18 research outputs found
CONVERGENCE OF COMPLEX UNCERTAIN TRIPLE SEQUENCE VIA METRIC OPERATOR, p-DISTANCE AND COMPLETE CONVERGENCE
No full textIn this paper, we have introduced three new types of convergence concepts, namely convergence in p-distance, completely convergence and convergence in metric by considering triple sequences of complex uncertain variable. We have established the interrelationships among these notions and also with the existing ones. In this process, we have proven that the notions of convergence in metric and convergence in almost surely are equivalent in nature. Overall, this study presents a more complete scenario of interconnections between the notions of convergences initiated in different directions
LINEAR TO NON-LINEAR TOPOLOGY VIA γ-OPEN SETS IN THE ENVIRONMENT OF BITOPOLOGICAL SPACES
No full textGeneralizations of open sets always gives a linear structure in an ordinary topological space. This paper proposes that there exists a non-linear structure in a given bitopological space via -open sets of the context. The new structure is also studied in the light of hyperconnectedness to show that it is completely independent with the original one. Also, the relationships between extremally disconnectedness, connectedness and hyperconnectedness are presented in the same environment by means of -open set. Moreover, the idea of maximal -hyperconnectedness is initiated in this work and some important results related to filter, ultrafilter, door space are established. Finally, some functions concerned with -open sets are introduced and interrelationships among them are produced. Some suitable examples and counter examples are properly placed to make the paper self sufficient
Some remarks on fuzzy infi topological spaces
No full textInduced fuzzy infi topological space is already introduced by Saha and Bhattacharya [Saha A.K., Bhattacharya D. 2015, Normal Induced Fuzzy Topological Spaces, Italian Journal of Pure and Applied Mathematics, 34, 45-56]. In this paper for the said space, we further analyse some properties viz. fuzzy I-continuity, fuzzy infi open mappings and fuzzy infi closed mappings etc. Also we study product fuzzy infi topological space and establish some results concerned with it
Some results on ?-deferred double ideal statistically convergent sequences in credibility space
No full textThe 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 mu -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.Acknowledgement. The authors would like to thank the anonymous referee for their comments that helped us improve this article
On Almost ?2-Convergence of Fuzzy Variables in Credibility Space
No full textWithin the framework of credibility theory, this paper delves into various notions of ideal convergence and almost convergence pertaining to sequences of fuzzy variables. Through the utilization of fuzzy variables, the investigation encompasses & Iscr;(2)-almost convergence in terms of almost surely, credibility, mean, distribution, and uniformly almost surely. Relationships between these notions are thoroughly examined. Furthermore, we explore different types of & Iscr;(2)-almost Cauchy sequences within the realm of credibility theory, yielding noteworthy results in the process
On fuzzy γµ-open sets in generalized fuzzy topological spaces
No full textIn this paper, we explore the existence of operation approach on open sets in a generalized fuzzy topological space. We introduce the concept of fuzzy γµ-open set and study some basic properties of it. We obtain an interesting result that the intersection of two fuzzy γµ-open sets may not be a fuzzy γµ-open set, but if the operation is regular then the intersection becomes a fuzzy γµ-open set. We also initiate the notions of fuzzy minimal γµ-open set and fuzzy γµ-locally finite space and establish various results related to these
Some observations on I-statistically pre-Cauchy sequences of complex uncertain variables defined by Orlicz functions
No full textIn this research article, we introduce I-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 I-statistically pre-Cauchy sequences and I-statistically convergent sequences using complex uncertain variables. Additionally, we initiate the study of I-statistically pre-Cauchy sequences of complex uncertain variables through Orlicz functions
Characterization of lacunary I-convergent sequences in credibility space
No full textThis research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly I*-lacunary Cauchy, and strongly I-lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships
