Abstract
In this paper, based on soft lattices, with the help of fuzzy level (cut) set, -level fuzzy soft sets and -level fuzzy soft lattices are defined, and the structure and characteristics of our definitions are explained with examples, at the same time, their di erences and relations are compared with classic soft set.
Highlights
In this paper, based on soft lattices, with the help of fuzzy level set, α-level fuzzy soft sets and α-level fuzzy soft lattices are defined, and the structure and characteristics of our definitions are explained with examples, at the same time, their differences and relations are compared with classic soft set
Many researchers studied soft sets combined with fuzzy sets (Zadeh, 1965), such as, the authors introduced the notion of fuzzy soft set based on Maji, Biswas and Roy (2001), and presented some more properties of fuzzy soft union and fuzzy soft intersection in Ahmad and Athar Kharal (2009), and in Majumdar and KSamanta (2010), authors defined generalized fuzzy soft sets and studied some of their properties and application
From the above discussion, this paper mainly define the α-level fuzzy soft sets and α-level fuzzy soft lattices, and at the same time, it gives some examples to understand the concept of α-level fuzzy soft sets
Summary
In this paper, based on soft lattices, with the help of fuzzy level (cut) set, α-level fuzzy soft sets and α-level fuzzy soft lattices are defined, and the structure and characteristics of our definitions are explained with examples, at the same time, their differences and relations are compared with classic soft set. (Fu, 2010) Let triplet M = (F, E, L), where L is a complete lattice, E is an attributes set, and F : E → L is a mapping, that is, ∀e ∈ E, F(e) ⊆ L and F(e) is a sublattice of L, the pair (e, F(e)) is a soft lattice over L, speaking, the triple M is called the soft lattice. Let A ⊆ E, the pair(F, A) is called a fuzzy soft set over U, where F : A → F (U).
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