In this article, the concept of dual hesitant fuzzy soft sets is applied to the subring and ideal structures of the classical rings. Further, based on level soft sets of the dual hesitant fuzzy soft... Show More

In this article, the concept of dual hesitant fuzzy soft sets is applied to the subring and ideal structures of the classical rings. Further, based on level soft sets of the dual hesitant fuzzy soft set, a characterization theorem for the dual hesitant fuzzy soft ring is established. Moreover, a counter-example is provided for a dual hesitant fuzzy soft ring which is not an idealistic dual hesitant fuzzy soft ring. Finally, the homomorphic and bi-soft homomorphic properties of a dual hesitant fuzzy soft ring are discussed.

In this article, the theoretical aspects of union-soft sets by extending the notions of equivalence relations, partition, composition of relations, and function to the framework of union-soft sets... Show More

In this article, the theoretical aspects of union-soft sets by extending the notions of equivalence relations, partition, composition of relations, and function to the framework of union-soft sets are introduced. Further the Cartesian product, the relation between union-soft sets, induced relations from the universal set and the attribute set with examples are discussed. Moreover, the composition of union-soft set relationships with examples and some related theorems are demonstrated. Finally, the concepts of a union-soft set function and their respective composition function are examined.

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... Show More

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.

This article describes how information technology and internet together infused organizations with huge amount of data. Consequently, accumulating, storing, understanding and analyzing data at a... Show More

This article describes how information technology and internet together infused organizations with huge amount of data. Consequently, accumulating, storing, understanding and analyzing data at a large scale is equally important and complex. Out of this data not all is information data, in order to extract information, one needs to discard redundant, irrelevant and unnecessary data. This article aims to introduce a data reduction technique which will be useful to discard irrelevant data. Here in data-reduction, the authors have used fuzzy-soft set techniques, namely fuzzy-soft information matrixes. Further, they have introduced a new fuzzy-soft information measure of fuzzy-soft matrixes.

In this article, some new basic operations and results of Ordered Intuitionistic Fuzzy Soft (OIFS) sets, such as equality, complement, subset, union, intersection, OR, and AND operators along with... Show More

In this article, some new basic operations and results of Ordered Intuitionistic Fuzzy Soft (OIFS) sets, such as equality, complement, subset, union, intersection, OR, and AND operators along with several examples are investigated. Further, based on the analysis of several operations on OIFS sets, numerous algebraic properties and famous De Morgans inclusions and De Morgans laws are established. Finally, using the notions of OIFS sets, an algorithm is developed and implemented in a numerical example.

This article describes how the lack of adequate parametrization in some of the earlier uncertainty based models like fuzzy sets, rough sets motivated Molodtsov to introduce a new model in soft set.... Show More

This article describes how the lack of adequate parametrization in some of the earlier uncertainty based models like fuzzy sets, rough sets motivated Molodtsov to introduce a new model in soft set. A suitable combination of individual models leads to hybrid models, which are more efficient than their individual components. So, the authors find the introduction of many hybrid models of soft sets, like the fuzzy soft set (FSS), intuitionistic fuzzy soft sets (IFSS), interval valued fuzzy soft set (IVFSS) and the interval valued intuitionistic fuzzy soft set (IVIFSS). Following the characteristic function approach to define soft sets introduced by Tripathy et al., they re-define IVIFSS in this article. One of the most attractive applications of soft set theory and its hybrid models has been decision making in the form of individual decision making or group decision making. Here, the authors propose a group decision making algorithm using IVIFSS, which generalises many of our earlier algorithms. They compute its complexity and establish the computation experimentally with graphical illustrations.