The lattice of pre-complements of a classic interval valued fuzzy graph
Authors :
S. Deepthi Mary Tresa 1 , S. Divya Mary Daise 2 and Shery Fernandez 3 *
Author Address :
1,2 Department of Mathematics, St. Alberts College, Ernakulam-682018, Kerala, India.
3 Department of Mathematics, Cochin University of Science and Technology, Ernakulam-682022, Kerala, India.
*Corresponding author.
Abstract :
We prove that a complement Interval Valued Fuzzy Graph (IVFG), unlike the crisp and fuzzy cases, may have several non-isomorphic pre-complements. We introduce the notion of complement numbers, and show that, by assigning complement numbers to the edges of a complement IVFG, we can ensure uniqueness of pre-complement. We introduce the concepts \textit{superior pre-complement} $\mathcal{G}^*$ and \textit{inferior pre-complement} $\mathcal{G}_*$, for any given classic IVFG $\mathcal{G}$. A partial order $_P^\subseteq$ is defined on $\mathscr{P} = C^{-1}(\mathcal{G})$, the collection of all pre-complements of $\mathcal{G}$. It is proved that ($\mathscr{P}$, $_P^\subseteq$ ) is a lattice with $\mathcal{G}^*$ as the greatest element and $\mathcal{G}_*$ as the least element. We derive a necessary and sufficient condition for this lattice to become a chain.
Keywords :
Interval Valued Fuzzy Graph, Complement, Complement Number, Lattice.
DOI :
Article Info :
Received : April 13, 2020; Accepted : July 19, 2020.
