Type-2 fuzzy linear systems

Abstract

Fuzzy linear systems (FLSs) are used in practical situations, where some of the systems’ parameters or variables are uncertain. To date, investigations conducted on FLSs are restricted to those in which the uncertainty is assumed to be modeled by Type-1 fuzzy sets (T1FSs). However, there are many situations, where considering the uncertainty as T1FSs may not be possible due to different interpretations of experts about the uncertainty. Moreover, solutions of FLSs are T1FSs which do not provide any information about a measure of the dispersion of uncertainty around the T1FSs. Therefore, in this research, a model of uncertain linear equations’ system called a type-2 fuzzy linear system is presented to overcome the shortcomings. The uncertainty is represented by a special class of type-2 fuzzy sets—triangular perfect quasi-type-2 fuzzy numbers. In addition, conditions for the existence of a unique type–2 fuzzy solution to the linear system are derived. A definition of a type-2 fuzzy solution is also given. The applicability of the proposed model is illustrated using examples in the pulp and paper industry and electrical engineering.