Linguistic Interval-Valued Spherical Fuzzy Soft Set and Its Application in Decision Making

Abstract

Under uncertain environments, how to characterize individual preferences more naturally and aggregate parameters better have been hot research topics in multiple attribute decision making (MADM). Fuzzy set theory provides a better mathematical tool to deal with uncertain data, which promotes substantial extended studies. In this paper, we propose a hybrid fuzzy set model by combining a linguistic interval-valued spherical fuzzy set with a soft set for MADM. The emergence of a linguistic interval-valued spherical fuzzy soft set (LIVSFSS) not only handles qualitative information and provides more freedom to decision makers, but also solves the inherent problem of insufficient parameterization tools for fuzzy set theory. To tackle the application challenges, we introduce the basic concepts and define some operations of LIVSFSS, e.g., the “complement”, the “AND”, the “OR”, the “necessity”, the “possibility” and so on. Subsequently, we prove De Morgan’s law, associative law, distribution law for operations on LIVSFSS. We further propose the linguistic weighted choice value and linguistic weighted overall choice value for MADM by taking parameter weights into account. Finally, the MADM algorithm and parameter reduction algorithm are provided based on LIVSFSS, together with examples and comparisons with some existing algorithms to illustrate the rationality and effectiveness of the proposed algorithms.