Images of imagination : an aesthetic approach to education

Visual art practice has generally been described as a lonely affair, thinking about what an artist has experienced in the outside world. This study is an inquiry into a visual art practice of another kind: the relational one. The research purpose is twofold. The first purpose is to shed light on a visual artist’s conceptions of art, education and scholarship. The second purpose is to by reasoning on imagination and a rhizomatic formation interpret the relations created between art, multimodality and literacy learning as an aesthetic approach to education. By inquiry into a specific collaborated long-term art practice, the study conveys how the meaning making elements of an arts based learning practice gradually transform an artist’s and a teacher’s concepts of art education to an aesthetic approach to education. In the art practice examined the typical Finnish rye bread and a poem have represented a cultural theme that has been elaborated through art conventions. The poem and the rye bread have in the art practice been articulated as cultural representations of as well as symbolic projections on the Swedishspeaking minority culture in Finland. The study connects art informed inquiry to a hermeneutic research rationale where the research reasoning is generated through a rhizomatic alliance between empiric data and theories. The reasoning is constructed as an interpretation pattern that expands throughout the study. The study arguments that the rhizome as an aesthetic formation can be appropriate to refer to when articulating arts based meaning making and when creating arts based educational strategies, dialogues, aesthetic learning and multimodal literacy in education. The study investigates an aesthetic approach to research in education, which means that the art practice surveyed is interpreted through articulation appropriate to poetic aspects of art, education and research.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.