Lattice-valued interval soft sets – A general frame of many soft set models

Abstract

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. As a generalization of soft sets, many new concepts have been introduced in the recent years. In this paper, a new notion of lattice-valued interval soft sets is introduced as a general frame of various soft set models, many concepts can be regarded as special lattice-valued interval soft sets including soft sets, interval soft sets, fuzzy soft sets, L-fuzzy soft sets, interval-valued fuzzy soft sets, vague soft sets, intuitionistic fuzzy soft sets, interval-valued intuitionistic fuzzy soft sets, rough soft sets et al. Moreover, basic algebraic operations of lattice-valued interval soft sets are investigated and some new lattice structures are constructed, the following fact is presented: many results related to algebraic operations in various soft set models are special cases of corresponding results in this paper.