Papers by Michael Voskoglou
arXiv (Cornell University), Apr 2, 2018
Fuzzy relation equations (FRE) are associated with the composition of binary fuzzy relations. In ... more Fuzzy relation equations (FRE) are associated with the composition of binary fuzzy relations. In the present work FRE are used as a tool for studying the process of learning a new subject matter by a student class. A classroom application and other suitable examples connected to the student learning of the derivative are also presented illustrating our results and useful conclusions are obtained.
Mathematics
The Neutrosophic Set (Nset) represents the uncertainty in data with fuzzy attributes beyond true ... more The Neutrosophic Set (Nset) represents the uncertainty in data with fuzzy attributes beyond true and false values independently. The problem arises when the summation of true (Tr), false (Fa), and indeterminacy In values crosses the membership value of one, that is, Tr+In+Fa<1. It becomes more crucial during decision-making processes like medical diagnoses or any data sets where Tr+In+Fa<1. To achieve this goal, the FNset is recently introduced. This study employs the Interval-Valued Fermatean Neutrosophic Set (IVFNset) as its chosen framework to address instances of partial ignorance within the domains of truth, falsehood, or uncertainty. This selection stands out due to its unique approach to managing such complexities within multi-decision processes when compared to alternative methodologies. Furthermore, the proposed method reduces the propensity for information loss often encountered in other techniques. IVFNS excels at preserving intricate relationships between variables...
Review of: "A Perspective for Economic and Social Unfoldings of AI
In this short article, which looks like an extended Abstract rather, the author expresses some pe... more In this short article, which looks like an extended Abstract rather, the author expresses some personal opinions about the use of AI in e-learning without any documentation. There is a list of References at the end, but none of them is mentioned in the text. The core of the article discusses the use of ChatGPT in e-learning. It speaks for a case study about this matter conducted in a "university setting", but no description and statistical analysis of it is given. In conclusion, although the theme of the article is interesting, it needs much more work and documentation in order to become publishable.
Artificial Intelligence (AI) is the branch of Computer Science that focuses on the theory and pra... more Artificial Intelligence (AI) is the branch of Computer Science that focuses on the theory and practice of creating “smart” devices mimicking human reasoning and behavior. The introduction of the techniques of AI to Education has brought significant benefits to the teaching and learning, to student and teacher assessment and training and to several other educational processes. The present paper focuses on the role that AI and the digital technologies play for Education in the forthcoming era of the Fourth Industrial Revolution, which, under normal conditions, is expected to lead humanity to an era of nearly free energy, goods and services. Thepaper discusses the benefits and limitations of the introduction of techniques of AI in Education. Namely, the role of computers isinvestigated and the expediency of teaching principles of Soft Computingin Education is studied. The advantages and disadvantages of e-learningwith respect to the traditional learning theories and teaching methods ar...
Mathematics
The topic of convex and nonconvex mapping has many applications in engineering and applied mathem... more The topic of convex and nonconvex mapping has many applications in engineering and applied mathematics. The Aumann and fuzzy Aumann integrals are the most significant interval and fuzzy operators that allow the classical theory of integrals to be generalized. This paper considers the well-known fuzzy Hermite–Hadamard (HH) type and associated inequalities. With the help of fuzzy Aumann integrals and the newly introduced fuzzy number valued up and down convexity (𝑈𝒟-convexity), we increase this mileage even further. Additionally, with the help of definitions of lower 𝑈𝒟-concave (lower 𝑈𝒟-concave) and upper 𝑈𝒟-convex (concave) fuzzy number valued mappings (ℱ𝒩𝒱ℳs), we have gathered a sizable collection of both well-known and new extraordinary cases that act as applications of the main conclusions. We also offer a few examples of fuzzy number valued 𝑈𝒟-convexity to further demonstrate the validity of the fuzzy inclusion relations presented in this study.
Cornell University - arXiv, Nov 21, 2013
Reasoning, the most important human brain operation, is characterized by a degree of fuzziness. I... more Reasoning, the most important human brain operation, is characterized by a degree of fuzziness. In the present paper we construct a fuzzy model for the reasoning process giving through the calculation of probabilities and possibilities of all possible individuals' profiles a quantitative/qualitative view of their behaviour during the above process. In this model the main stages of human reasoning (imagination, visualisation and generation of ideas) are represented as fuzzy subsets of a set of linguistic labels characterizing a person's performance in each stage. Further, using the coordinates of the centre of gravity of the graph of the corresponding membership function we develop a method of measuring the reasoning skills of a group of individuals. We also present a number of classroom experiments with student groups' of T. E. I. of Patras, Greece, illustrating our results in practice.
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz
The APOS/ACE instructional treatment for learning and teaching mathematics was developed during t... more The APOS/ACE instructional treatment for learning and teaching mathematics was developed during the 1990’s by a team of mathematicians and mathematics educators led by Ed Dubinsky. In the present article we design in terms of the APOS/ACE treatment a general plan for teaching the real numbers at an elementary level (high school and college introductory mathematical courses). Our didactic approach is based on multiple representations of real numbers and on flexible transformations among them. Two classroom experiments performed during the last two academic years with students of my institution (T. E. I. of Patras, Greece) are also reported illustrating the effectiveness of our teaching design in practice. Introduction Research focussed on the comprehension of irrational numbers shows that, apart from the earlier incomplete comprehension of rational numbers, they are also other obstacles (cognitive and epistemological) making it even more difficult (Herscovics 1989, Sierpinska 1994, S...
A Combined Use of Soft and Neutrosophic Sets for Student Assessment with Qualitative Grades
Journal of Neutrosophic and Fuzzy Systems
A hybrid assessment method of a group’s overall performance with respect to a certain activity is... more A hybrid assessment method of a group’s overall performance with respect to a certain activity is developed in this paper using soft and neutrosophic sets as tools and it is applied for student assessment. The present method is compared with another method developed in an earlier authors’ work, which uses soft sets and grey numbers as tools for the assessment.
American Journal of Educational Research
Grey numbers, which are defined with the help of the real intervals, are very useful in the every... more Grey numbers, which are defined with the help of the real intervals, are very useful in the everyday life for handling approximate data. In the present paper grey numbers are used as a tool for assessing, with linguistic expressions, the student understanding of the graphical representation of the derivative. Although the proposed new assessment method is proved to be equivalent with an analogous method using Triangular Fuzzy Numbers developed in earlier works, the required computational burden is significantly reduced. A classroom application is also presented illustrating our results.
Computational thinking (CT) is a new problem solving method named for its extensive use of comput... more Computational thinking (CT) is a new problem solving method named for its extensive use of computer science techniques. In this paper we use principles of fuzzy logic to develop a mathematical model representing the CT and the centre of mass of the graph of the membership function involved to obtain a measure of students' CT skills. We also present two classroom experiments performed recently at the Graduate Technological Educational Institute (TEI) of Patras, Greece illustrating the use of our fuzzy model in practice. AMS Mathematics Subject Classification (2010): 03E72, 97C80 Keywords: Fuzzy sets and logic, centre of mass of a fuzzy graph, computational and critical thinking, problem solving, mathematical modelling.
We apply a Triangular Fuzzy Model (TFM) for assessing students' problem solving skills. The T... more We apply a Triangular Fuzzy Model (TFM) for assessing students' problem solving skills. The TFM is a variation of a special form of the Centre of Gravity (COG) defuzzification technique that we have used in earlier papers for assessing students' performance in several mathematical tasks. The main idea of the TFM is the replacement of the rectangles appearing in the graph of the COG technique by isosceles triangles sharing common parts. In this way we cover the ambiguous cases of students' scores being in the limits between two successive grades (e.g. between A and B). A classroom experiment is also presented illustrating our results in practice.
In this paper we develop a method for assessing the overall performance of groups of individuals ... more In this paper we develop a method for assessing the overall performance of groups of individuals participating in any kind of human activities. For this, we represent each of the group under assessment as a fuzzy subset of a set U of linguistic labels characterizing its members' performance and we apply a recently developed Trapezoidal Fuzzy Assessment Model (TRFAM) for converting the fuzzy data collected from the corresponding activity to a crisp number. The TRFAM is a variation of the popular in fuzzy mathematics centre of gravity (COG) defuzzification technique, which has been properly adapted and used as an assessment method in earlier papers. According to the TRFAM the higher is an individual's performance the more its "contribution" to the corresponding group's overall performance (weighted performance). Two real life applications are also presented, related to the bridge players' performance and to the students' assessment respectively, illustrat...
Case-Based Reasoning (CBR) and Fuzzy Systems are intended as cognitively more plausible approache... more Case-Based Reasoning (CBR) and Fuzzy Systems are intended as cognitively more plausible approaches to problem-solving and learning. The two corresponding fields have emphasized different aspects that complement each other in a reasonable way. In the present paper we introduce a fuzzy model for the representation of a CBR system, which is based on the formalization of CBR as a four steps process (retrieve, reuse, revise, retain), and we use the total possibilistic uncertainty as a measurement tool for the effectiveness of the model in solving new related commercial problems. An example is also presented to illustrate our results in practice.
Advanced Methodologies and Technologies in Artificial Intelligence, Computer Simulation, and Human-Computer Interaction, 2019
A fuzzy number (FN) is a special kind of FS on the set R of real numbers. The four classical arit... more A fuzzy number (FN) is a special kind of FS on the set R of real numbers. The four classical arithmetic operations can be defined on FNs, which play an important role in fuzzy mathematics analogous to the role played by the ordinary numbers in crisp mathematics. The simplest form of FNs is the triangular FNs (TFNs), while the trapezoidal FNs (TpFNs) are straightforward generalizations of the TFNs. In the chapter, a combination of the COG defuzzification technique and of the TFNs (or TpFNs) is used as an assessment tool. Examples of assessing student problem-solving abilities and basketball player skills are also presented illustrating in practice the results obtained. This new fuzzy assessment method is validated by comparing its outcomes in the above examples with the corresponding outcomes of two commonly used assessment methods of the traditional logic, the calculation of the mean values, and of the grade point average (GPA) index. Finally, the perspectives of future research on ...
Much of our cognitive activity depends on our abili ty to reason analogically. When we encounter ... more Much of our cognitive activity depends on our abili ty to reason analogically. When we encounter a new problem we are often reminded of similar proble ms solved in past and may use the solution procedure of an old problem to solve the new one (a nalogical problem solving). In this paper we develop two mathematical models for the description of the process of analogical problem solving. The first one is a stochastic model constructed by introducing a finite, ergodic Markov chain on the steps of the analogical reasoning process. Through this we obtain a measure of the solvers’ difficulti es during the process. The second is a fuzzy model con structed by representing the main steps of the process as fuzzy subsets of a set of linguistic lab els characterizing the individuals’ performance in each of these steps. In this case we introduce the Shannon’s entropy (total probabilistic uncertainty) properly modified for use in a fuzzy environment as a measure of the solvers’ performance. The t...
In this article Fuzzy Logic is used as a tool in developing a new method for assessing the of bri... more In this article Fuzzy Logic is used as a tool in developing a new method for assessing the of bridge-playersâĂŹ performance. For this, the cohorts of playerrs’ under assessment are represented as fuzzy subsets of a set of linguistic labels characterizing their performance and the technique of the âĂŸcenter of gravityâĂŹ (COG) is used to convert the fuzzy data collected from the game to a crisp number. Our method could be used informally as a complement of the official bridge-scoring methods (match points or IMPs) for statistical and other obvious reasons. Two real applications related to simultaneous tournaments with pre-dealt boards, organized by the Hellenic Bridge Federation, are also presented, illustrating the importance of our results in practice. MSC: 03E72 • 68T27
American Journal of Applied Mathematics and Statistics, 2015
In an earlier work, recently published in this journal, we have used the Triangular Fuzzy Numbers... more In an earlier work, recently published in this journal, we have used the Triangular Fuzzy Numbers (TFNs) as an assessment tool of student skills. This approach led to an approximate linguistic characterization of the students’ overall performance, but it was not proved to be sufficient in all cases for comparing the performance of two different student groups, since two TFNs are not always comparable. In the present paper we complete the above fuzzy assessment approach by presenting a defuzzification method of TFNS based on the Center of Gravity (COG) technique, which enables the required comparison. In addition we extend our results by using the Trapezoidal Fuzzy Numbers (TpFNs) too, which are a generalization of the TFNs, for student assessment and we present suitable examples illustrating our new results in practice.
Uploads
Papers by Michael Voskoglou