Decision making using fuzzy soft set (FSS) and its extensions has become the most significant research area in the age of uncertainty. In this article, the authors survey the evolution of fuzzy soft... Show More

Decision making using fuzzy soft set (FSS) and its extensions has become the most significant research area in the age of uncertainty. In this article, the authors survey the evolution of fuzzy soft sets (FSSs) during the last decade and a half (2001-2015) to analyze the impact of FSS and its extension in the decision-making paradigm. Based on some selected journals, conferences, and online databases, this article classifies the decision-making process mainly into ten different categories, which are based on different types of FSSs. This article briefly explores each individual category by mentioning the theoretical/algorithmic approaches proposed by the respected authors. Furthermore, all papers are categorized with respect to publication year, published journal, application type, and decision-making criteria. This literature survey provides a platform to the researchers to find out the dimensions of future research works in FSSs by analyzing the present state and potential areas.

As seed selection is a challenging task due to the presence of hundreds of varieties of seeds of each kind, some homework is necessary for selecting suitable seeds as new varieties and kinds of... Show More

As seed selection is a challenging task due to the presence of hundreds of varieties of seeds of each kind, some homework is necessary for selecting suitable seeds as new varieties and kinds of seeds are introduced in the market every year having their own strengths and weaknesses. The complexities involved in the characteristics in the form of parameters results in uncertainties and as a result some uncertainty based model or hybrid models of more than is required to model the scenario and come out with a decision. Soft sets have enough of parameterization tools to support and hence is the most suitable one for such a study. However, as hybrid models are more efficient, the authors select a model called the interval valued fuzzy soft set (IVFSS) and propose a decision-making algorithm for the selection of seeds. A real database of seeds is used for experimental verification of the efficiency of the algorithm. This is the first attempt for such a study. The use of signed priorities and intervals for the membership of values for entities makes the study more efficient and realistic.

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It... Show More

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

Feature selection is one of the widely used pre-processing techniques to deal with large data sets. In this context, rough set theory has been successfully implemented for feature selection of... Show More

Feature selection is one of the widely used pre-processing techniques to deal with large data sets. In this context, rough set theory has been successfully implemented for feature selection of discrete data set but in case of continuous data set it requires discretization, which may cause information loss. Fuzzy rough set theory approaches have also been used successfully to resolve this issue as it can handle continuous data directly. Moreover, almost all feature selection techniques are used to handle homogeneous data set. In this article, the center of attraction is on heterogeneous feature subset reduction. A novel intuitionistic fuzzy neighborhood models have been proposed by combining intuitionistic fuzzy sets and neighborhood rough set models by taking an appropriate pair of lower and upper approximations and generalize it for feature selection, supported with theory and its validation. An appropriate algorithm along with application to a data set has been added.

Soft set theory has a rich potential for application in many scientific areas such as medical science, engineering and computer science. This theory can deal uncertainties in nature by... Show More

Soft set theory has a rich potential for application in many scientific areas such as medical science, engineering and computer science. This theory can deal uncertainties in nature by parametrization process. In this article, the authors explore the concepts of soft relation on a soft set, soft equivalence relation on a soft set, soft graphs using soft relation, vertex chained soft graphs and edge chained soft graphs and investigate various types of operations on soft graphs such as union, join and complement. Also, it is established that every fuzzy graph is an edge chained soft graph.

As a generalization of fuzzy sets, soft set and neutrosophic sets are applied to many branches of mathematics to overcome the complexities arising from uncertain data. Combining these notions, in... Show More

As a generalization of fuzzy sets, soft set and neutrosophic sets are applied to many branches of mathematics to overcome the complexities arising from uncertain data. Combining these notions, in this article, the author initiates the study of $\Gamma$-semirings, an extension of semirings, and its ideals by neutrosophic soft sets. After defining some necessary definitions, they investigate neutrosophic soft $\Gamma$-semiring, neutrosophic soft ideals, idealistic neutrosophic soft $\Gamma$-semiring and obtain some of its characterizations.