The posterity of Zadeh's 50-year-old paper: A retrospective in 101 Easy Pieces – and a Few More

International audienceThis article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed “important (significant, seminal, etc.)” by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in “Fuzzy Sets 101”. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them - almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times

A Unifying Theory for Graph Transformation

The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

CAMILA: formal software engineering supported by functional programming

This paper describes two experiences in teaching a formal approach to software engineering at undergraduate level supported by Camila a functional programming based tool Carried on in diferent institutions each of them addresses a particular topic in the area requirement analysis and generic systems design in the first case specification and implementation development in the second Camila the common framework to both experiences animates a set based language extended with a mild use of category theory which can be reasoned upon for program calculation and classification purpose. The project afiliates itself to but is not restricted to the research in exploring Functional Programming as a rapid prototyping environment for formal software model. Its kernel is fully connectable to external applications and equipped with a component repository and distribution facilities. The paper explains how Camila is being used in the educational practice as a tool to think with providing a kind of cross fertilization between students under standing of diferent parts of the curriculum. Furthermore it helps in developinga number of engineering skills namely the ability to analyze and classify information problems and models and to resort to the combined use of diferent programming frameworks in approaching them

On the analytical engagement of social semiotics and variation theory in physics education research

In this licentiate thesis, I explore how two theoretical frameworks—social semiotics and the variation theory of learning—used in physics education research, can be fruitfully combined to obtain additional analytical tools for analysing student learning in introductory level university physics. Each theoretical framework has on their own, or together with other frameworks, been successfully applied for analysing both individual and collective learning, but the combination of the two has yet not been fully explored. Social semiotics is concerned with the communication, using different semiotic resources (such as spoken and written language, mathematics, diagrams, gestures, and apparatus), between people within a certain discourse. Variation theory suggests that learning can only be successful if a person is able to discern the critical aspects of a phenomenon. This discernment is seen to be dependent on being exposed to purposeful variation within this aspect. In order to study this analytical combination, I made use of two case studies; I studied (1) physics students’ understanding of plus (+) and minus (–) signs in a one-dimensional kinematics contexts; and, (2) students’ collective communication and learning progression in group work activities solving problems in circular motion. In both cases I explored how the concept of ‘relevance structure’ could be used analytically to understanding students’ learning challenges in physics. For the first case study I was able to identify four qualitative different categories of students’ individual relevance structure for of how students ‘read’ and ‘use’ these algebraic signs in this context. Through the analysis connected to the data set used for the second case study I was also able to identify two different approaches to viewing a circular motion problem—a static and dynamic approach—suggested to be the result of students’ ‘enacted relevance structure’, and also empirically show how social semiotics and variation theory could be analytically combined in a powerful way in qualitative analysis. Conclusions that I can draw from the research presented in this thesis is that students’ relevance structure— what they perceive as being relevant—seem to have a high influence on students’ ability to discern disciplinary relevant aspects (DRAs) of the phenomenon which they are studying. I suggest that the relevance structure may act as a ‘filter’ for students to be able to make the appropriate disciplinary discernment even though they experience purposeful variation within a dimension of variation. From the research presented in this licentiate thesis, I have been able to identify and suggest both theoretical and methodological contributions to physics education research and I end this thesis with suggesting implications for teaching and learning, as well as making suggestions for future research