Fuzzy Logic Aggregation Functions

Description

Information aggregation is of common interest to various engineering fields in which there is a need to combine information from various sources into a single value, as for example, aggregation of expert opinions in group decision making, sensor data fusion, color mixing etc. The mean operators which are related to the present work on aggregation operators have been classified as compensative operators. In compensative operators the lower values are compensated by the higher values, so that the result of aggregation will be medium. Properties of the aggregation operator for a given application depend on the nature of the values to be aggregated, the invariance of order or preference, and the nature of the scale which is used. In this book, new fuzzy aggregation operators which are based on the geometric characteristics of the membership lines which constitute the membership functions of triangular and trapezoidal fuzzy numbers have been proposed. The mathematical expressions of the new aggregation operators have been derived starting vi from their definitions, i.e., starting from first principles. A family of new aggregation operators for both triangular and trapezoidal fuzzy number has been proposed. These operators are based on the use of geometrical properties of the membership lines of the corresponding fuzzy sets. As a result they are conceptually simple, easy to understand and intuitive. They use the spread information for the purpose of aggregating fuzzy numbers. These characteristics make these operators elegant for use in real world applications.

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