arXiv subjects

Abha Tripathi

Publications and source records attributed to Abha Tripathi.

4 recordsLinked to original sources

arXiv2025

On unification of categories associated with F -transforms and fuzzy pretopological spaces as Qua category

In this contribution, our motive is to unify the categories associated with F-transforms and fuzzy pretopological spaces as a new category Qua, whose object classes are success measurements of answers and morphisms are pairs of success measurements of transformations. Specifically, the categories of spaces with L-valued fuzzy partitions, L-valued fuzzy lower transformation systems, L-valued fuzzy pretopological spaces, and Cech L-valued fuzzy interior spaces with the morphisms as pairs of L-valued fuzzy relations between the underlying sets of corresponding objects have intriguing relationships with the category Qua.

math.CT↗

arXiv2022

On categories of spaces with L-fuzzy partitions, L-fuzzy closure system spaces and coalgebras (dialgebras)

In this contribution, we aim to introduce and study L-fuzzy partition spaces and L-fuzzy closure system spaces in a categorical framework. Further, we present the concepts of coalgebras and dialgebras corresponding to a direct upper F -transform under certain conditions and show the functorial relationship between the category of spaces with L-fuzzy partition and the category of coalgebras (dialgebras). Moreover, we show that the categories of coalgebras and dialgebras are isomorphic and introduce a pair of adjoint functors between the coalgebras and dialgebras.

math.CT↗

arXiv2022

F-transforms determined by overlap and grouping maps over a complete lattice

This paper is about the study of F-transforms based on overlap and grouping maps, residual and co-residual implicator over complete lattice from both constructive and axiomatic approaches. Further, the duality, basic properties, and the inverse of proposed F-transforms have been studied, and axiomatic characterizations of proposed direct F-transforms are investigated.

math.RA↗

arXiv2022

Granular F-transform and its application

This contribution introduces the concept of granular F-transform and investigates its basic properties by using the theory of fuzzy numbers and horizontal membership functions. Further, we present a numerical method based on granular F-transform to solve a fuzzy prey-predator model consisting of two prey and one predator due to its natural variability and investigate the existence of the equilibrium points and their stability

math.NA↗