The main concept of a type-1 fuzzy set (fuzzy set) is introduced by Zadeh in 1965 . In , he introduced the concept, namely, type-2 fuzzy set in 1973 to classify a fuzzy set of type-1 fuzzy set when dealing with type-2 fuzzy set. Many of the scientists then introduced the concepts of type-2 fuzzy set, in 1976 introducing Mizumoto and Tanaka some properties of type-2 fuzzy set  and how to find the operations of type-2 fuzzy sets using the extension principle, it is the same rule that it has established Zadeh in 1973. Scientists then introduced several important concepts of the type-2 fuzzy set that correspond to the main concepts of the type-1 fuzzy set. In , Liu introduced the -plane concept of type-2 fuzzy set corresponding to the concept -level of the type-1 fuzzy set and the concept of support type-2 fuzzy set was developed by Mendel  corresponding to the concept of support type-1 fuzzy set. Mendel then introduced a very important concept interval type-2 fuzzy sets . The study of type-2 fuzzy sets was expanded to include the topology study of type-1 fuzzy set with the introduction of fuzzy topology by Chang in 1968 . Zhang in 2013 offered the interval type-2 fuzzy topological space  and then introduced Mohammad and Munir General type-2 fuzzy topological space . The type-2 fuzzy open sets such as type-2 fuzzy -preopen set and type-2 fuzzy -open set, we cannot configure its own definition only after introduce type-2 fuzzy point concept that belongs to the general fuzzy type-2 topological space.
This section paves the way to introducing the concept of type-2 fuzzy point by providing definitions of special important concept type-1 fuzzy set and type-2 fuzzy set after submitting the special definition to the clusters.
2.1. Definition 
If X is a collection of objects with generic element , then a fuzzy subset in X is characterized by a membership function; , where I is the closed unit interval [0, 1], then we write a fuzzy set by the set of points: .
2.2. Definition 
The support of a type-1 fuzzy set (denoted by ) which is the crisp set of all , .
In order to represent an element of a type-1fuzzy set , we provide a concept in type-1 fuzzy set theory that is a special case of -level sets, which is called fuzzy points used for inclusion of elements to fuzzy sets.
2.3. Definition 
A type-1 fuzzy point in a set X is also a type-1 fuzzy set with membership function:
where and , is called the support of and the value of . We denote this type-1 fuzzy point by . Two fuzzy points and are said to be distinct if and only if . A type-1 fuzzy point is said to belong to a type-1 fuzzy subset in X, denoted by if and only if .
2.4. Definition  
Let X be a finite and non-empty set , which is referred to as the universe a type-2 fuzzy set, denoted by is characterized by a type-2 memberships function , as
where and , that is .
We can give a new wording to
where and denote the union in discrete sets and ∑ is replaced by ∫ is continuous universes are set. The class of all type-2 fuzzy set of denoted by .
A type-2 fuzzy set universes set , denoted by, such that
A type-2 fuzzy empty set , denoted by
Interval type-2 fuzzy set , when all the , for all .
The operations of type-2 fuzzy set , consider and are two type-2 fuzzy sets and the membership grades of and respectively, we can represented by
The union of two type-2 fuzzy sets is defined as
The intersection of two type-2 fuzzy sets is defined as
The containment type-2 fuzzy sets are defined as .
The complement of type-2 fuzzy set defined as .
A normal type-1 fuzzy set is one for height equals 1, otherwise it is called subnormal .
2.5. Definition 
A normal type-2 fuzzy set is one for which .
2.6. Definition 
The support of a type-2 fuzzy set denoted comprises all such that .
2.7. Definition 
The two damnation -plane , denoted is the union of all primary membership whose secondary grades are greater than or equal special value that
2.8. Definition 
Let be the collection of type-2 fuzzy sets over then is called to be general type-2 fuzzy topology on .
3) for .
The pair is said to general type-2 fuzzy topological space over X and
the member of is said to be type-2 fuzzy open sets in X and type-2 fuzzy sets are said type-2 fuzzy closed sets in X, if its complement .
We must note that all the type-2 fuzzy sets are normal type-2 fuzzy sets so as to complete the topological construction and especially check identity law ( ).
3. Type-2 Fuzzy Point
The introduction of this section is the end of which the paper developed by the special case of -plane, which claims type-2 fuzzy point.
A type-2 fuzzy point in a set X is also a type-2 fuzzy set with secondary membership function:
where and , is called the support of and the value of .
Let , is a type-2 fuzzy point
and we have
We denote this a type-2 fuzzy point by . Two a type-2 points and are said to be distinct if and only if .
3.3. Serious Results
The means of determining belonging set or fuzzy point in the subject of the fuzzy set is to compare with the membership function, but in the second type-2 fuzzy set we use the containment property given by Mizumotoand Tanaka .
The important role played by the type-2 fuzzy point in configuring continuous function after building new concepts from open type-2 fuzzy set made us offer this new concept. This concept allows for future dealings with the concept of neighborhood in general type-2 fuzzy topological space. In order for us to be able to configure such as type-2 fuzzy -preopenset and type-2 fuzzy -open set only and to examine the relationships among them.
Thanks and appreciation to all who contributed to the publication and composition of the main idea of the research and especially Prof. Jerry Mendel and Prof. Mohammad Reza Rajati.