In this study, ?-interval valued set is defined whose elements are closed
sub-intervals including ? of unit interval that is I = [0, 1]. With
different order relation on this set, the properties of ?-interval valued
set are examined. By the help of this order relation, it is shown that
?-interval valued set is complete lattice. Negation function on ?-interval
valued set is given in order to study the theoretical properties of this
set. By means of discussions on ?-interval valued set, the fundamental
features of ?-interval valued set are studied. By the help of ?-interval
valued set, ?-interval valued fuzzy sets are defined. The fundamental
algebraic properties of these sets are examined. The level subsets of
?-interval valued fuzzy sets are defined to give the relations between
?-interval valued sets and crisp sets. With the help of this definition,
some propositions and examples are given.
In this paper, (α,β)-interval valued set is studied. The order relation on (α,β)-interval valued set is defined. It is shown that (α,β)-interval valued set is complete lattice by giving the definitions of infumum and supremum on these sets. Then, negation function on these sets is introduced.
With the help of (α,β)-interval valued set ,(α,β)-interval valued intuitionistic fuzzy sets are defined. The fundamental algebraic properties of these sets are examined. The level subsets of (α,β)-interval valued intuitionistic fuzzy sets are given. Some propositions and examples are studied.
In this study, the resolution theorems for IFSs were given by using the α-t sheet level set and strict α-t sheet level set of IFSs. For the second resolution theorem, the definition of strict α-t sheet level set of IFSs was given in this paper. Because of the nature of IFSs, one might give those theorems using fuzzy sets. In this paper, that problem was solved.
In this paper, the new set difference is defined between intervalued intuitionistic fuzzy sets (IVIFSs).A different perspective is reduced to the formal set difference between IVIFSs. This new set difference (−•) between IVIFSs is introduced by using. operation. Instead of comparing this operator with all other set difference operations, the set difference operation (−∩) which is defined by using ∩ is used. Some fundamental properties which are provided and not provided on −∩ are examined whether satisfy or not satisfy on −• operation. By the help of these examinations, it is seen that −∩ and −• operations have different properties. The new properties about −• are studied.
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