TY - JOUR
TI - The α-interval valued fuzzy sets defined on α-interval valued set
AU - Cuvalcioglu Gokhan
AU - Bal Arif
AU - Citil Mehmet
JN - Thermal Science
PY - 2022
VL - 26
IS - 102
SP - 665
EP - 679
PT - Article
AB - In this study, α-interval valued set is defined whose elements are closed  sub-intervals including α of unit interval that is I = [0, 1]. With  different order relation on this set, the properties of α-interval valued  set are examined. By the help of this order relation, it is shown that  α-interval valued set is complete lattice. Negation function on α-interval  valued set is given in order to study the theoretical properties of this  set. By means of discussions on α-interval valued set, the fundamental  features of α-interval valued set are studied. By the help of α-interval  valued set, α-interval valued fuzzy sets are defined. The fundamental  algebraic properties of these sets are examined. The level subsets of  α-interval valued fuzzy sets are defined to give the relations between  α-interval valued sets and crisp sets. With the help of this definition,  some propositions and examples are given.