Knowledge Maps and Mathematical Modelling

Abstract

The aim of our paper is to explain a mathematical model as a special case of symbolic knowledge map. Each knowledge mapping is a visualization of knowledge for the purpose of eliciting, sharing and expanding. Tools of such visualization can be of various types. But in reality many types of so‑called knowledge maps are only data flow or information flow diagrams. Our paper will define the most important features which every knowledge map must satisfy, for instance it must include chronological, hierarchical, associative, causal and evaluative relationships, it must improve the quality of knowledge etc. In our paper we will prove that a mathematical model satisfies all requirements to be called a knowledge map. Neither definition nor categorization and taxonomy of knowledge mapping are unified in the literature so the authors try to start with working on this field. Knowledge map is a visual interception of knowledge with the aim of its storage, sharing and development. Weak descriptive knowledge maps may be used for explaining the ideas and concepts connected with OR models, as well as for explaining the new knowledge gained with the models, in a well‑ structured form. Strong descriptive knowledge maps can serve to describe real relations between the objects of the models or real elements in relation to their positioning. In this case the object placing does not describe only its physical position but also, for instance, its economical indexes. Like the normative OR models, the normative knowledge maps show the normative solution, or help to find the best, desirable or advisable solution. After suggestions of how to categorize knowledge maps (above) mathematical models of various types with all features and properties are presented as a knowledge map.