Paper type: Essay Pages: 5 (1205 words)
A Study on the age group of people who are mostly affected by the Mobile Radiation using Intuitionistic Fuzzy Soft MatrixDr.J.Jon Arockiaraj1, M.Sivapriya21Head of the Department, Department of Mathematics, St.Joseph’s College of Arts and Science (Autonomous),Cuddalore.2PG Student, Department of Mathematics,St.Joseph’s College of Arts and Science (Autonomous),Cuddalore.ABSTRACT: Mobile Radiation leads to Cardio vascular problem, Respiratory problems and Cancer. The most common symptoms include Headache, Visual disorder, Stress, Dizziness, Insomnia.
In this paper, we have analyzed the effects of mobile Radiation to the people in the age group of 5-70 years. Further, it is discussed about the effects of Mobile Radiation using Intuitionistic fuzzy soft matrix. KEYWORDS: Mobile Radiation,Intuitionistic fuzzy soft matrixIntroduction:Cell phones emit signals via radio waves comprised of mobile frequency ( RF ) energy, a form of Electromagnetic radiation.Mobile radiation is very harmful to human health and it affects the other organisms as the use of mobile phones increasing throughout the world.
Any cell phones at or below the Specific Absorption Rate(SAR) level [1.6watts per kg] is safe. Molodtsov pointed out the important existing theories viz, probability theory, fuzzy soft set theory, intuitionistic fuzzy soft theory, rough set theory etc., Which can be considered as the mathematical tool for dealing with uncertainities have their own difficulties. Matrices plays an important role in the broad area of science and engineering.The concept of Intutionistic Fuzzy Soft Matrix is applied to identify the group of people (based on age) mostly affected. Basic DefinitionsDefinition 1 : Let U be a non-empty finite set of objects called Universe and Let E be a non-empty set of parameters. An ordered pair (F,E) is said to be a soft set over U, if F is a mapping from E to the set of all subsets of U.Definition 2: Let U be a universe. A fuzzy set X over U is a set defined be a function ,representing a mapping , here called a membership function of and the value is called the grade of membership of The value represents the degree of u belonging to the fuzzy set X. Thus a fuzzy set X over u can be represented as follows,.Definition 3 : Let U be a universe set E, A be a set of parameters and A‚E. Then a pair (F,A) is called fuzzy soft set over U, where F is a mapping from A to the set of all fuzzy subsets of U. Definition 4 : An Intuitionistic fuzzy set A is a non-empty set U having the form A=x, јAx, vAx:U ’ 0,1, where the function јAx:U’ 0,1, vAx:U’ 0,1, denotes the degree of membership and degree of non-membership of each element x€€U to the set A respectively and0‰¤јAx+vA(x)‰¤1 for all x€€U. Given an universal set U and a set of parameters E, for AE, the pair (F,A) is called an Intuitionistic fuzzy soft set over U if F is a mapping from A to the set of all Intuitionistic fuzzy subsets of U.Definition 5 : Let U=c1,c2,c3,c4,,cm be the universal set and E=e1,e2,e3,,en be the set of parameters. Let AE and (F,A) be a intuitionistic fuzzy soft set in the fuzzy soft class (U,E). Then the intuitionistic fuzzy soft set (F,A) can be represented in matrix form as Sm n=aijm n (or)S=aij, i=1,2,,m, j=1,2,,n Where,aij=јjci, Vjci, if ej€€A0,1, if ej €‰AHere јjci represents the membership of ci in the Intuitionistic fuzzy set Fej and Vjci represents the non-membership of ci in the Intuitionistic fuzzy )et Fej. The matrix Sm n is called Intuitionistic fuzzy soft matrix. This matrix S can also be written as S=јA,іA or S=јij, іij.Definition 6 : Let A=aijm n be an Intuitionistic fuzzy soft matrix, where aij= јjci,іjci. Then we define the value matrix of Intuitionistic fuzzy soft matrix A is VA=aij=јij-іij, i=1,2,,m, j=1,2,,n.Definition 7 : Let A=aijm n, B= bijm n be two intuitionistic fuzzy soft matrices then we define Score matrix of A and B as SA,B=dijm n where dij=VA-VB.Definition 8 : Let A=aijm n, B= bijm n be two intuitionistic fuzzy soft matrices. Let the corresponding value matrix be V(A), V(B) and then we define score matrix of A and B as S(A,B)=dijm n, and we define total score for each ci in U is Si=j=1ndij. AlgorithmAlgorithm for decision making method by using Intuitionistic fuzzy soft matrices.Step 1: Construct the Intuitionistic fuzzy soft set (F,c) and obtain the Intuitionistic fuzzy soft matrix A corresponding to (F,c) respectively.Step 2: Find the Intuitionistic fuzzy soft complement matrix Ac.Step 3: Compute VA, V(Ac) and SAAc.Step 4: Calculate the total score Si for each ui in U.Step 5: Find ui for which maxSi. Incase maxSi occur for more than one value, and then repeat the process by reassessing more than one value the parameters.Application of Intuitionistic fuzzy soft matricesSuppose U=u1,u2,u3,u4,u5 be the five categories based on the age group of respondents which forms the alternative set or universal set and Let C=c1, c2,c3,c4,c5 be the criteria set.Group of Respondents (Universal set U) (Based on age of People) u1 – 5 to 17 years u2 – 18 to 30 years u3 – 31 to 43 years u4 – 44 to 56 years u5 – 57 to 70 yearsCriteria Set C (Symptoms) c1 – Headache c2 – Visual disorder c3 – Stress c4 – Dizziness c5 – InsomniaIn order to collect data an interview schedule was developed pre tested and managed to the respondents. A sample of 100 respondents (20 in each group) was selected for sampling technique.The corresponding intuitionistic fuzzy soft set isF, c=Fc1=u1, 0.6,0.2u2,0.8,0.2u3,0.6,0.2u4 , 0.5,0.1u5,0.3,0.1Fc2 =u1,0.5,0.1u2,0.9, 0.1u3,0.5,0.1u4,0.5,0.2u5,0.2,0.1Fc3=u1,0.2,0u2,0.7,0.2u3,0.2,0.1u4,0.1,0u5,0.1,0Fc4=u1,0.2,0u2,0.4,0.1u3,0.5,0.1(u4,0.4,0.1)(u5(0.2,0.1)Fc5=u1,0.5,0.1u2,0.9,0.2u3,0.3,0.2(u4,0.3,0.2)(u5,0.3,0.2)The Intuitionistic fuzzy soft matrix c1 c2 c3 c4 c5 The Intuitionistic fuzzy soft matrix c1 c2 c3 c4 c5 c1 c2 c3 c4 c5 Total score = This implies that the group u2 has the maximum group.Therefore the people in the age group 18-30 years are affected by mobile radiation.Conclusion:We conclude that some people are affected by the mobile radiation. The rapid advent in technology of Electromagnetic Radiation Pollution had started having ill effects on human health and other organisms. The study alerts everyone to the aware of significant defects. 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