Computing the Fuzzy Topological Relations of Countries Affected by Congenital Disease

There are many studies have emerged to develop a descriptive concept of the topological relationship between spatial data. In this paper, a definition based on the interior operator and the closure operator for a fuzzy computational topology was used. The concept of the basic idea is that for each element there is an interior, exterior (complement), and boundary. The interior, the exterior and the boundary of the sample of countries affected by the congenital disease based on UNICEF database were computed.


Introduction
In geographic information system (GIS) with positional and attribute information, topological relations' information can be used for quality control, analyses, queries in spatial data and others.Topological relations are important in many tasks of object recognition, scene description and spatial reasoning.Topological relations' information play a fundamental role in GIS modeling.It is an important matter is to understand the relationships between spatial features.When a topology deals with the geometric object it deals with its structural and spatial properties regardless of their type, extension or geometric shape.Topological relationships between objects are a type of topological properties that remain invariant when any continuous deformation occurs in space [26].Topological relationships between objects are a type of topological properties that remains invariant when continuous deformation occurs in space [26].Many approaches have been suggested for defining the topological relations between crisp spatial objects; in 1979, Corbett present the algebraic topological structure of map modeling [7].In 1983, Allen described a method of representing the relationships between temporal intervals [1].In 1991-1995, after the submitted of 4-intersection and 9-intersections by Egenhofer and Franzosa, significant progress occurred on the topological relations between spatial objects [8][9].After that, a lot of studies have been done in this field for example [6,10,20,24,28].The topological relationship between spatial data can be used to describe the inaccuracy of data in GIS and the fuzzy sets were used as a useful tool in this area.There are many possible relationships in spatial data which many important for the analysis in GIS, Where many studies used the relationships in spatial data [5, 21-23, 25, 27].In this paper, we compute the interior, the exterior and the boundary of spatial data for an optional set of countries to derive the topological relations between the spatial data by using data from UNICEF database [29].In this paper, description of the study field (a congenital disease in each country) and the basic definitions of fuzzy topological space and definitions of topological relations in this space are mentioned, then the data topological relationships are computed according to the fuzzy topological model.

Study Field (Congenital Disease in each Country)
A congenital disorder or a birth defect is a condition existent during childbirth regardless of why.A congenital disorder may produce in disabled handicaps that might be developmental, intellectual, or physical [4,11,30].There are two fundamental types of congenital disorders: If there is a problem with the functioning of a certain part of the body then it is called functional disorder.While, when there is a problem in the state of a particular part of the body then it is called structural disorder.Some congenital disorders incorporate both functional and structural disorders [12].Congenital disorders may consequence for hereditary or chromosomal disorders, exposure to chemicals or specific drugs, or certain contagions through pregnancy [2,3,13].Risk elements incorporate folate inadequacy, drinking liquor or smoking through this phase, diabetes and parent's age.Furthermore there are different factors, for example, poisonous substances, prescriptions and enhancements, harmful substances, diseases, absence of supplements, physical limitation, hereditary qualities, economics, radiation, there are likewise obscure causes [14,15].Many are accepted to include numerous factors [15].Congenital disorders might be noticeable during childbirth or analyzed by screening tests.Various imperfections can be distinguished before birth by various prenatal tests [17].Treatment differs relying upon the imperfection being referred to.This may incorporate treatment, medicine, medical procedure, or assistive technology [16].Birth defects influence around 96 million individuals in 2015 [19].Congenital heart disease tops the list in terms of annual deaths by 303,000, followed by neural tube defects (65,000) [18].Topological relationships were computed for data obtained from the UNICEF global databases of deaths of newborns for each country due to congenital disease.[29].(3) For any

Definition 3.4
The family of fuzzy closed sets is denoted by ℱ ⊂   , and defined as  ∈ ℱ = ~ ∈ , where ~ is the complement of  [21].

Fuzzy Topology Induced by the Interior and Closure Operators
In general, when interior and closure operators are defined, each of them will define a fuzzy topology separately [21].The coherent between these two topologies may not exist.Following are the definitions for two operators, interior and closure defined coherent two fuzzy topologies.

Case Study
The mortality rate of congenital disease in each country was marked by a rate within the interval [0,1] [5].We try to determine the interior, exterior and boundary for the sample set of countries, to determine the countries most affected by congenital diseases for different value of α.The effect in the countries will be low if the closure value is close to zero.While, it will be high if the interior value is close to 1.This is evident from Table (1), compared to the percentage of deaths from this disease.Table (1) shows that for different values of α, the fuzzy interior, closure, exterior and boundary are different.The table shows for the larger value of α, the interior value will be smaller.When α=0.15, the nonzero values for countries ID greater than 39.When α=0.25, the nonzero values for countries ID greater that 66.When α=0.35, the nonzero values for countries ID greater than 95.This shows that the relation between interior value and the closure value are proportional to each other, while the relation between exterior value and the interior value are inversely proportional.Following are the graphs showing the values of the topological relationships which obtained in Table 2 for the different α values

Conclusion
The topological relationships were computed on the spatial objects of data from a geographic information system (GIS) for a particular geographical area to measure the extent of (for example) the impact of the flood on that region [5] or applied to land cover change [27].In this research, data of a different type (death rate of congenital disease) were used for each country, then the topological relationships were found for those data.we were attempted to calculate the topological relationships between spatial data.We use the application of fuzzy topology to compute the