الفهرس 
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Abstract
In most of cases in our life, the data obtained for decision making are only approximately known. In1965, Zadeh [76] introduced the concept of fuzzy set theory to meet those problems.
Fuzzy sets since their introduction (Zadeh [76] and Zimmermann, [50]) have received a great deal of interest.
For an ordinary set, a given object either belongs or does not belong to the set, whereas for a fuzzy set the degree of membership of an object is given by the value of the membership function for the object. Hence, one can say that there is an uncertainty associated with the membership of an element to a given fuzzy set.
After the introduction of the concept of fuzzy sets, Atanassov [71, 72, 73, 74, and 75] introduced another type of fuzzy sets that is called intuitionistic fuzzy set (IFS) as a generalization of fuzzy sets.
Atanassov added in the definition of fuzzy set a new component which determines the degree of nonmembership. Fuzzy sets give the degree of membership of an element in a given set (the nonmembership of degree equals one minus the degree of membership), while intuitionistic fuzzy sets give both a degree of membership and a degree of nonmembership, which are more-or- less independent from each other; the only requirement is that the sum of these two degrees is not greater than 1.
Since the world is full of indeterminacy, the neutrosophic found their place into contemporary researches.
Neutrosophy was pioneered by Smarandache [39]. It is a branch of philosophy which studies the origin, nature, and scope of neutralities. Neutrosophic set theory is a powerful formal framework which generalizes the concept of the classic set, fuzzy set [76] and intuitionistic fuzzy set [71, 73]. Neutrosophy introduces a new concept represents indeterminacy with respect to <A>. It can solve certain problems that cannot be solved by fuzzy logic. For example, a paper is sent to two reviewers, one says it is 90% acceptable and another says it is 90% unacceptable. But the two reviewers may have different backgrounds. One is an expert, and other is not. The impacts on the final decision of the paper by the two reviewers should be different, even though they give the same grade level of the acceptance.
The fundamental concepts of neutrosophic set, introduced by Smarandache [39, 40, 41] and Salama [1, 2, 3, 4 and 5], provide a natural foundation for treating mathematically the neutrosophic phenomena which exist pervasive in our real world and for building new branches of neutrosophic mathematically.
Several researchers dealing with the concept of neutrosophic set such as Smarandache [42, 43, 44], Bhowmik and Pal in [80, 81], Salama in [6, 7, 8, 9, … , 23], Wang in [54] and Kroumov [95].
After introducing and developing fuzzy set, intuitionistic fuzzy set and neutrosophic set theory, a lot of studies have been done to combine statistical methods and fuzzy set theory. This works, called fuzzy statistics, intuitionistic fuzzy statistics and neutrosophic statistics have been developed in some branches [26, 27, 28, 29, 30, 31, 33, 34, …, 102].
In this thesis, some concepts of statistics in neutrosophic data are discussed such as: correlation coefficient, regression and probability.
First: A method to calculate the correlation coefficient of generalized intuitionistic fuzzy sets is proposed (which introduced by Mondal [91]) by means of ”centroid”.
Second: A statistical concept of correlation for data represented as neutrosophic sets is discussed adopting point view. It is calculated by showing both positive and negative relationship of the sets, and showing that it is important to take into account all three terms describing neutrosophic sets.
Third: A formula for correlation coefficient is derived. The formal was defined on the domain of neutrosophic sets in two cases: finite space and probability spaces.
Finally: The classical probability to the notion of neutrosophic probability is introduced. This kind of probability is necessary because it provides a better representation than classical probability to uncertain events. Possible applications to computer sciences are touched upon. The thesis consists of four chapters:
Chapter one:
Is concerning with the basic ideas from fuzzy sets and Intuitionistic fuzzy set theory and some relations and operations. An overview is given for the combination of statistical methods and fuzzy set and intuitionistic fuzzy set theory such as fuzzy correlation, fuzzy probability and intuitionistic fuzzy correlation.
Chapter two:
A method is proposed to calculate the correlation coefficient in a sense of generalized intuitionistic fuzzy sets (which introduced by Mondal [91]) by means of ”centroid”. It is by showing both positive and negative relationship of the sets.
The results of this chapter have been published see [56].
Chapter three
An overview is given for the definition of neutrosophic sets and the fundamental concepts of neutrosophic sets.
Chapter four:
Some concepts of statistics are discussed such as: correlation coefficient as statistical measure is discussed in deferent forms. Method of calculating correlation coefficient is proposed in neutrosophic sets. A formula in correlation coefficient defined on the domain of neutrosophic sets is discussed and derived, as well as another formal defined on the domain of neutrosophic sets probability space.
Finally: A formula in the simple linear regression in neutrosophic sets is derived.
The results of this chapter have been published in five papers see [8, 10, 55, 57 and 59]
Chapter five:
The classical probability to the notion of neutrosophic probability is introduced. The neutrosophic probability is necessary because it provides a better representation than classical probability to uncertain events.
This result has been published in [58].