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In this research article, we introduce -statistically pre-Cauchy sequences of complex uncertain variables in five different aspects of uncertainty, namely: in mean, in measure, in distribution, in almost sure, and in uniformly almost sure. We also explore the connection between -statistically pre-Cauchy sequences and -statistically convergent sequences using complex uncertain variables. Additionally, we initiate the study of -statistically pre-Cauchy sequences of complex uncertain variables through Orlicz functions.

The central objective of this treatise is to introduce the concept ( j , k ) γ ∗ –operation in fuzzy bitopological spaces. The same operation is applied to study the concept of ( j , k ) ∗ -fuzzy open sets in a given fuzzy bitopological space. Existence of all the conceptions are shown by considering different operations. Various properties of the newly introduced notion are presented and justifications are provided by placing suitable examples. Furthermore, minimality of fuzzy open sets are also being studied up to some extent. Finally, results on locally finiteness of a given fuzzy bitopological space are established via operation approach.

In this paper, we introduce statistical convergence of triple sequences which are defined in a topological space. Various results on statistically convergent triple sequences are produced by using the notion of triple natural density operator. Moreover, we initiate the concept of -convergence of triple sequence and establish the interrelationship among -convergence and -converegnce. We see that the first one implies the second one but it’s not vice-versa. But if we restrict the triple sequences to hold the property of first countability, we verify that these notions becomes equivalent. Finally, we prove that the family of all statistically convergent triple sequences under some conditions generates a topological structure within the topological space where they have been defined.

Uncertainty theory has significantly advanced and expanded over the past ten years. In this article, we introduce the notions of uncertain α-dual, uncertain β-dual and uncertain γ-dual of complex uncertain sequence spaces. Convergence and boundedness of complex uncertain sequences are taken in the sense of almost surely due to B. Liu and then few characterizations of the newly introduced uncertain dual spaces are established. Furthermore, our goal is to propose and establish inclusion relations within these sequence spaces.

Convergence of real sequences, as well as complex sequences are studied by B. Liu and X. Chen respectively in uncertain environment. In this treatise, we extend the study of almost convergence by introducing double sequences of complex uncertain variable. Almost convergence with respect to almost surely, mean, measure, distribution and uniformly almost surely are presented and interrelationships among them are studied and depicted in the form of a diagram. We also define almost Cauchy sequence in the same format and establish some results. Conventionally we have, every convergent sequence is a Cauchy sequence and the converse case is not true in general. But taking complex uncertain variable in a double sequence, we find that a complex uncertain double sequence is a almost Cauchy sequence if and only if it is almost convergent. Some suitable examples and counter examples are properly placed to make the paper self suffcient.

The main purpose of this paper is to investigate different types of deferred convergent double sequences of fuzzy variables by using the notions of ideal convergence and μ-density in a given credibility space. We also establish a number of instances to illustrate the newly introduced notions in the same environment. In this study, we also present important findings that reveal the connections between these concepts.

In this paper, we introduce the concept of convergence of complex uncertain series. We initiate matrix transformation of complex uncertain sequence and extend the study via linearity and boundedness. In this context, we prove Silverman-Toeplitz theorem and Kojima-Schur theorem considering complex uncertain sequences. Finally, we establish some results on co-regular matrices.

In this paper, we introduce statistical convergence of triple sequences which are defined in a topological space. Various results on statistically convergent triple sequences are produced by using the notion of triple natural density operator. Moreover, we initiate the concept of -convergence of triple sequence and establish the interrelationship among -convergence and -converegnce.  We see that the first one implies the second one but it’s not vice-versa. But if we restrict the triple sequences to hold the property of first countability, we verify that these notions becomes equivalent. Finally, we prove that the family of all statistically convergent triple sequences under some conditions generates a topological structure within the topological space where they have been defined. En este artículo, introducimos la convergencia estadística de sucesiones triples definidas en un espacio topológico. Se obtienen diversos resultados sobre sucesiones triples estadísticamente convergentes utilizando la noción del operador de densidad natural triple. Además, iniciamos el concepto de convergencia s* de sucesiones triples y establecemos la interrelación entre la convergencia s* y la convergencia s. Observamos que la primera implica la segunda, pero no ocurre lo contrario. Sin embargo, si restringimos las sucesiones triples a cumplir con la propiedad de primer numerabilidad, verificamos que estas nociones se vuelven equivalentes. Finalmente, demostramos que la familia de todas las sucesiones triples estadísticamente convergentes, bajo ciertas condiciones, genera una estructura topológica dentro del espacio topológico en el cual han sido definidas.