Convex and Concave Soft Sets and Some Properties

TL;DR

This paper introduces convex and concave soft sets, exploring their properties and significance in optimization and operation research, based on fuzzy set theory.

Contribution

It defines convex and concave soft sets, extending the concept of soft sets with properties inspired by fuzzy set theory, and discusses their applications.

Findings

Defined convex soft sets and their properties

Defined concave soft sets and their properties

Established relationships between convex and concave soft sets

Abstract

In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give some properties for the concave sets. For these, we will use definition and properties of convex-concave fuzzy sets in literature. We also give different some properties for the convex and concave soft sets.