An interval-valued picture fuzzy set (IVPFS) is one of the generalizations of an interval-valued fuzzy set to handle the uncertainties in the data during analysis. The aim of this paper is to introduce and study new operations of IVPFS, along with its properties, and examples. In addition, we present the notion of the interval-valued picture fuzzy soft set theory and investigated their properties. Several operations on such as subset, equal, complement, inf product, sup product, union, and intersection are defined over the interval-valued picture fuzzy soft set and discussed their basic properties. Furthermore, we construct an algorithm using an interval-valued picture fuzzy soft set to solve the decision-making problems and illustrate its applicability through a numerical example. From the study, we conclude that the proposed approach is viable in order to handle the uncertainties during the decision-making problems.

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.

The major concern of this paper is to highlight the notion of possibility m -polar fuzzy soft set (because it is useful in decision-making and other similar problems). For convenience of practical applications, several operations (such as subset, equ

In this paper, we generalize six kinds of rough set models based on j-neighborhood space (i.e., reflexive 1 j-neighborhood rough set, reflexive 2 j-neighborhood rough set, reflexive 3 j-neighborhood rough set, similarity 4 j-neighborhood rough set, similarity 5 j-neighborhood rough set, and similarity 6 j-neighborhood rough set) and investigate some of their basic properties. Further, we propose a new neighborhood space called j-adhesion neighborhood based on six types of rough set models (i.e., reflexive 7 j-adhesion neighborhood rough set, reflexive 8 j-adhesion neighborhood rough set, reflexive 9 j-adhesion neighborhood rough set, similarity 10 j-adhesion neighborhood rough set, similarity 11 j-adhesion neighborhood rough set, and similarity 12 j-neighborhood rough set) to reduce the boundary region and the accuracy. The fundamental properties of approximation operators based on j-adhesion neighborhood space are investigated. The relationship between the properties of these types is explained. Finally, we give comparisons between the proposed approach with the previous approach (i.e., Abo-Tabl’s approach and Dai et al.’s approach) from six types of rough set models. Consequently, the accuracy from the proposed approach is improved.