Fuzzy Soft Sets and Fuzzy Soft Lattices

Abstract

The theory of soft sets was introduced by Molodtsov in 1999 in order to deal with uncertainties. In this paper, the notion of fuzzy soft lattice is defined and some related properties are derived, which extends the notion of a fuzzy lattice to include the algebraic structures of soft sets. Then the lattice structure of fuzzy soft lattices are discussed. At last, the concept of fuzzy soft ideal over a lattice is presented and the lattice structures of fuzzy soft ideal over a lattice are discussed.

The Order Structure of the Soft Lattice

“…For example, Estaji et al [3] introduced the notion of  -upper and  -lower approximations of a fuzzy subset of a lattice. The study of constructing the lattice structures of soft sets are begun by Qin et al [9] and the study of lattice structure have become one of hot spots in related fields [10]. In this paper, based on the notions of soft lattice presented by Shao et al in [10], we discuss the lattice structure of soft lattice.…”

“…The study of constructing the lattice structures of soft sets are begun by Qin et al [9] and the study of lattice structure have become one of hot spots in related fields [10]. In this paper, based on the notions of soft lattice presented by Shao et al in [10], we discuss the lattice structure of soft lattice. This paper is organized as follows: Section 2 presents some basic concepts of the soft set and the soft lattice which we use in this paper.…”

A New Criterion for Soft Set Based Decision Making Problems under Incomplete Information

“…Maji, Biswas and Roy 17 introduce fuzzy soft sets (see also Ali and Shabir 9 for techniques that permit to study logic connectives for soft sets and fuzzy soft sets, and Alcantud 2 for a recent decision-making procedure based on fuzzy soft sets). Relatedly, Shao and Qin 27 define fuzzy soft lattices and discuss their structure. Wang, Li and Chen 29 introduce hesitant fuzzy soft sets.…”

A Method for Fuzzy Soft Sets in Decision-Making Based on an Ideal Solution

“…Zhang [5] studies interval soft sets. Shao and Qin [6] define fuzzy soft lattices and discuss their structure. Basu [7] introduce the structure and form of soft set theory.…”