Multidimensional interval type ۲ epistemic fuzzy arithmetic

The article presents a new, multidimensional arithmetic of type ۲ fuzzy numbers (M-IT۲-F arithmetic) in which the result is a multidimensional fuzzy set. This arithmetic increases the accuracy of calculations and the scope of problems solved in relation to the currently used interval type ۲ standard fuzzy arithmetic (IT۲-SF arithmetic). The proposed M-IT۲-F arithmetic has mathematical properties that IT۲-SF arithmetic does not have. Thanks to these properties, it provides accurate calculation results that are not over- or under-estimated in terms of uncertainty. The paper contains comparisons of both types of arithmetic in application to two problems. Fuzzy arithmetic is not a finished work and is in a phase of continuous improvement and development. M-IT۲-F arithmetic is a higher form of M-IT۲ (non-fuzzy) arithmetic.

Keywords:

Fuzzy arithmetic , epistemic fuzzy arithmetic , multidimensional fuzzy arithmetic , fuzzy arithmetic type ۲ , arithmetic of interval type ۲ fuzzy numbers , Granular computing , Soft computing , Uncertainty Analysis , Artificial Intelligence