Fuzzy arithmetic type 1 with horizontal membership functions

Abstract

The chapter shortly (because of the volume limitation) presents multidimensional fuzzy arithmetic based on relative-distance-measure (RDM) and horizontal membership functions which considerably facilitate calculations. This arithmetic will be denoted as MD-RDM-F one. It delivers full, multidimensional problem solutions that further enable determining, in an accurate and unique way, various representations of the solutions such as span (maximal uncertainty of the solution), cardinality distribution of possible solution values, center of gravity of the solution granule, etc. It also allows for taking into account relations and dependencies existing between variables, what is absolutely necessary e.g. in calculations with fuzzy probabilities that always should sum up to 1 or in equation system solving.