A heuristic algorithm for generating the numerical terms of a linguistic variable

Abstract

In this paper we describe an easy-to-implement algorithm for automated generation of the linguistic variable term membership functions to allow for information search in a relational database based on qualitative criteria by means of the SQL query language. The proposed algorithm makes it possible to calculate the parameters of the triangular and trapezoid membership functions taking into account the distribution of the variable of interest stored in the database. The algorithm defi nes the intervals covered by the term bases, so that each interval contains about the same number of values. Upper bounds of the defi ned intervals are used to calculate the parameters of membership functions. The parameters of the membership functions generated with this algorithm can be easily calculated with the limited computational means of the SQL language. We review the algorithm realizations for the generation of 3 and 5 terms of a linguistic variable based on a sample from a database containing 100 or 500 diff erent values. The membership functions obtained through the algorithm have the required properties of orderliness, completeness, consistency and normality. They do not require further approximation. Unlike the known methods, the algorithm does not require signifi cant computing resources, the use of specialized software, settings confi guring, or a training set formation. The algorithm implementation creates opportunities to support fuzzy search queries in relational databases using the means of the SQL language, as limited as they are. Thus, the system's level of intelligence would be increased, and the user would be provided with the means of search query formulation in a natural language. The linguistic variable terms generated using our algorithm can be used within the framework of a fuzzy rule-based knowledge base of an information system, as well as to perform fuzzy inference.