Open AccessA bird’s eye view of the connections among L-fuzzy i-covers, c-covers and (L-fuzzy) tolerances of L-fuzzy (point) set.
Author(s) -
G. Prasanthi,
Pusuluri V. N. H. Ravi,
Nistala V. E. S. Murthy
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1767/1/012052
Subject(s) - mathematics , fuzzy logic , partially ordered set , fuzzy set , fuzzy classification , fuzzy set operations , fuzzy subalgebra , defuzzification , commutative property , type 2 fuzzy sets and systems , discrete mathematics , fuzzy number , set (abstract data type) , point (geometry) , combinatorics , algebra over a field , pure mathematics , computer science , artificial intelligence , geometry , programming language
It is known that, for any L- fuzzy set X , there is an associated L- fuzzy point set, which is a crisp set. Further, for these sets X and, there are four associated objects of study, namely: the poset of L -fuzzy i -covers of X , the poset of L -fuzzy tolerance relations on X , and the poset of L -fuzzy sc -covers of, the poset of tolerance relations on . In this paper, we establish Lagois connection between certain type of crisp covers of L -fuzzy point set, certain type of tolerance relations on the same set and construct a commutative diagram involving the said four objects in terms of Galois/Lagois connections among them. Further, we show how the Galois/Lagois connections among the sets of L -fuzzy i -covers, L -fuzzy tolerance relations, and their associated objects, together capture the improvement in strengthening the fuzzy membership grade of L -fuzzy i -covers, L -fuzzy tolerance relations.