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Inconsistent Data Processing Using Vague Set and Neutrosophic Set for Justifying Better Outcome

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Inconsistent Data Processing Using Vague Set and Neutrosophic Set for Justifying Better Outcome International Conference on Inventive Communication and Computational Technologies (ICICCT 2017) Inconsistent Data Processing using Vague Set and Neutrosophic Set for Justifying Better Outcome Soumitra De and Jaydev Mishra Computer Science & Engineering Department College of Engineering and Management, Kolaghat Purba Medinipur, 721171, West Bengal, India [email protected], [email protected] Abstract- Here, we have focused to process inconsistent and we have used the neutrosophic set boundary as data through imprecise queries from a database which per our belief. A few applications using neutrosophic consists of neutrosophic and vague set. Neutrosophic set set has been published [4, 5, 6, 7, 8]. In the present is based on truth, indeterminacy and false membership work, we have attempted to use two different values where as vague set is based on truth and false similarity measure formulas which are worked upon membership value. Firstly, we have applied two different similarity measure formulas to measure vague and neutrosophic data to perform uncertain closeness of two neutrosophic data and vague data queries. Several authors have used fuzzy or vague set which in turn are used to get the similarity value for [9, 10, 11, 12, 13] to execute imprecise queries but no each row with the query for vague and neutrosophic set such work has been reported literature using and the query is totally based on imprecise data. Next, neutrosophic set. In this paper, our objectives are to we provide a similarity measure based α-cut value to execute a query using vague and neutrosophic data generate a SQL command for the imprecise query and both data are uncertain in nature. So, first we which is act upon both set. The query return back have used a similarity measure (S.M.) formula for different result sets for different α-cut values for finding similarity value of two neutrosophic data also checking the closeness between two different set. Finally, we have given suitable examples of vague and we used other similarity measure formula for getting neutrosophic set where we established that neutrosophic similarity value of two vague data. Then for these set gives much more accurate result for any kind of two different set of similarity measure values, we uncertain query rather than vague set. considered a tolerance (α-cut) value for which the given imprecise query is executed. For different α Keywords- vague set; neutrosophic set; vague data; values, different output table will be generated from neutrosophic data; similarity measure; ∝- cut . the main database. In this purpose, we have chosen a Student database to perform imprecise query using vague and neutrosophic data. I INTRODUCTION We have planned to organize the paper as follows. Smarandache [1] introduced the neutrosophic set in Definition of vague and neutrosophic set both are 2001, which is used for handling problems involving mentioned in Section II. Different Similarity measure imprecise data. A neutrosophic set, which is formulas between two vague values and two considered as next advancement of vague set [2], is neutrosophic values are defined in section III. Section based on truthness, indeterminacy and falseness IV executes an imprecise queries using similarity instead of truth and false memberships used in vague measure values of two different set which are came sets. A vague set, which came from the fuzzy set [3], from vague and neutrosophic data oriented student uses the thought of interval-based membership database. Section V is the conclusion part of the instead of point-based membership in fuzzy set. The paper. three interval-based memberships in neutrosophic sets is more expressive for making decision than two interval based memberships in vague set. Research works on neutrosophic set based applications in different fields are progressing fast 978-1-5090-5297-4/17/$31.00 ©2017 IEEE 26 International Conference on Inventive Communication and Computational Technologies (ICICCT 2017) II VAGUE AND NEUTROSOPHIC two vague data to find the similarity value between SET two vague data. Let U be the universe of discourse where an IV PROCESS IMPRECISE QUERY OF VAGUE element of U is denoted by u. AND NEUTROSOPHIC SET Definition 1 In the current portion, we have given an example A vague set is characterized by two membership through which we have made two different column functions given by: which are based on vague and neutrosophic value (i) truth membership function tUx :[0,1]o , from a specific column value then using the formulas we got two different set of similarity measure value (ii) false membership function and fUx :[0,1]o on which a given uncertain query have been worked The rules are tx(u)+fx(u) ≤ 1 and vague set is and retrieved two different set of result as per the bounded by a subinterval [tx(u), 1- fx(u)] of [0,1] i.e, tolerance value is concerned. To demonstrate this fact, we have used the following Student relational tx(u)≤ Px (u) ≤ 1- fx(u) database as given in Table I and uncertain query is mentioned below: Definition 2 Stu_N Stu_A Stu_M A neutrosophic set is characterized by three (yrs) (100) membership functions given by: Rohit 18 57 (i) truth membership function tUx :[0,1]o , Komal 20 79 Bikas 17 78 (ii) false membership function fUx :[0,1]o and Titas 22 65 (iii) indeterminacy membership function Milon 24 76 IU:[0,1]o such that t (u)+f (u) ≤ 1 and Ajit 21 80 x x x Dipak 23 72 tx (u) + ix (u) + fx(u) ≤ 2 . Table I. Student Relation . Uncertain query III SIMILARITY MEASURE OF TWO “List the name of the students whose marks is very NEUTROSOPHIC VALUES close to 78”. In this paper, we have mentioned a similarity Solution measure formula using neutrosophic data to measure closeness between two neutrosophic values which is Firstly, we have made the vague and neutrosophic given below. attributes of student marks column (Stu_M).These two newly formed columns are used to finding the Definition 3 similarity measure between two vague values and Similarity Measure (S.M.) between two two neutrosophic values. Here, vague and neutrosophic values: neutrosophic attribute of Stu_M is shown in the Let x and y be any two neutrosophic values such Table II. that xtif [,, ]and ytif [,, ] where 0≤ tx xx x yy y Stu_N Stu_M Vague form of Neutrosophic form ≤1, 0≤ ix ≤1 , 0≤ fx ≤1 and 0≤ ty ≤1, 0≤ iy ≤1 , 0≤ fy ≤1 (100) Stu_M of Stu_M with 0≤ tx+fx≤1, 0≤ ty+fy≤1, tx+ix+fx ≤2 , ty+iy+fy≤2. Rohit 57 <57, [44,.44]> <57, [.44,.55,.52]> Komal 79 <79,[.98,.98]> <79,[.98, .025,.01]> Let SE(, x y )denote the similarity measure between Bikas 78 <78, [1,1]> <78, [1,0,0]> x and y . Titas 65 <65, [.80,.80]> <65, [.8,.2, .18]> Then, Milon 76 <76, [.96,.96]> <76, [.96,.10, .03]> Ajit 80 <80, [.92,.92]> <80, [.92,.15, .06]> §· ()()()ttxy ii xy f x f y SE(,) x y ¨¸ 1 1(txy t )( i xy i )( f x f y ) Dipak 72 <72, [.85,.85]> <72, [.85, .3,.12]> ¨¸3 ©¹ Table II. Vague and Neutrosophic Representation of Stu_M attribute in Student Relation We are using the similarity measure formula [13] for 978-1-5090-5297-4/17/$31.00 ©2017 IEEE 27 International Conference on Inventive Communication and Computational Technologies (ICICCT 2017) Stu_N S.M S.M Vague form of with Neutrosophic form with Stu_M <78, of Stu_M <78, Next, we calculate the closeness value for vague [1,1]> [1,0,0]> and neutrosophic representation of Stu_M attribute Rohit <57, [44,.44]> .66 <57, [.44,.55,.52]> .47 separately which are shown in Table III. Komal <79,[.98,.98]> .99 <79,[.98, .025,.01]> .98 Bikas <78, [1,1]> 1 <78, [1,0,0]> 1 For example, let us consider the two vague data Titas <65, [.80,.80]> .89 <65, [.8,.2, .18]> .81 x = <78, [1, 1]> and y = <79, [.98, .98]>. Milon <76, [.96,.96]> .98 <76, [.96,.10, .03]> .93 Ajit <80, [.92,.92]> .96 <80, [.92,.15, .06]> .89 Here, tft 1, 0, .98, f .02 xxy y Dipak <72, [.85,.85]> .92 <72, [.85, .3,.12]> .77 Then Table III. S. M. calculations of vague and §·(1 .98) (0 .02) SM. .( x , y ) ¨¸ 1 1 (1 .98) (0 .02) neutrosophic attribute of Stu_M ©¹2 §·.04 ¨¸1 0.98 0.989 Next, we process the same imprecise query for 2 ©¹ neutrosophic sets: Again, for x = <78, [1, 1]> and y = <80, [.92,.92]>, SELECT * FROM STUDENT WHERE S.M. t 0.9 tftxxy 1, 0, .92, f y .08 . This gives With the tolerance value 0.90, the above SQL §·(1 .92) (0 .08) command of imprecise query for vague and SM. .( x , y ) ¨¸ 1 1 (1 .92) (0 .08) neutrosophic set will be generated separately. 2 ©¹ §·.16 The resultant tuples thus retrieved are shown in Table ¨¸1 0.92 0.959 ©¹2 IV and V for vague and neutrosophic data separately. and so on. Stu_N Stu_A Stu_M . Komal 20 79 Bikas 17 78 For example, let us consider the two neutrosophic data x = <78, [1, 0, 0]> and y = <79, [.98, .025, .01]>. Milon 24 76 Ajit 21 80 Here, Dipak 23 72 ti 1, 0, f 0, t .98, i .025, f .01 xx x y y y Table IV. Resultant tuples of a given imprecise Then Query for vague set at T.V D = 0.90 §·(1 .98) (0 .025) (0 0.01) SM. .( x , y ) ¨¸ 1 1 (1 .98) (0 .025) (0 0.01) ©¹3 §·.055 ¨¸1 1 .015 0.98166u 0.985 .96693 0.983 ©¹3 Stu_N Stu_A Stu_M Komal 20 79 Again, for x = <78, [1, 0, 0]> and y = <80, [.92, .15, Bikas 17 78 .06]>, Milon 24 76 .
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