The application of horizontal membership functions to fuzzy arithmetic operations

The fuzzy numbers arise in decision making, control theory, fuzzy systems and approximate reasoning problems. The operations on them are becoming more and more popular. The aim of this paper is to present the fuzzy arithmetic operations on fuzzy numbers in a new way, using the horizontal membership functions (HMFs). The horizontal membership functions enable to introduce uncertain, interval or fuzzy variable-values together with crisp values in arithmetic operations without using Zadeh's extension principle. Thus, a relatively easy aggregation of crisp and uncertain knowledge has become possible. The numerical example of this developed method is also provided.