Uninorms and their applications

Abstract

In human life, we constantly receive a lot of information from the world around us. We have to make decisions based on them, so we have to process and combine them. One way to combine information is to aggregate it (from a mathematical point of view). The data to be aggregated in each case may vary due to different types of information, from quantitative to qualitative information. Therefore, they should be processed in such a way that the data aggregated gave the expected results. These processes have been accompanying man for a very long time. The arithmetic mean was used as early as the time of the Babylonians. However, a detailed study of aggregation functions in general and their formalization and classification is quite more recent, and has experienced a rapid growth from 1970’s to nowadays. Recently, many researchers have studied aggregation functions, and these operations have become an indispensable tool in many applications, from mathematics to the social sciences. For this reason, there is a lot of interest in aggregation functions and most of the known results on this topic have been summarized in several monographs entirely devoted to aggregation functions from both a theoretical and application point of view. In addition, we can find tons of types of aggregation functions to choose from, depending on the area in which we want to use them. One of the possible divisions of aggregation is the division into conjunctive, disjunctive, average and mixed or hybrid aggregations. In this book we will take a look at uninorms, which are hybrid aggregations and show their main properties and some applications. The key part of the monograph is the description of the original classification algorithms based on uninorms. The described algorithms may be applied in decision support systems, for example, in medicine or other disciplines. The book presents the main classes of uninorms presented by various authors. Some of the approaches have been supplemented and in some cases more intuitive approaches have been proposed.