In this paper, we present a new method for students’ answerscripts evaluation based on interval-valued intuitionistic fuzzy sets, where the fuzzy marks awarded to the answers of students’ ...answerscripts are represented by interval-valued intuitionistic fuzzy sets. An index of optimism λ determined by an evaluator is used, where λ∈0, 1. The larger the value of λ, the more optimistic is the evaluator. The smaller the value of λ, the more pessimistic is the evaluator. Moreover, an index of uncertainty β is calculated denoting the degree of uncertainty of an interval-valued intuitionistic fuzzy mark, where β∈0, 1. The larger the value of β, the more the uncertainty of an interval-valued intuitionistic fuzzy mark. We also present a generalized method for students’ answerscripts evaluation using interval-valued intuitionistic fuzzy sets. The proposed method can overcome the drawbacks of the existing methods for students’ answerscripts evaluation. The proposed methods can evaluate students’ answerscripts in a more flexible and more intelligent manner.
This paper presents a new approach for evaluating students' answerscripts using fuzzy numbers associated with degrees of confidence of the evaluator. The satisfaction levels awarded to the questions ...of students' answerscripts are represented by fuzzy numbers associated with degrees of confidence between zero and one. The arithmetic operations between the alpha-cuts of fuzzy numbers are used to evaluate the total mark of each student, where alpha isin 0,1. The proposed method can overcome the drawbacks of the methods presented by Biswas (1994) and Chen and Lee (1999). It can evaluate students' answerscripts in a more flexible and more intelligent manner.
Increasing demand for lightweight materials in the field of automotive and some structural applications has led to the development of natural hybrid fiber-reinforced composites due to their high ...specific strength and strength-to-weight ratios. Thus, this work is an attempt to produce a hybrid-reinforced composite with natural fibers (kenaf/snake grass) as reinforcement and epoxy as a matrix. Several researchers have highly recommended using hybridization process with chemical pretreatments of natural fibers for effective application. Therefore, the natural fibers chosen were pretreated with NaOH solution before fabricating the samples. The treated fibers were then fabricated considering different parameters viz., weight fraction (5, 10, 15, and 20% by wts), NaOH concentrations (0%, 3%, 5% and 8%), molding pressure (10, 12, 14 and 16 MPa), and molding temperature (100 and 120 °C). The samples were prepared as per ASTM standards, and using the Taguchi L
16
array, the experimental testing parameters were assessed and underwent mechanical tests, namely tensile, flexural, and impact, to experimentally find their properties. A Taguchi fuzzy multi-response optimization technique provides accurate and faster results relative to other widely used studies in many engineering applications. Therefore, it is used in Fuzzy model interference system based on grey relational analysis. Grey fuzzy grade results were found to be higher (0.8924) for the composition fabricated with 15% (by wt) kenaf/snake grass fibers, 5% NaOH, 10 MPa molding pressure, and 100 °C molding temperature. Further, an analysis of variance was carried out to find the most and least significant factors. It revealed that weight fraction of snake grass fiber was the most significant factor whereas the molding temperature was the least significant factor for enhancing the mechanical properties. The Taguchi fuzzy-based optimization was adopted to perform the multi-response optimization and to improve the decision-making of different input and output parameters. In addition, the thermal stability of the optimized combination of the hybrid composite was analyzed with the aid of thermogravimetric analysis and derivative thermogravimetry.
Graphical abstract
This paper deals with connections between hypergroupoids and Atanassov’s intuitionistic fuzzy sets. First a sequence of join spaces is associated with a hypergroupoid
H; the length of the sequence is ...called Atanassov’s intuitionistic fuzzy grade of
H. Second, a theorem about the existence of a hypergroup with Atanassov’s intuitionistic fuzzy grade equal to
n is proved. Furthermore, some properties of the complete hypergroups in connection with this argument are presented and discussed.
Hypergroups associated with HX-groups Corsini, Piergiulio
Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică,
7/2017, Volume:
25, Issue:
2
Journal Article
Peer reviewed
Open access
We have already studied a correspondence between HX-groups and hypergroups. Now we extend this correspondence to semigroups of sub- sets of a group G (and to begin, we considered ℤ
× ℤ
as group G). ...Moreover these subsets can have non empty intersection, they can be contained, one in another one. One calculates the fuzzy grade and we find always ∂H = 1.
HX-groups and Hypergroups Corsini, Piergiulio
Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică,
11/2016, Volume:
24, Issue:
3
Journal Article
Peer reviewed
Open access
One considers the hypergroups associated with the HX-groups Z=nZ and with the set of square matrices of order 2, with coefficients in Z=2Z and one calculates their fuzzy grade.
In this paper, we propose two new methods for evaluating students’ answerscripts based on interval-valued fuzzy grade sheets. The marks awarded to the answers in the students’ answerscripts are ...represented by interval-valued fuzzy sets. Each element in the universe of discourse belonging to an interval-valued fuzzy set is represented by an interval between zero and one. The degree of similarity between an interval-valued fuzzy mark and a standard interval-valued fuzzy set is calculated by a similarity function. An index of optimism λ determined by the evaluator is used to indicate the degree of optimism of the evaluator, where λ∈0,1. The experimental results show that the proposed methods are more stable than Biswas’s method for students’ answerscripts evaluation. They can evaluate students’ answerscripts in a more flexible and more intelligent manner.
On the fuzzy grade of hypergroups Ştefănescu, M.; Cristea, I.
Fuzzy sets and systems,
05/2008, Volume:
159, Issue:
9
Journal Article
Peer reviewed
In some previous papers, the second author studied the possibility to associate a sequence of membership functions and of join spaces with a hypergroupoid
H. Here we establish a sufficient condition ...in order to have two consecutive associated join spaces
i
H
and
i
+
1
H
non-isomorphic. We find also a property of the quotient hypergroup determined by the join space
i
H
and the relation associated with the fuzzy set
μ
˜
and finally, we determine a necessary and sufficient condition for the join space
i
H
in order to be a reduced hypergroup.
In an earlier work, Biswas (1995) presented two methods for the application of fuzzy sets in students' answerscripts evaluation. In this paper, we extend his work to propose two new methods for ...evaluating students' answerscripts using fuzzy sets. The proposed methods can overcome the drawbacks in Biswas (1995) due to the fact that they do not need to perform the complicated matching operations and they can evaluate students' answerscripts in a more fair manner.
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