On b-open Sets via Infra Soft Topological Spaces

Abstract

This work aims to present the concept of infra soft $b$-open sets(IS-b-open sets) as a generalized new class of infra open sets(IS-open sets). We first investigate their basic properties and study their behaviours under infra soft homeomorphism maps and finite product of soft spaces. Then, we establish some soft operators such as interior, closure, limit and boundary using IS-b-open sets and IS-$b$-closed sets. The relationships between them are illustrated and discussed. Finally, we display some soft maps(S-map) defined using IS-$b$-open and IS-$b$-closed sets and scrutinize their master properties.

The accurate diagnosis for COVID-19 variants using nearly initial-rough sets

“…In this section, we outline the main ideas about some previous studies of rough sets (namely, Yao [ 3 ], Abd El-Monsef et al [ 11 ], Dai et al [ 6 ], El-Sayed et al[ 19 ], and Abu-Gadairi [ 39 ]).…”

“…[ 39 ] Let be a binary relation on . Then, we define the following neighborhoods of : -initial neighborhood [ 19 ]: .…”

“…[ 39 ] In a - where , the -initial lower and -initial upper approximations of are respectively defined as: …”

“…In this section, we present comparisons between the proposed methods and previous proposals, specifically Yao [ 3 ], Abd El-Monsef et al [ 11 ], Dai et al [ 6 ], El-Sayed et al [ 19 ], and Abu-Gadairi [ 39 ], through established results and counterexamples. Our aim is to demonstrate the superior accuracy of the suggested methods over these prior approaches.…”

n<SUP>th</SUP> Power Root Fuzzy Sets and Its Topology

“…Atanassov [17] defined intuitionistic fuzzy sets as one of the intriguing generalizations of fuzzy sets with excellent application. Applications of intuitionistic fuzzy sets can be found in a variety of domains, including optimization issues, decisionmaking, and medical diagnostics [22][23][24]. However, in many circumstances, the decision maker may assign degrees of membership and non-membership to a given attribute such that their aggregate is larger than one.…”