Search Results (375)

We consider restricted forms of the algorithmic problem of definability of first-order sentences by propositional formulas with intuitionistic Kripke frames semantics. We demonstrate positive resolutions for classes of intuitionistic Kripke frames based on linear orders and conversely show that a few natural first-order definable classes give rise to undecidable definability problems by applying the model-theoretic in the nature technique of stable classes of Kripke frames. Full article

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching $\mathcal{O}\left(n^{-1.5}\right)$ under Caputo derivatives, using parameters $\lambda =3.5$, $q=1.8$, and $n=100$. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

The selection of an appropriate cloud platform represents a highly important strategic decision for any IT company. In pursuit of business optimization, cost reduction, improved reliability, and enhanced market competitiveness, selecting the most suitable cloud platform has become a major practical challenge. This paper proposes a novel two-stage multi-attribute decision-making (MADM) model, enhanced through the use of interval type-2 fuzzy sets (IT2FMADM). This was demonstrated through a case study in an IT company based in Serbia. In the first stage, three experts from the company were surveyed to assess the relative importance of the attributes, and their evaluations were aggregated using the fuzzy harmonic mean operator. As a result, unified fuzzy weight vectors were obtained. In the second stage, two MADM methods extended with interval type-2 fuzzy sets, namely COmplex PRoportional Assessment (IT2FCOPRAS) and Evaluation based on Distance from Average Solution (IT2FEDAS), were applied to support the selection of the most suitable cloud platform. Each platform was evaluated by decision-makers (DMs), who reached a consensus in their assessments, supported by data from company records. A comparative analysis of the results revealed that different methods may produce varying rankings of alternatives, particularly when the alternatives are objectively similar in their characteristics. Nevertheless, the proposed model can serve as a highly useful decision-support tool for company management. Full article

Discrete Sugeno integrals form a significant family of aggregation functions. Several variants of these integrals have been proposed, most of which replace the minimum operation with alternative operations, such as product, overlap functions, and t-norms. Notably, the associativity of t-norms in discrete Sugeno integrals has no significant consequences, leading us to relinquish this property and introduce the concept of partial t-norms. Although interval-valued versions of the discrete Sugeno integral or its variants have been limited, this paper presents a novel approach based on interval-valued partial t-norms, admissible orders, and interval-valued fuzzy measures. We provide rigorous proofs of the properties of this operator class. Full article

The logic sqŁ^* is closely related to complex fuzzy sets. In this paper, we continue our study on sqŁ^* by establishing a system that includes all formulas with values $\mathbf{0}$ in sqŁ^*. This system has paraconsistent formulas within sqŁ^*. Moreover, we show that this logical system is both sound and weakly complete. Full article

This article presents a new approach to solving fuzzy advection–diffusion equations using double fuzzy transforms, called the double fuzzy Yang–General transform. This unique double fuzzy transformation is a combination of single fuzzy Yang and General transforms. Some of the basic properties of this new transform include existence and linearity and how they relate to partial derivatives. A solution framework for the linear fuzzy advection–diffusion equation is developed to show the application of the double fuzzy Yang–General transform. To illustrate the proposed method for solving these equations, we have included a solution to a numerical problem. Full article

This article describes solutions to control problems using fuzzy logic, which facilitates the development of decision support systems across various fields. However, addressing this task through the manual creation of rules in specific fields necessitates significant expert knowledge. Machine learning methods can identify hidden patterns. A key novelty of this approach is the algorithm for generating fuzzy rules for a fuzzy controller, derived from interpreting a decision tree. The proposed algorithm allows the quality of the control actions in organizational and technical systems to be enhanced. This article presents an example of generating a set of fuzzy rules through the analysis of a decision tree model. The proposed algorithm allows for the creation of a set of fuzzy rules for constructing fuzzy rule-based systems (FRBSs). Additionally, it autogenerates membership functions and linguistic term labels for all of the input and output parameters. The machine learning model and the FRBS obtained were assessed using the coefficient of determination ($R^2$). The experimental results demonstrated that the constructed FRBS performed on average 2% worse than the original decision tree model. While the quality of the FRBS could be enhanced by optimizing the membership functions, this topic falls outside the scope of the current article. Full article

In many real-world situations, we deal with data that exhibit both randomness and vagueness. To manage such uncertain information, fuzzy theory provides a useful framework. Specifically, to explore causal relationships in these datasets, a lot of fuzzy regression models have been introduced. However, while fuzzy regression analysis focuses on estimation, it is equally important to study the mathematical characteristics of fuzzy regression estimates. Despite the statistical significance of optimal properties in large-sample scenarios, only limited research has addressed these topics. This study establishes key optimal properties, such as strong consistency and asymptotic normality, for the fuzzy least-squares estimator (FLSE) in general linear regression models involving fuzzy input–output data and random errors. To achieve this, fuzzy analogues of traditional normal equations and FLSEs are derived using a suitable fuzzy metric. Additionally, a confidence region based on FLSEs is proposed to facilitate inference. The asymptotic relative efficiency of FLSEs, compared to conventional least-squares estimators, is also analyzed to highlight the efficiency of the proposed estimators. Full article

With his research on Aristotle’s syllogistic, Jan Łukasiewicz initiates the branch of logic known as the calculus of names. This field deals with axiomatic systems that analyse various fragments of the logic of names, i.e., that branch of logic that studies various forms of names and functors acting on them, as well as logical relationships between sentences in which these names and functors occur. In this work, we want not only to present the genesis of the calculus of names and its first system created by Łukasiewicz, but we also want to deliver systems that extend the first. In this work, we will also show that, from the point of view of modern logic, Łukasiewicz’s approach to the syllogistic is not the only possible one. However, this does not diminish Łukasiewicz’s role in the study of syllogism. We believe that the calculus of names is undoubtedly the legacy of Łukasiewicz. Full article

It was recently proposed to extend the spherical fuzzy set to spherical fuzzy credibility sets (SFCSs). In this paper, we define the concept of SFCSs. We then define new operational laws for SFCSs using Dombi operational laws. Various spherical fuzzy credibility aggregation operators such as spherical fuzzy credibility Dombi weighted averaging (SFCDWA), spherical fuzzy credibility Dombi ordered weighted averaging (SFCDOWA), spherical fuzzy credibility Dombi weighted geometric (SFCDWG), and spherical fuzzy credibility Dombi ordered weighted geometric (SFCDOWG) are defined. We also show the boundedness, monotonicity, and idempotency aspects of the suggested operators. We proposed the spherical fuzzy credibility entropy to find the unknown weight information of the attributes. Symmetry analysis is a useful and important tool in artificial intelligence that may be used in a variety of fields. To calculate the significant factor, we determine the multi-attribute decision-making (MADM) method using the suggested operators for SFCSs to increase the value of the assessed operators. To demonstrate the effectiveness and superiority of the suggested approach, we compare our findings to those of many other approaches. Full article

Since the early 2000s, fuzzy mathematics has fostered a stream of research on the financial valuation of assets incorporating optionality. This paper makes two contributions to this field. First, it conducts a bibliographical analysis of contributions from fuzzy set theory to option pricing, focusing on fuzzy-random option pricing (FROP) and its applications in binomial and trinomial lattice approaches. Second, it extends the FROP to yield curve modeling within a binomial framework. The bibliographical analysis followed the PRISMA guidelines and was conducted via the SCOPUS and WoS databases. We present a structured review of papers on FROP in discrete time (FROPDT), identifying the principal papers and outlets. The findings reveal that this focus has been applied to price options on stocks, stock indices, and real options. However, the exploration of its application to the term structure of interest-sensitive interest rate assets is very rare. To address this gap, we develop a fuzzy-random extension of the Ho–Lee term structure model, applying it to the European interbank market and price caplet options. Full article

The overlap function has been extensively utilized across various fields. In this paper, we introduce the concepts of the similarity and $\delta$-equality of overlap functions to measure the degree of similarity between two overlap functions. Subsequently, we examine the $\delta$-equality of several operations on overlap functions, including meet, join, and weighted sum, to assess how these operations maintain the similarity. Finally, we discuss the robustness of fuzzy reasoning for FMP, FMT, and FHS models based on the $\delta$-equality of the overlap functions. Full article

In certain stages of the application of a type-2 fuzzy logic system, it is necessary to perform operations between input or output fuzzy variables in order to compute the union, intersection, aggregation, complement, and so forth. In this context, operators that satisfy the axioms of t-norms and t-conorms are of particular significance, as they are applied to model intersection and union, respectively. Furthermore, the existence of a range of these operators allows for the selection of the t-norm or t-conorm that offers the optimal performance, in accordance with the specific context of the system. In this paper, we obtain new t-norms and t-conorms on some important subfamilies of the set of functions from $[0,1]$ to $[0,1]$. The structure of these families provides a more solid algebraic foundation for the applications. In particular, we define these new operators on the subsets of the functions that are convex, normal, and normal and convex, as well as the functions taking only the values 0 or 1 and the subset of functions whose support is a finite union of closed intervals. These t-norms and t-conorms are generalized to the type-2 fuzzy set framework. Full article

The fundamental notions of the intuitionistic hesitant fuzzy set (IHFS) and rough set (RS) are general mathematical tools that may easily manage imprecise and uncertain information. The EDAS (Evaluation based on Distance from Average Solution) approach has an important role in decision-making (DM) problems, particularly in multi-attribute group decision-making (MAGDM) scenarios, where there are many conflicting criteria. This paper aims to introduce the IHFR-EDAS approach, which utilizes the IHF rough averaging aggregation operator. The aggregation operator is crucial for aggregating intuitionistic hesitant fuzzy numbers into a cohesive component. Additionally, we introduce the concepts of the IHF rough weighted averaging (IHFRWA) operator. For the proposed operator, a new accuracy function (AF) and score function (SF) are established. Subsequently, the suggested approach is used to show the IHFR-EDAS model for MAGDM and its stepwise procedure. In conclusion, a numerical example of the constructed model is demonstrated, and a general comparison between the investigated models and the current methods demonstrates that the investigated models are more feasible and efficient than the present methods. Full article

As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the residual implication derived from it; then it explores the construction of a semi-overlap function on complete lattices and some fundamental properties. Especially, this paper introduces a more generalized concept of the ‘semi-Θ-Ξ function’, which innovatively unifies the semi-overlap function and semi-grouping function. Additionally, it provides methods for constructing and characterizing the semi-Θ-Ξ function. Furthermore, this paper characterizes the semi-overlap function on complete lattices and the semi-Θ-Ξ function on [0, 1] from an algebraic point of view and proves that the algebraic structures corresponding to the inflationary semi-overlap function, the inflationary semi-Θ-Ξ function, and residual implications derived by each of them are inflationary MTL algebras. This paper further discusses the properties of inflationary MTL algebra and its relationship with non-associative MTL algebra, and it explores the connections between some related algebraic structures. Full article