Fuzzy Soft Matrices Applied In Yoga On Hemorrhoid

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1 International Journal of Engineering cience Invention (IJEI IN (Online: , IN (rint: Volume 7 Issue 10 Ver III Oct Dr. T. Geetha ** n. Usha* **Department of Mathematics K.N.G College for women (utonoums, Tanjore, Tamilnau, Inia. *Research cholar Department of Mathematics K.N.G College for women (utonoums, Tanjore, Tamilnau, Inia. Corresponing uthor; Dr. T. Geetha bstract :In this paper, we efine fuzzy soft matrices an their basic properties. We then efine fuzzy soft matrices which are matrix representation of the fuzzy soft sets. The purpose of this paper is to efine ifferent hyper of matrices in fuzzy soft set theory, we have introuce here some new operations on these matrices an iscusse here all these efinitions an operations by appropriate example.in this work, we efine soft matrices an their operations which are more functional to make theoretical stuies in the soft set theory. We then efine proucts of soft matrices an their properties. We finally construction on soft max min ecision making metho which can be successfully applie to the problems that contain uncertainties. Key Wors :oft set, fuzzy soft set (F, Fuzzy oft Matrices (FM, Fuzzy oft Complement Matrices, Null et, Fuzzy oft Class, Hemorrhois Date of ubmission: Date of acceptance: I. Introuction Molotsov [1] also escribe the concept of oft et Theory having arameterizations tools for ealing with uncertainties. Researchers on soft set theory have receive much attention in recent years. Magi an Roy [,4] first introuce soft set into ecision making problems. Maji et al., [] introuce the concept of fuzzy soft sets by combining soft sets an fuzzy sets. Cagman an Enginoglu [5] efine soft matrices which were a matrix representation of the soft sets an constructe a soft max min ecision making metho. Cagman an Enginoglue [6] efine fuzzy soft matrices an constructe a ecision making problem. orah et al.,[7] extene fuzzy soft matrix theory an its application. Maji an Roy[8] presente a novel metho of object from an imprecise multi observer ata to eal with ecision making base on fuzzy soft sets. Yoga can be very beneficial in relieving bowel troubles. s a first line of efense, it might be useful to focus asanas on the mi section. Yoga helps in the removal of the toxins in the boy which can give a free an active feeling to the boy an once the toxins are out from the boy. It helps to restore the normal balance of the boy an provie freeom from the pain cause ue to piles. iles may cause back pain in several iniviuals because of its critical positions in the boy. Yoga exercises can helps to greatly in the treatment of piles an the back pain. One of the key elements of the yogi lifestyle is strict vegetarianism. Various asunas can be use for the treatment of piles an a few which have guarantee results like sarvangasana, tuasan, surya namaskar an a few quite challenging poses like shirshsana. II. reliminaries Definition (.1 : oft et : Let U be an Initial universe set an E be a set of arameters. Let (U enotes the power set of U. Let E. pair (F,E is calle a soft set over U, Where F is a mapping given by, F : (U In other wors, a soft set over U is a parameterize family of subsets of the universe U. Definition (. : Fuzzy oft et Let U be an initial universe, E be the set of all parameter an E. pair (F, is calle a fuzzy soft set over U where F : (U is a mapping from into (U, Where (U enotes the collection of all subsets of U. Definition (. : age

2 Fuzzy soft Class : Let U be an initial universe set an E be the set of attributes. Then the air (U,E enotes the collection of all fuzzy soft sets on U with attributes from E an is calle a fuzzy soft class. Definition (.4: Fuzzy oft ub et : For two fuzzy sets (F,E an (G,E Over a common universe U, we have (F,E (G,E if an for all e, F ( e is a fuzzy soft subset of G (e, i.e., (F,E is a fuzzy soft subset of (G,E Definition (.5: Fuzzy soft complement set : The complement of fuzzy soft sets (F,E enote by (F,E is efine by F : E I U is a mapping given by F ( e = [(e], for all e E ( F, E = (F, E, where Definition (.6: Fuzzy oft Null et : fuzzy oft set (F,E over U is sai to be null fuzzy soft set with respect to the parameter enote by, if F ( e for all e E Definition (.7: Fuzzy oft Matrix : Let U = {u 1,u,u,u 4,.um} be the universal set an E be the set of parameters given by E= {1,e 1,e, e n }. Then the fuzzy soft set (F,E can be expresse in matrix from as or simply by [ a ], I = 1,,. m; j = 1,,..n an [ a ] = [(, ]; where an membership function an fuzzy reference function U in the fuzzy set F (e j so that [ a ] represent the fuzzy gives the fuzzy membership value of U. We shall ientify a fuzzy soft set with its fuzzy soft matrix an use these two concepts interchangeable. The set of all fuzzy soft matrices over U will be enote by FM. For usual fuzzy sets with fuzzy reference function 0, it is obvious to see that a [(,0] for all i,j. Definition (.8 : Membership value function : The membership value matrix corresponing to the matrix an as for all I = 1,,, m, j = 1,,,. n where function an fuzzy reference function respectively of U in the fuzzy set F (e j. where MV ( [ ] represent the fuzzy membership Definition (.9 : Fuzzy oft Complement Matrix : Let = a, then complement of is enote by c = 1- a for all i an j. = (c where Definition (.10 : ition of Fuzzy oft Matrices : Let U = {u 1,u,u,u 4,.u m } be the universal set an E be the set of parameters given by E = FM, where {e l,e,..e n }. Let the set of all fuzzy soft matrices over U be FM. Let, a, a (, ; an = b, b = (, to avoi egemerate aiton (+ between an as + = C, case we assume that min,, Max for all i an j we efine the operation age

3 where c = c, c (max(,,min(,, an ubtraction (- between an as C where max (, c c c c, C = (c, c =(min(,, Definition (.11 core Matrix : Let, FM. Let the corresponing membership value matrices be ( = MV an MV ( =, i = 1,,,..m; j = 1,,,..n. Then the core matrix (, woul be efine as (, Where = - Definition (.1 : Total core Matrix : Let, FM. Let the Corresponing membership Value Matrix be MV ( [ ] respectively an the score matrix be (, i = 1,,,...m, j = 1,,,...n Then the total score for each u, in U woul be calculate by the formula = - (, - (, Definition (.1 : Hemorrhois, also calle pices, are vascular structures in the anal canal. In the normal state, they are cushions that help with stool control. They become a isease when swollen or in flame; the unqualifie term hemorrhoi is often use to refer to the isease. The sign an symptoms of hemorrhois epen on the type present. Internal hemorrhois often result in painless. right re rectal bleeing when efecating External hemorrhois often result in pain an swelling in the area of the anus. If bleeing occurs it is usually arker. ymptoms frequently get better after a few ays. skin tag may remain after the healing of an external hemorrhoi. III. lgorithm : 1. Input the fuzzy soft Matrices (F,E an (G,E lso write the fuzzy soft Matrices commensurate to (F,E an (G,E respectively.. Write the fuzzy soft matrices corresponing to ( F, E an (G,E respectively.. Compute MV ( 4. Compute MV ( 5. Compute the score matrix an ( F, E an (G,E lso write the fuzzy soft matrices an (,( 6. Compute the total score i for Ruch u i in v. 7. Fin k = max ( i 8. If k has more than one value, then go to step (1 an repeat the process by reassessing the parameters. IV. Case tuy : Consier 4 atients aritha, alan, Velu, Vaya are enote by the set ={aritha, alan, Velu, Vaya} an the set of symptoms = {ainless bleeing, itching or irritation, painful lump, swelling aroun your anus}. Let the set of isease D = {Internal Hemorrhois, rolapse Hemorrhois, External hemorrhois, Thrombose hemorrhois} Yoga Therapy for Hemorrhois yoga therapy (ILE. Yoga is beneficial to either treat to prevent hemorrohois. It can both alleviate the iscomfort or help prevent it from forming Hemorrhois, also known as piles, are swellings that evelop from the lining of the anus an lower rectum. 4 age

4 tep 1 : tep : (F,E = (F,e 1 = {(u 1,0.6,0.0,(u,0.8,0.0(u,0.5,0.0(u 4,0.,0.0} (F,e = {(u 1,0.9,0.0,(u,0.7,0.0,(u,0.4,0.0,(u 4,0.7,0.0} (F,e ={(u 1,0.6,0.0,(u,0.8,0.0,(u,0.6,0.0,(u 4,0.,0.0} (F,e 4 = {(u 1,0.8,0.0,(u,0.,0.0(u,0.4,0.0,(u 4,0.5,0.0} (G,E = {G e 1 } = {(u 1,0.8,0.0(u,0.9,0.0(u,0.6,0.0(u 4,0.,0.0} (G,e = {(u 1,0.,0.0;(u,0.4,0.0(u,0.5,0.0(u 4,0.7,0.0} (G,e = {(u 1,0.9,0.0;(u,0.7,0.0(u,0.6,0.0(u 4,0.,0.0} (G,e 4 = {(u 1,0.7,0.0;(u,0.6,0.0;(u,0.5,0.0;(u 4,0.,0.0} (1, 0.6 (1, 0.8 (1, 0.5 (1, 0. (1, 0.9 (1, 0.7 (1, 0.4 (1, 0.7 (1, 0.6 (1, 0.8 (1, 0.6 (1, 0. (1, 0.8 (1, 0. (1, 0.4 (1, (1, 0.8 (1, 0.9 (1, 0.6 (1, 0. (1, 0. (1, 0.4 (1, 0.5 (1, 0.7 (1, 0.9 (1, 0.7 (1, 0.6 (1, 0. (1, 0.7 (1, 0.6 (1, 0.5 (1, 0. tep : (0.6, 0.0 (0.8, 0.0 (0.5, 0.0 (0., 0.0 (0., 0.0 (0.4, 0.0 (0.4, 0.0 (0.7, 0.0 (0.6, 0.0 (0.7, 0.0 (0.6, 0.0 (0., 0.0 (0.7, 0.0 (0., 0.0 (0.4, 0.0 (0., 0.0 tep 4 : v (1, 0.8 (1, 0.9 (1, 0.6 (1, 0. (1, 0.9 (1, 0.7 (1, 0.5 (1, 0.7 (1, 0.9 (1, 0.8 (1, 0.6 (1, 0. (1, 0.8 (1, 0.6 (1, 0.5 (1, v (0.6, 0.0 (0.8, 0.0 (0.5, 0.0 (0., 0.0 (0.9, 0.0 (0.7, 0.0 (0.4, 0.0 (0.7, 0.0 (0.6, 0.0 (0.7, 0.0 (0.6, 0.0 (0., (0.8, 0.0 (0., 0.0 (0.4, 0.0 (0.5, age

5 tep 5 : (0.8, 0.0 (0.9, 0.0 (0.6, 0.0 (0., 0.0 (0., 0.0 (0.4, 0.0 (0.5, 0.0 (0.7, 0.0 (0.9, 0.0 (0.7, 0.0 (0.6, 0.0 (0., (0.7, 0.0 (0.6, 0.0 (0.5, 0.0 (0., 0.0 ( v( v( = tep 6 : Total core V. Conclusion : We see that, atient 1 suffering more than others. We represent new operations hanling fuzzy soft matrices. ccoring to these operations we establishe new result on fuzzy soft matrices. Finally a problem base on ecision making theory is solve by on algorithm which we presente in this paper. tressful life style an lack of exercise can loa to hemorrhois. Yoga is beneficial to either treat or prevent hemorrhois. It can both alleviate the iscomfort or help prevent it from forming. Reference : [1].. hma an.kharal, on fuzzy soft sets, avances in fuzzy systems, (009, 1-6 []. []. [4]. Krass im tanassor. Intuitionistic fuzzy sets, Theory an pplication, hysica Verlag, wyrzburg(1999 [5]. Molotsor Dmitri. oft set Theory, First Result, Computers an Mathematics with pplications, 7 ( [6]. Manash jyoti orach, Triiv Jyoti Neog, Dusmanta Kumar ut, fuzzy soft matrix theory an its international journal of moern engineering Research 01; ( : [7]. Y.. Jun an (H. ark, pplications of soft sets in ieal theory of CK / CI algebras, Information sciences, 178(008, [8]. Y.. Jun, K.J. Lee, J. Zhan, oft - ieals of oft CI algebras, computers an mathematics with application, 58 (009, [9]. Yong yang, Chenli Ji, Fuzzy soft matrices an Their applications. ICI part I, LN1700,011, [10]. Zeeh La. Fuzzy sets information an control. 1965; Dr. T. Geetha " "International Journal of Engineering cience Invention (IJEI, vol. 07, no. 10, 018, pp -6 6 age