Assistance to assessing rating students by language tuple-4 scale

In this paper, we introduce an assistance to assessing rating the annual learning and process training of students in the opinion of experts, the approach of hedge algebra. It is advisary to make optimally fuzzy parameters with neural network in order to scale tuple-4 in accordance with current regulations on student assessment annual ranking including 7 levels.


Introduction
The problem supports the decision on evaluating based on the expert opinions upon the valuation for the treatment of linguistic terms for the professionals often to make judgment about a plan, which is the aggregation of the fuzzy values to get the results that each expert feels happy because it is close to their evaluation.There are many approaches according to the fuzzy tuple theory as the authors [1-2-3-4], focusing mainly on using the same operator as Iowa.The hedge algebraic approach uses a scale of tuple-4 to record the comments of the experts.The advantages of this approach are preserving semantic results in aggregating the evaluations and optimally facilitating the fuzzy parameter tuple to summarize the results of the feedbacks from the experts on the same object to be close to each expert's evaluation of that object.
In [5] we mentioned building tools to assist to rate students with the scale of the previous standard fuzzy tuples.The result of evaluating each student is a vector where each component is an evaluation criterion implemented by the experts (teachers or school organizations).In this paper we use a fuzzy scale (Fuzzy grade sheet) to record the students evaluated by the experts as in [5], but the rating system is tuple-4 mentioned above.The results of evaluating each student is the sum of the opinions of the experts on those students.The results are ranked according to the degrees Poor, Weak, Average, Fair Average, Fair, Good, Excellent.The problem is of fuzzy classification.Then we optimize the fuzzy parameters by means of neural network using the supervised reverse statutory, based on the evaluation of specialized data recorded simultaneously with the figures and linguistic terms.The rest of the paper consisting of the parts of section two introduces hedge algebra of two hedges and the tuple-4.Section 3 presents the support of deciding on grading students with the tuple-4.Section 4 gives optimal algorithm of fuzzy parameter tuples and concluding remarks.

Hedge algebra and construction of tuple-4
Full linear hedge algebra AX of language variable X is a set of six components AX= (X, G, H, , ,) where X = Dom(X), G = {c−, c+}{0, 1, W} is the set of generative elements, H is the set of hedges H = H−H+, H− = {h−q,…, h−1}, H+ = {h1, h2,…, hp} satisfying h−q >… >h−1 and h1 <h2 <…<hp,and ,  are 2 expanding operators, while "" is the relationship to X with induced semantics of natural language.Unlike the fuzzy sets in which the semantic is represented via fuzzy sets, in hedge algebra the semantics is represented by the order structures between the linguistic values.This relationship indicates the relative and quantitative semantics of linguistic values in X, such as weakrather weakfairly goodgoodvery good.This structure is also the basis for quantifying qualitative semantics of the elements in hedge algebra.
Quantitative semantics is also represented by fuzzy notion of the elements in X and is defined as the "size" of the set H (x), where H (x) is the set of elements of X generated from x by hedges.So quantitative opacity of x is defined as follows: Definition 1.1 [8].Given a complete hedge algebra AX= (X, G, H, , ,).Function fm: X  [0,1] is called a function measuring the fuzzy space of the elements in x, if: , this rate does not depend on x, y and it is called the degree measuring the opacity of hedge h, signified (h).
The quantification of the word semantics allows to put the relationship between the assessment of the information on the label criteria and the assessment according to traditional methods.Quantitative semantics is a mapping assigning real values to the language values given by the definition: Definition 1.2 [8] m f is a function measuring the fuzzy space over X and complete linear hedge algebra AX = (X, G, H, , ,).Quantitative semantic function  in AX in combination with m f is defined recursively as follows:

and with j [−q^p],
we have: The functionality of hedges generates set H(x).With that property of set H(x), it is taken as a model of the fuzzy from x and its size is considered the fuzzy measurement of x, denoted fm(x)  [0,1].
We see fm(x) completely determined if we give the values fm(c), fm(c+) and (h), hH(x), called the parameters of the fuzzy space of X.These parameters are very important for the computation of other quantitative characteristics.
) the class length from x, approximately equivalent fuzzy level g ) 1 (  g of x is roughly made up of two adjacent fuzzy space about the same level k+g including Where  is the combination of the two adjacent fuzzy spaces. identify the similar fuzzy space g(x)


and two similar fuzzy space close to g(x) as follows: Where y,z are two grades defining two similar fuzzy space neighbors left and right of g(x).Assistance to assessing rating students by language tuple-4 scale The classes of the fuzzy of X form a base of the topology of X, that is, it defines a topology on [0,1] for each open set of [0.1] to be a set of fuzzy space numbers.Considering the fuzzy of the Xk+2 and parting the spaces into the grades Ck(x), xX(k), so that they contain at least 2 fuzzy spaces of Xk+2 but their common ends are quantitative value (x).Put Sk(x) = {k+1:k+1Ck(x)}.The class {Sk(x): xX(k)} is a partition of [0,1] and each Sk(x) called similar space level k of xX(k) of the same relation of level k, denoted as Sk (see [8]).In summary, the similar spaces have the following characteristics: (i) {Sk(x): xX(k)} makes up a partition [0,1].
(ii) (x)Sk(x) and is the common ends of at least 2 spaces of Xk+2.
Definition 1.6 [7].Given the fuzzy parameter values, performing tuple 4 of x X(l) set 4: (x, (x), r, Sl(x)), with rSl(x) where (x) is the quantitative value of x, Sl(x) is the same semantic space of level l of x, called the same level.There is always (x) Sl(x) and the meaning of (x) like the center (core) of a fuzzy tuple, meaning that it is compatible with the values of semantics of x.  Value Definition 1.7.[7] The language scale of tuple-4 consists of verbal values of tuple-4 as follows: {(x, (x), r, Sl(x)): xS,r [0,1]}.

Constructing a verbal scale
Regarding the method, the different number scales as 5, 10, 20, 100, ... may provide for a scale of 10 to build a scale of language.Because application-oriented approach is to evaluate the results related to the students, so we should take the example of ranking the learning outcomes, student's training as a base for building.The classification of the learning and training outcomes of students (based on the criteria available) out of 10 is defined as follows: Excellent : from 9 to 10 marks; Good : from 8 to 9 marks; Fair : from 7 to over 8 marks; Fair-average : from 6 to under 7 marks; Average : from 5 to under 6 marks; Weak : from 3 to under 5 marks; Poor : under 3 Since hedge algebra indicates naturally quantitative semantics, symmetry, that is, the graph structure demonstrates the order relation between the elements generated from c  , the symmetric with neutral element with the graph denoting the order relation between elements generated from c + , and our goal is to build a scale of language instead of a scale of 10, so we use hedge algebra with: Generated element: Good, Bad Hedge: V (very) ,L(Little), with H + ={V}, H -={L}, =(V), =(L).
Hedge W is selected to ensure maximum symmetry of the language labels and thus it ensures all hedges are of the same nature yin-yang.As a rule, the evaluation results should put on a scale of 100 and ranking.The results presented in Item a. ensure that we always have a quantitative mapping with precision acceptable enough to move the assessments of language labels on a scale of 10 or 100.
At the end of the school-year, each student should have the evaluation results of their training.The results are based on a synthesis of the results evaluated by criterion 27.Each criterion has corresponding evaluation scale in 100.Based on the contents of each criterion and self discipline of students, members of the board (in class) will give points.These points are in form of qualitative assessment, ie the language comments.Through quantitative functions in hedge algebra, qualitative points will be converted to scores on the interval [0,1], then the provisions will be made into 100 point scale.Pursuant to the provisions on the evaluation and grading of students annual assessment of students, we build supporting systems rated by fuzzy classification method based on hedge algebras 2 (HA 2) (see table 1).-The second expert (EXP (1)): Evaluating the sense and the results to follow the rules -regulations at school.

Building rules
-The third expert (EXP (1)): Evaluating the sense and the results participating in the political and social activities, culture, arts, sports, prevention of social evils.
-The fourth expert (EXP (1)): Assessing the civic quality and community relations.
-The fifth expert (EXP (1)): Assessing the sense and the participation results in charge of classes.According to a rating of 100 students of a university and method of generating fuzzy rule based on similar space systems [7], we have a system of 19 following rules: r1:=if (Ev-exp(1)=(LG,2.5))and (Ev-exp(2)=(LVG,2.0)) and (Ev-exp(3) =(VG,2.0))and (Ev-exp(4)=(VG,1.9))and (Ev-exp( 5 ) .goodLL  is the left adjacency of fair rank, so: is the left adjacency of good rank, so: In the fact of the assessment of students, the distinction between fair adjacency (ie head at the fair top) and fair as the distinction between good adjacency (ie, they are in the good top) and good enough is required to take a closer look as well as evaluating a student not to achieve average rank should be prudent.The poor students are usually disciplined in the school-year, while the outstanding students are rare and demonstrate the clear superiority.So it is found that for the tuple-4 scale to match the current scale for assessing and ranking, the fuzzy parameters are required to satisfy the conditions (1), ( 3) and ( 4), including the binding inferred from (1) and (2): 5 <w <6 and μ (L) <0.5.
The conditions (1), ( 2), (3) are the system of Level 3 equations with two unknowns w and μ (L), therefore the answer is merely approximate; or otherwise, the conditions agree with only allowed errors.Therefore we use regression neural network with 3 layers in which the input layers have two buttons for entering parameters, the hidden layer has 3 and the output has 5 to announce after achieving the results with allowed errors.
The following table presents 20 results with good errors.(see Table 2) According to this scale tuple-4 and the assessment of experts in pair of number values and the value of language, we have calculated the reliability and the support of each rule to corporate and select the system of 19 rules in 3.2 and the results of the system include the following rules: r1:=if (Ev-exp(1)=(LG,2.

r 1 . 2 .[ 8 ]
appears in the third component in the performance of tuple-4, where r(x) Offset r -(x) is called the appropriate semantic deviation of value r .There is Clause If rr' , words x(r) and x(r') in the representation of tuple-4 of r and r' satisfy inequality x(r) x(r').

Table 1 .
Expert's assessment card for rating students EAI Endorsed Transactions on Context-aware Systems and Applications 02 -03 2016 | Volume 3 | Issue 8 | e3