Definition and selection of fuzzy sets in genetic‐fuzzy systems using the concept of fuzzimetric arcs

This paper seeks to identify and propose a standard approach for the selection and optimization of fuzzy sets used in fuzzy decision‐making systems.

The design was based on two principles: selection and optimization. The selection methodology was based on the “Fuzzimetric Arcs” principle, which is an analogy of the trigonometric circle principle. This would allow an initial sinusoidal fuzzy set shape. Other shapes may also be selected using the described formula (trapezoidal, triangular, … , etc.). As the proposal methodology is based on the trigonometric circle, other trigonometric formulae can be applied. For example, linguistic hedges can be defined using standard trigonometric formulae. Regarding optimization, the initial fuzzy set selection was assumed to be of regular shape (sinusoidal, trapezoidal or triangular). An irregular shape may be required by some systems. Hence, a genetic algorithm was proposed as a methodology to optimize the performance of fuzzy systems by mutating different regular shapes.

A simplified business decision‐making application was described and the proposed selection methodology was explained in the form of an example. Currently, there is no standard for the selection of fuzzy sets as this is dependent on knowledge engineering and the type of application chosen. The proposed methodology offers an easy‐to‐use possible standard which all developers/researchers may adopt irrespective of their application field. Moreover, the proposed methodology may integrate well with object‐oriented technology.

The paper presents standardization of the fuzzy sets selection and optimization technique used in any type of management information systems. This will aid all developers and researchers to enhance their technical communication. It would also enhance the simplicity and effectiveness of optimizing the performance of such systems.