unital -groups. It helped us to show that each MV-algebra with
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Localization relations Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-13 D. Boixader, J. Recasens
Localization Relations are symmetric and -transitive fuzzy relations that are representable as suprema of conjunctions of fuzzy subsets. This paper shows that not all symmetric and -transitive fuzzy relations may be obtained in such way, provides an easy condition for characterizing those that may, and states a representation theorem for this class of relations. The logical and geometric implications
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Analysis of smooth and enhanced smooth quadrature-inspired generalized Choquet integral Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-04 Paweł Karczmarek, Adam Gregosiewicz, Zbigniew A. Łagodowski, Michał Dolecki, Łukasz Gałka, Paweł Powroźnik, Witold Pedrycz, Kamil Jonak
Enhancing the ability to make informed decisions stands as a significant challenge in modern IT. Specifically, there is a growing need to improve the efficiency of classification algorithms. When faced with multiple results derived from various methods, one can select the most probable decision using a robust aggregation operator. A common class of algorithms employed for this purpose is based on extensions
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Fixed/predefined-time projective synchronization for a class of fuzzy inertial discontinuous neural networks with distributed delays Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-02 Jing Han, Guici Chen, Guodong Zhang, Junhao Hu
In this article, fixed-time projective synchronization (FTPS) and predefined-time projective synchronization (PTPS) for a class of discontinuous fuzzy inertial neural networks (FINNs) with distributed delays are considered. To this end, regarding differential inclusion theories and the Lyapunov stability method, more precise and improved setting times of FTPS are systematically constructed. Furthermore
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A strengthening of Jensen's inequality for asymmetric Choquet integral Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-03-01 Hamzeh Agahi
Recently, Zhang et al. (2022) , (2023) proposed some Jensen's inequalities for asymmetric Choquet integral. Then Wang (2023) investigated some refinements of Jensen's inequalities for Choquet integral. In this paper, sharp inequalities related to Jensen for asymmetric Choquet integral are studied. Our results have many benefits such as applicability, simplicity, easy to use and require only knowledge
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Nonfragile switched sampled-data control for ship electric propulsion systems with stochastic actuator failures: A dual-sided looped fuzzy Lyapunov functional Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-29 Xiaoqing Li, Kun She, Kaibo Shi, Jun Cheng, Shouming Zhong, Zhinan Peng
In this article, by incorporating with the skills of fuzzy modeling method and fuzzy switching control technique, the nonfragile sampled-data control (SDC) synthesis problem for the ship electric propulsion systems (SEPSs) with lag transmission signal and stochastic actuator failures (SAFs) has been addressed. Firstly, to delineate the SAFs, the control input model is incorporated with semi-Markovian
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A two-way accelerator for feature selection using a monotonic fuzzy conditional entropy Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-29 Yanyan Yang, Degang Chen, Zhenyan Ji, Xiao Zhang, Lianjie Dong
Fuzzy rough set is a highly effective mathematical method for feature selection, which offers clear interpretability without expert knowledge. However, most of fuzzy-rough feature selection methods are to rely on all samples and candidate features during the selection of a best feature at each iteration. This often shares high computation complexity and is inefficient for large datasets. Therefore
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Sliding mode control for discrete interval type-2 fuzzy semi-Markov jump models with delay in controller mode switching Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-28 Runkun Li, Wenhai Qi, Ju H. Park, Jun Cheng, Kaibo Shi
The problem of asynchronous sliding mode control (SMC) for discrete nonlinear semi-Markov jump models is investigated by the semi-Markov kernel strategy, where asynchronous mechanism means that there is a one-step delay in the controller mode switching related to the system mode. Unlike traditional T-S fuzzy model, the interval type-2 fuzzy model is applied to represent discrete semi-Markov jump systems
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Fixed-time synchronization of discontinuous fuzzy competitive neural networks via quantized control Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-23 Caicai Zheng, Juan Yu, Fanchao Kong, Cheng Hu
This article concentrates on fixed-time synchronization for discontinuous fuzzy competitive neural networks including time-varying delays. Firstly, to cut down the signal transmission cost, two kinds of nontrivial control strategies, namely quantized control protocols without the linear part, are developed to investigate fixed-time synchronization of discontinuous fuzzy competitive neural networks
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Generalized cycle connectivity in fuzzy graphs Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-19 Aswathi Prabhath, Sunil Mathew, J.N. Mordeson
Cyclic flow is a very crucial concept in most interconnection networks. The cycle connectivity of a network allows one to identify the cyclic flow and hence determine its cyclic reachability. The cycle connectivity of a fuzzy graph depends on the strengths of all strong cycles in the graph. In this paper, we discuss generalized cycle connectivity of fuzzy graphs, which takes into account the strength
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Monometrics on betweenness sets: A general construction Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-15 Kavit Nanavati
Recently, the study of monometrics on betweenness relations has gathered impetus, with their applications ranging from rationalisation of ranking rules to penalty-based aggregation. The main challenge herein is to find a monometric with respect to the considered betweenness relation. While methods to generate monometrics on specific betweenness relations are known, no research has been done to investigate
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On the handling of inconsistent systems of max-min fuzzy relational equations Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-15 Ismaïl Baaj
In this article, we study the inconsistency of systems of max-min fuzzy relational equations. We first compute by an explicit analytical formula the Chebyshev distance (defined by the L-infinity norm) between the second member of an inconsistent system and the set of second members of consistent systems defined with the same matrix: that of the inconsistent system. Then we study the set of Chebyshev
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A formalization of constraint interval: A precussor to fuzzy interval analysis Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-13 Marina T. Mizukoshi, Tiago M. Costa, Yurilev Chalco-Cano, Weldon A. Lodwick
This presentation outlines some aspects of interval analysis from the constraint interval point of view, focusing on some issues associated with mathematical analysis, especially those that are fundamental to fuzzy mathematical analysis. We begin by reviewing interval representations from the standard interval point of view and the study of intervals as functions of parameters varying in hypercubes
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Inferring from an imprecise Plackett–Luce model: Application to label ranking Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-13 Loïc Adam, Arthur Van Camp, Sébastien Destercke, Benjamin Quost
The Plackett–Luce model is a popular parametric probabilistic model to define distributions between rankings of objects, modelling for instance observed preferences of users or ranked performances of algorithms. Since such observations may be scarce (users may provide partial preferences, or not all algorithms are run for a given experiment), it may be useful to consider the case where the parameters
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The fuzzy degree of nondensifiability and applications Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-09 G. García, G. Mora
We introduce the notion of fuzzy degree of nondensifiability (FDND for short) as a non-negative real number that measures the Hausdorff distance between a bounded set of a fuzzy metric space and its closest Peano continuum. The FDND allows us to analyze the precompact subsets of a fuzzy metric space. In fact, we present a characterization of the family of precompact and arc-connected subsets in terms
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The median under orness Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-08 István Á. Harmati, Lucian Coroianu, Robert Fullér
Besides the mean, the median is the most widely used single-valued descriptor of data sets. It is well-known that the orness level of the median operator is 1/2. In this paper we provide approximations of the median operator under a given level of orness. We find the exact optimal weighting vector for the 1-norm approximation problem in all conceivable cases and for 2-norm approximation up to nine
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Uninorms on bounded trellises Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-07 Yu Kong, Bin Zhao
In this paper, we construct uninorms on a bounded trellis based on t-(co)norms on a -semi-trellis and closure (interior) operators. The key is how to ensure the monotonicity of the constructed binary operation, which is closely related to the neutral element. We propose the uninorms on bounded trellises and study some basic properties. Specially, the neutral element must be middle-transitive if there
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Minimizing fuzzy interpretations in fuzzy description logics by using crisp bisimulations Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-06 Linh Anh Nguyen
The problem of minimizing finite fuzzy interpretations in fuzzy description logics (FDLs) is worth studying. For example, the structure of a fuzzy/weighted social network can be treated as a fuzzy interpretation in FDLs, where actors are individuals and actions are roles. Minimizing the structure of a fuzzy/weighted social network makes it more compact, thus making network analysis tasks more efficient
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Online sequential type-2 fuzzy wavelet extreme learning machine: A nonlinear observer application Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-06 Mohammadreza Esmaeilidehkordi, Maryam Zekri, Iman Izadi, Farid Sheikholeslam
The aim of this paper is to combine the time-frequency attributes of wavelets and neural network learning ability besides approximate reasoning features of type 2- fuzzy systems, and the advantages of online sequential extreme learning machine (one-pass learning and valid generalization achievement with extremely fast learning) in order to present a new effective algorithm in many applications. The
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A new approach to the fractional Abel k−integral equations and linear fractional differential equations in a fuzzy environment Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-06 Ngo Van Hoa, Tofigh Allahviranloo, Witold Pedrycz
This paper introduces some recent approaches to the fuzzy fractional Abel integral equations with respect to another function, which is called the fuzzy fractional Abel − integral equations. The problem proposed here allows for the interpolation of different types of fuzzy classical fractional Abel integral equations, and the solvability of each type of integral equation is also discussed. Additionally
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A note on representations of the Choquet integral via bases and transforms Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-05 Michał Boczek, Ondrej Hutník, Miriam Kleinová
In this note, we discuss the validity of formula (4.54) in Grabisch's book from 2016. This equation expresses the Choquet integral of nonnegative functions w.r.t. a game in the form of linear invertible transform of set functions. However, the formula (erroneously) excludes the empty set, which has consequences for deriving Choquet integral representations in the literature using this approach. We
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Modal reduction principles across relational semantics Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-05 Willem Conradie, Andrea De Domenico, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere, Daira Pinto Prieto, Apostolos Tzimoulis
The present paper establishes systematic connections among the first-order correspondents of Sahlqvist modal reduction principles in various relational semantic settings, including crisp and many-valued Kripke frames, and crisp and many-valued polarity-based frames (aka enriched formal contexts). Building on unified correspondence theory, we aim at introducing a theoretical environment which makes
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Robust Hybrid Learning Approach for Adaptive Neuro-Fuzzy Inference Systems Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-30 Ali Nik-Khorasani, Hadi Sadoghi-Yazdi, Ali Mehrizi
The Adaptive Neuro-Fuzzy Inference System (ANFIS) is a regression model that uses fuzzy logic and neural networks, making it suitable for modeling the uncertainty of regression problems. However, the non-robust loss function in ANFIS's hybrid learning algorithm can make it susceptible to the direct effects of noise and outliers. This paper introduces a new procedure that uses robust loss functions
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Multigranulation fuzzy probabilistic rough sets induced by overlap functions and their applications Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-02 Nana Han, Junsheng Qiao, Tengbiao Li, Weiping Ding
As we all know, t-norms can be used to construct fuzzy probabilistic rough set (FPRS). Meanwhile, overlap functions (OFs), as a sort of novel aggregation functions different from t-norms, have shown a flourishing situation in terms of applications and theory, especially for the study involving combination of OFs with rough sets. In this paper, we propose a novel OFs-based FPRS named as OFPRS. Specifically
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Updating information based on generalized credal sets. Part 1: Finite case Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-30 Andrey G. Bronevich, Igor N. Rozenberg
This paper considers updating information and statistical inference based on generalized credal sets. In the first part, we define possible ways of conditioning for generalized credal sets in a finite setting, and its realization based on generalized upper previsions with applications to decision making. We compare the obtained results with the generalized Bayes rule from the theory of imprecise probabilities
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Katětov-Tong insertion theorem for functions with values in a tensor product of complete lattices Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-02-01 Tomasz Kubiak, Iraide Mardones-Pérez
It is shown that Katětov-Tong insertion theorem continues to hold for normal -topological spaces and functions with values in appropriately -topologized tensor product where is a complete lattice with an order-reversing involution and is a completely distributive lattice with a countable join base free of supercompact elements. When the first factor is the real unit interval, the tensor product can
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Smooth compositions enhance safety of the fuzzy systems Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-30 Ebrahim Navid Sadjadi
Fuzzy models provide an empirical structure for controller design upon the experience of the operator, where the system output is delivered from a block box. Hence, there is a lack of effective way for assuring the safety specifications during the system transitions. This is to say, there are safety-oriented restrictions where the system stated are prohibited to enter under the fuzzy based controller
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Simplification of ANFIS based on Importance-Confidence-Similarity Measures Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-29 Yali Jin, Weihua Cao, Min Wu, Yan Yuan, Yang Shi
Adaptive-network-based fuzzy inference system (ANFIS) is a well-known neuro-fuzzy system, which is widely implemented in nonlinear system approximation, prediction, control, and pattern classification. However, either too many fuzzy sets or fuzzy rules are indispensable to establish an accurate ANFIS for a high-dimensional system, which increases the complexity and limits the widespread application
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Necessary and sufficient conditions for the existence of fuzzy doubly strong equilibria in generalized fuzzy games Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-22 Jiuqiang Liu
The concept of doubly strong equilibrium is a refinement of the concept of strong Nash equilibrium which represents the most desirable situations for generalized games, where all players get the best among the available outcomes. In this paper, we use necessary and sufficient conditions for the existence of solutions of the Ky Fan minimax inequality to establish necessary and sufficient conditions
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Translation structures for fuzzy model theory Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-17 Răzvan Diaconescu
The theory of L-institutions is a fully axiomatic and abstract approach to fuzzy / many-valued truth model theory, which is based on category theory. In this paper we develop a series of mathematical structures and results that empower at various levels the logic translation paradigm for L-institutions. Our development parallels the well established logic translation themes in ordinary (binary truth)
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Linearity and linear extensions of fuzzy orders revisited Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-19 Tomas Urbanec
The famous Szpilrajn's extension theorem demonstrating existence of linear extension of any order is one of the most important results in order theory. Inevitably its various generalizations were studied also in the setting of fuzzy logic, where up to date results are rather pessimistic. Focusing on the arguably most developed approach to fuzzy orders where order relation is defined with respect to
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Fuzzy and rough approach to the problem of missing data in fall detection system Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-18 Teresa Mroczek, Dorota Gil, Barbara Pękala
Two new methods for mining incomplete data based on interval-valued fuzzy set theory and rough set theory, particularly maximal consistent blocks were proposed, and their application to the fall detection system, exactly to the posture detection system. The suggested methods are based on interval-valued aggregation operators supporting decision-making involving uncertainty. Additionally, the new measure
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A new decision analysis framework for multi-attribute decision-making under interval uncertainty Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-17 Xiao-Hong Pan, Shi-Fan He, Ying-Ming Wang
In decision-making analysis, the description on decision makers' risk attitude under uncertainty is a focus topic. This paper presents a novel decision analysis framework that considers uncertainty and risk using the cumulative prospect theory. The proposed approach describes uncertain preference information using interval-valued fuzzy sets, maintaining this representation without converting intervals
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Exact upper bound for copulas with a given diagonal section Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-15 Damjana Kokol Bukovšek, Blaž Mojškerc, Nik Stopar
We answer a 15-year-old open question about the exact upper bound for bivariate copulas with a given diagonal section by giving an explicit formula for this bound. As an application, we determine the maximal asymmetry of bivariate copulas with a given diagonal section and construct a copula that attains it. We derive a formula for the maximal asymmetry that is simple enough to be used by practitioners
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New fractal dimensions of measures and decompositions of singularly continuous measures Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-10 Rim Achour, Jihed Hattab, Bilel Selmi
By introducing a novel expression for the Hausdorff and packing measures with respect to gauge functions, we establish a connection between different approaches to defining the exact Hausdorff and packing dimensions of measures. Furthermore, we define the upper and lower Hausdorff and packing dimensions of a Borel probability measure and demonstrate that these dimensions can be represented using an
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Functional description of free algebras in subvarieties of BL-algebras Fuzzy Set. Syst. (IF 3.9) Pub Date : 2024-01-15 J.P. Díaz Varela, N. Lubomirsky
In this paper, we present a method to describe (functionally) free algebras in some subvarieties of BL-algebras. Particularly, we give a description of free algebras in subvarieties of the subvariety MG, where MG is the subvariety of BL generated by the algebra [0,1]MV⊕[0,1]G.