Multidimensional Type 2 Epistemic Fuzzy Arithmetic Based on the Body Definition of the Type 2 Fuzzy Set

Abstract

The article presents a multidimensional type 2 epistemic fuzzy arithmetic (MT2EF-arithmetic) based on the new body definition of fuzzy set type 2 (T2FS), which in the authors’ opinion, is more suitable for fuzzy computing than the current versions of fuzzy arithmetic (FA) based on the border definition of T2FS. The proposed MT2EF-arithmetic is designed for epistemic variables and has mathematical properties that allow for obtaining universal algebraic calculation results. MT2EF-arithmetic performs calculations, not only with borders of fuzzy numbers, but also with whole bodies of FNs. Thanks to this, computational tasks are solved in the full space of the problem and not in a limited, low-dimensional space. As a result, MT2EF-arithmetic provides precise solutions to problems, solutions that are neither overestimated, underestimated, nor shifted. The paper contains an example of MT2EF-application to optimal fertilization of beetroot cultivation with nitrogen.

Keywords

• fuzzy arithmetic
• type 2 fuzzy arithmetic
• epistemic fuzzy arithmetic
• type 2 fuzzy numbers
• fuzzy systems
• granular computing