Explore the vast range of titles available.

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

This article describes how recently, a paper by D. Ezhilmaran and K. Sankar called Morphism of bipolar intuitionistic fuzzy graphs, has introduced bipolar intuitionistic fuzzy sets and morphism of bipolar intuitionistic fuzzy graphs. By using this concept, the authors of this article have combined a bipolar intuitionistic fuzzy set and a soft set. They introduce the notion of bipolar intuitionistic fuzzy soft set and study their basic properties. Also, presented in this article are the basic operations on bipolar intuitionistic fuzzy soft sets, extended unions, and the intersection of two bipolar intuitionistic fuzzy soft sets. An application of bipolar intuitionistic fuzzy soft set provides into a decision-making problem and a general algorithm to solve this decision making problem.

We introduce the concept of an effective neutrosophic soft set, which aims to capture the influence on three independent membership functions representing degrees of truth (T), indeterminacy (I) and falsity (F). We go further by presenting a generalization of the effective neutrosophic soft set, which includes the incorporation of a degree to signify the potential for an approximate value-set. This enhancement contributes to improved efficiency and realism in the concept. Notably, this innovative approach leverages the strengths of both the generalized neutrosophic set and the effective neutrosophic soft set. The subsequent sections delve into fundamental operations on the generalized effective neutrosophic soft set, providing clarity through illustrative examples and propositions. Furthermore, we demonstrate the practical application of the generalized effective neutrosophic soft set in addressing decision-making problems and medical diagnoses.

-This study introduces the concept of time-soft sets (T-SS), which are an extension of traditional soft sets. We will define and explore the key operations associated with T-SS, including complement, union, intersection, and difference, among others. Ultimately, we will apply this methodology to respond to youth-developing cities in evaluation problems.

The goal of this paper is to introduce a novel hybrid model called multi-fuzzy N -soft set, and to design an adjustable decision-making methodology for solving problems where the inputs appear in this form. The new model enhances the virtues of multi-fuzzy set theory with the benefits of N -soft sets, two models that have been extensively investigated in recent years. The theoretical setting that arises allows us to incorporate data on the occurrence of ratings or grades (the defining characteristic of N -soft sets) in a multi-fuzzy environment. We perform a set-theoretical analysis of multi-fuzzy N -soft sets in order to establish the fundamental properties of their behavior. Then we develop a highly adaptable approach to decision-making in this new setting. This methodology takes advantage of a flexible procedure for the conversion of the original data to a hesitant N -soft setting, where we can resort to scores. Examples illustrate its application and the role of each parameter in the decision-making procedure.

In this manuscript we demonstrate interval-valued bipolar complex fuzzy set (IVBCFS) and then interval-valued bipolar complex fuzzy soft set (IVBCFSS), as a generalization of fuzzy set, interval-valued fuzzy set, bipolar fuzzy set, complex fuzzy set and soft set. We also initiate operational laws and basic results and properties for IVBCFS and IVBCFSS. Further explanation is given for the basic algebraic operations like complement, extended union, extended intersection, restricted union, and restricted intersection, AND product and OR product for IVBCFSS. Moreover, we demonstrate some fundamental aggregation operators like IVBCFS average aggregation, IVBCFS geometric and as well as their properties. To emphasize the usefulness and application of the system, we also develop the decision-making method and joint instances of the IVBCFSS (set-ups 1 and 2). In order to describe the effectiveness and influence of the approaching novel work, this study uses a comparative analysis of the new creating concept with prevailing ideas.

This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft open sets modulo soft sets of the first category, known as soft sets of the Baire property, is a soft σ-algebra. In this work, we mainly focus on the soft σ-algebra of soft sets with the Baire property. We show that soft sets with the Baire property can be represented in terms of various natural classes of soft sets in soft topological spaces. In addition, we see that the soft σ-algebra of soft sets with the Baire property includes the soft Borel σ-algebra. We further show that soft sets with the Baire property in a certain soft topology are equal to soft Borel sets in the cluster soft topology formed by the original one.

The concept of binary soft topological spaces defined on two universal sets and a parameter set is investigated in this paper. We define and examine the properties of the binary soft nowhere dense, binary soft dense, binary soft Gδ-set, and binary soft first and second category sets. Also, we introduced binary soft baire spaces and studied their characterizations.

Intuitionistic fuzzy sets (IFSs) can effectively represent and simulate the uncertainty and diversity of judgment information offered by decision-makers (DMs). In comparison to fuzzy sets (FSs), IFSs are highly beneficial for expressing vagueness and uncertainty more accurately. As a result, in this paper, we offer an approach for solving group decision-making problems (DMPs) with intuitionistic fuzzy parameterized (IFP) intuitionistic multi fuzzy N- soft set of dimension q (briefly, IFPIMFNSS) by introducing its induced IFP-hesitant N-soft set (IFPHNSS) as an extension of the multi-fuzzy N -soft set (MFNSS) based decision-making method (DMM). MFNSS is a fantastic and useful tool to deal with DMPs, but it has some limitations to solve group DMPs, but the constructed method in this paper is very advantageous for group-DMPs. To demonstrate the applicability of our methodology in practical situations, some examples are used, and also, we have compared the ranking performances of the proposed method with the Fatimah-Alcantud method. Finally, we bring the paper to a conclusion and our future work.

Many effective tools in fuzzy soft set theory have been proposed to handle various complicated problems in different fields of our real life, especially in decision making. Molodtsov’s soft set theory has been regarded as a newly emerging mathematical tool to deal with uncertainty and vagueness. Lattice ordered multi-fuzzy soft set (LMFSS) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of LMFSS is proposed to calculate the similarity between two LMFSSs. Moreover, some of its properties are introduced and proved. Finally, an application of LMFSS in decision making using similarity measure is analysed.