Special Types of Fuzzy Sets and Their Applications in Decision Making: Theory and Applications

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 practical problems with a view to find more realistic solutions without imposing rigid and unrealistic conditions as in the case with the existing classical methods. The quantum of research work carried out in both theoretical and application areas of fuzzy set theory is enormous. The developments in the application areas of fuzzy set theory can be classified broadly into two types namely, theory-oriented and practical problem-oriented. The major aim of research in these areas is to develop parallel mathematical theories in a fuzzy theoretical setup in line with the existing classical theories.