The study of topology is extended in many fields. Various types of topologies have been introduced in different types of sets such as fuzzy sets, intuitionistic fuzzy sets, soft sets, rough sets, neutrosophic sets and so on. These topologies found numerous applications in medical diagnosis, decision making, multi-criteria decision making, image processing, pattern recognition, COVID-19, etc. Decision making plays a vital role in every activity of human life. Decision making is a step-by-step process consisting of narrating the problem, collecting the information or data, calculating critical...

A cubic set is a hybrid structure involving an interval-valued fuzzy set and a fuzzy set. A cubic soft set is a parameterized family of cubic sets. It is yet another hybrid structure obtained by combining cubic sets with soft sets. A generalized interval-valued intuitionistic fuzzy soft set is a further generalization of a cubic soft set where instead of interval component of cubic sets, we consider interval-valued intuitionistic fuzzy sets. This book is the outcome of the research work carried out by us towards finding the application of soft sets, cubic soft sets, Neutrosophic cubic soft...

One of the successful modern theories that have excelled in the analysis of uncertainty or vagueness is the fuzzy set theory introduced by Zadeh nearly more than five decades ago. Though the original intention of fuzzy set theory was to scientifically analyse vagueness or uncertainty arising out of linguistic expressions, its versatility and adaptability have widened the scope of this theory through its developments, generalizations and subjectiveness, which make this theory more suitable for applying to, complicated real-life problems. Fuzzy theory has been applied to a large number of...

A number of methods like Linear programming, Dynamic programming, Assignment problem, Transportation problem, Game theory etc., are examples of decision making under certainty. When there are uncertainties or vagueness in the data regarding alternatives and criteria, we can use different techniques for decision making based on whether the data involves probabilities, fuzzy sets, soft sets, rough sets and so on. This situation is called Multi-Criteria Decision Making (MCDM) under uncertainty. MCDM is considered to be a sub discipline of operations research that deals with structuring, planning...

A number of methods like Linear programming, Dynamic programming, Assignment problem, Transportation problem, Game theory etc. are examples of decision making under certainty. When there are uncertainties or vagueness in the data regarding alternatives and /or criteria, we use different techniques for decision making based on whether the data involves probabilities, fuzzy sets, soft sets, rough sets, neutrosophic sets or any other hybrid structure. Decision problem involving the evaluation of multiple criteria and alternatives are called multi-criteria decision making (MCDM) problem. The...