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Chapter 16
DOI: 10.4018/978-1-4666-4936-1.ch016
Soft Sets:
Theory and Applications
ABSTRACT
This chapter is about soft sets. A brief account of the developments that took place in last 14 years in
the field of Soft Sets Theory (SST) has been presented. It begins with a brief introduction on soft sets
and then it describes many generalizations of it. The notions of generalized fuzzy soft sets are defined
and their properties are studied. After that, a notion of mapping, called soft mapping, in soft set setting
is introduced. Later, algebraic structures on soft sets like soft group, soft ring, etc. are discussed. Then
the next section deals with the concept of topology on soft sets. Here two notions of topology in soft sets
are introduced, which are the topology of soft subsets and the soft topology, respectively. The idea of
entropy for soft sets is defined in the later section. Next, some applications of hybrid soft sets in solving
real life problems like medical diagnosis, decision-making, etc. are shown. Issues like measurement of
similarity of soft sets are also addressed.
INTRODUCTION
Uncertainty is a common phenomenon of our daily
existence because our world is full of uncertain-
ties. In our daily life we encounter many situations
where we do take account of these uncertainties.
Therefore it is natural for man to understand and
try to model this uncertainty prevailing in physi-
cal world. From centuries, in almost all branches
of Science or in Philosophy, attempts have been
made to understand and represent the features
of uncertainty. Perhaps that is the main reason
behind the development of Probability theory
and Stochastic techniques which started in early
eighteenth century. Till mid-twentieth century,
Probability theory was the only tool for handling
Pinaki Majumdar
M.U.C. Women’s College, India & Visva-Bharati University, India