Annals of Communications in Mathematics

AbstractDynamics fuzzy sets outperform fuzzy sets for dealing with unclear situations. There are many applications for fuzzy similarity metrics, including cluster analysis, problem classification, and even medical diagnosis. Lean entropy measurements are essential to determine the weights of the criteria in a situation involving multi-criteria decision-making. In this paper, we introduce and suggest alternative similarity measures for Dynamics fuzzy collections. We developed some new entropy metrics for using recommended similarity assessments. Dynamics fuzzy collections. Finally, in a Dynamics fuzzy environment, a novel multi-attribute decision-making method is developed that solves a significant limitation of the famous decision-making methodology, namely, the technique for order preference by similarity to the ideal solution.

AbstractAvian influenza is known as one of the respiratory diseases that causes high morbidity and mortality rate predominately among the immunodeficiency persons world- wide. Treatment and vaccination remain the optimal strategies in curbing the spread of avian infuenza infection.In this work, a mathematical model of the dynamics of influenza infection is formulated and was computed analytically and numerically. The analytic com- putation of the model is given in terms of the basic reproduction number, equilibria points and their stabilities. Thus, the disease dies out whenever the basic reproduction number is less than one. The disease free equilibrium (DFE) is locally asymptotically stable pro- vided R0 < 1 and unstable if otherwise. The endemic equilibrium only occurs whenever the disease threshold is greater than a unit. The endemic equilibrium, is locally, globally asymptotically stable under certain conditions. Numerical solution shows that vaccination and treatment of the susceptible and the infected individuals respectively have high impact for eradicating the disease. The non-linear incidence as a force of infection with param- eter, θ,Ψ1, u1 and u2 have great impact for reducing the pandemic of influenza disease. In conclusion, vaccination of susceptible individuals, isolation of exposed individuals and treatment of infected individuals are imperative for curbing the spread of an avian influenza infection. Modelling style or structure especially, the type of force of infection adopted for modelling an avian influenza disease depends on whether the disease, can easily be put under control.

AbstractThis article provides an in-depth examination of (m, n, γ)-regular le-Γ- semigroups, focusing on the characterization and properties of various types of ideal el- ements within these structures. Specifically, the discussion encompasses (m, n, γ)-ideal elements, (m, 0, γ)-ideal elements, and (0, n, γ)-ideal elements, highlighting their sig- nificance and interrelationships. Furthermore, the article investigates the (m, n, α, β)- regularity associated with the set denoted as I(m,n,α,β), which consists of all (m, n, α, β)- ideal elements. In conjunction, the study explores the set Q(m,n,α,β), which comprises all (m, n, α, β)-quasi-ideal elements of le-Γ-semigroups, detailing the implications of these classifications on the structure and behavior of the semigroups. Additionally, the research delves into the concept of 0-minimality, particularly concerning (0, m, γ)-ideal elements in both poe-Γ-semigroups and le-Γ-semigroups. This aspect of the study aims to clarify the foundational properties of ideal elements and their roles in the broader context of semi- group theory. The findings presented in this article contribute to a deeper understanding of the algebraic properties of le-Γ-semigroups and their ideal elements, paving the way for future research in this area.

AbstractIn this paper the concept of somewhat neutrosophic regular semi continuous functions, somewhat neutrosophic regular semi-open functions are introduced and studied. Besides giving characterizations of these functions, several interesting properties of these functions are also given. More examples are given to illustrate the concepts introduced in this paper.

AbstractThe concept of fuzzy right multiplication Γ-semigroup is introduced by means of fuzzy right Γ-ideals, and some properties are investigated with the help of some classes of Γ-semigroups. It is shown that for any fuzzy right Γ-ideal ϑ of X, ϑ ⊆ X ◦Γ ϑ. More- over, if a Γ-semigroup X is simple with a ∈ aΓX for every a ∈ X, then X is a fuzzy right multiplication Γ-semigroup.

AbstractIn this paper, the concept of the direct product of a group is studied from the classical settings. We then propose the notion of the direct product of a soft multigroup and investigate some of its structural properties. Finally, the concept of upper and lower cuts of soft multigroup is introduced, exemplified and some related results are established.

AbstractIn this paper, we introduce the concept of tri-quasi hyperideal in Γ-semihyperring generalizing the classical ideal, left ideal, right ideal, bi-ideal, quasi ideal, interior ideal, bi-interior ideal, weak interior ideal, bi-quasi ideal, tri-ideal, quasi-interior ideal and bi- quasi-interior ideal of Γ-semihyperring and semiring. Furthermore, charecterizations of Γ-semihyperring, regular Γ-semihyperring and simple Γ-semihyperring with relative tri- quasi hyperideals are provided discussing the characteristics of Γ-semihyperring of relative tri-quasi hyperideals.

AbstractFrullani’s Integral Formula is an old formula that was known to hold under strict conditions. Iyengar, and later Ostrowski, provided necessary and sufficient conditions for the existence of the Frullani Integral Formula. Their conditions were different but equivalent. In this article, we identify other conditions that are equivalent. We show that these conditions are, in fact, solutions to a family of linear differential equations of the first order. We study the limiting behavior of these solutions at zero and infinity, and in doing so, arrive at a new proof of the equivalence of Iyengar’s and Ostrowski’s conditions. Lastly, we provide applications of our results.

AbstractIn this article we study the univariate quantitative smooth approximation, real and complex, ordinary and fractional under differentiation of functions. The approximators here are neural network operators activated by the symmetrized and perturbed hyperbolic tangent function. All domains used are of the whole real line. The neural network operators here are of quasi-interpolation type: the basic ones, the Kantorovich type ones, and of the quadrature type. We give pointwise and uniform approximations with rates. We finish with interesting illustrations.

AbstractThis paper introduces the ”anti fuzzy semigroup,” a novel algebraic structure that integrates the concepts of semigroups and anti fuzzy sets. We demonstrate, through a specific example, how a Kinship system can be represented as an anti fuzzy semigroup, effectively capturing the relationships between managers and subordinates. This appli- cation underscores the potential of anti fuzzy semigroups to model complex hierarchical structures and relationships within organizational settings. Furthermore, we investigate the representation of DNA sequences using this framework. We delve into the algebraic properties of anti fuzzy semigroups, proving that the union of two such semigroups always results in another anti fuzzy semigroup. However, we provide a counterexample to demon- strate that the intersection of two anti fuzzy semigroups may not necessarily preserve the anti fuzzy semigroup property. Finally, the Cartesian product of two anti fuzzy semigroups forms an anti fuzzy semigroup.

AbstractIn this paper, we introduce the concept of neutrosophic weakly regular semi continuous, neutrosophic regular semi q-neighbourhood in neutrosophic topological spaces. Also, we investigate the relationship among neutrosophic weakly regular semi continuous and other existing continuous functions. Moreover, some counter examples to show that these types of mappings are not equivalent. Finally, Neutrosophic retracts, neutrosophic regular semi retracts, neutrosophic regular semi quasi Urysohn space and neutrosophic regular semi Hausdorff spaces are introduced and studied.

AbstractThe Riemann problem is stated as follows: find an analytic in a domain D+ ∪ D− function Φ(z) such that (∗) Φ+(t) = G(t)Φ−(t) + g(t), t ∈ S. Here S is the boundary of D+, D− complements the complex plane to D+ ∪ S, the functions G = G(t) and g = g(t) belong to Hμ(S), the space of H¨older-continuous functions. The theory of problem (*) is developed also for continuous G. If G = 1, S ∈ C∞ and g is a tempered distribution, then problem (∗) has a solution in tempered distributions. It is proved that problem (∗) for G ∈ Lp(S) and g a tempered distribution does not make sense. It is proved that if G ∈ C∞(S), G̸ = 0 on S, and g is a distribution of the class D′, then the Riemann problem makes sense and a method for solving this problem is given. It is proved that if S = R = (−∞, ∞) and G ∈ Lp(R), where p ≥ 1 is a fixed number, then | ln G| does not belong to Lq (R) for any q ≥ 1.

AbstractBCK/BCI-algebra is a class of logical algebras that was defined by K. Iseki and S. Tanaka. BCK-algebras have a lot of generalizations. One of them is d-algebras. Near set theory which is a generalization of rough set theory. This theory is based on the determination of universal sets according to the available information of the objects. Based on the image analysis, the near set theory was created. ¨Ozt¨urk applied the notion of near sets defined by J. F. Peters to the theory of d-algebras. In this paper we introduce upper-nearness d-ideal, upper-near (upper-nearness) d#- ideal, upper-near (upper-nearness) d∗-ideal. We explored what conditions we should put on the ideal for quotient nearness d-algebra to become an nearness d-algebra again. More- over, we introduce quotient nearness d-algebras with the help of upper-nearness d∗-ideals of nearness d-algebras. Finally, we present a theorem involving the canonical homomor- phism and the structure of the kernel for nearness d-algebras. Thus, we aim to make preliminary preparations for proving isomorphism theorems for nearness d-algebras.

AbstractThis paper introduces a novel approach to the study of filters in BL-algebras by leveraging the principles of bipolar fuzzy set theory and investigating some of their properties. Filters are essential in the structural analysis of BL-algebras, affecting their properties and applications across various fields. Moreover, Bipolar-valued fuzzy filters generated by a fuzzy set are discussed. By integrating bipolar fuzzy set concepts, we provide a new framework that enhances the representation of uncertainty and vagueness inherent in filter operations.  We explore the foundational aspects of bipolar fuzzy sets and demonstrate their applicability in defining and characterizing filters within BL-algebras. Our findings highlight the potential of bipolar fuzzy set theory to enrich the understanding of filters in BL-algebras.