Revisiting fuzzy set and fuzzy arithmetic operators and constructing new operators in the land of probabilistic linguistic computing

In this paper, we use a framework known as probabilistic linguistic computing (PLC) to achieve two goals. First, we demonstrate it as an easy-to-use laboratory for understanding existing fuzzy operators. This is achieved by projecting a fuzzy operator of interest into the PLC setting, arriving at a corresponding PLC operator, and hence revealing assumptions initially hidden in that operator. Second, we demonstrate PLC as a simple and general approach for the engineers to construct a wide range of fuzzy operators and measures that can be robustly used in their specialized applications. In particular, by explicating the assumptions hidden in the commonly used fuzzy set and fuzzy arithmetic operators, one is in position to develop other potentially more complex operators
(such as fuzzy entropy measure or fuzzy partial correlation measures) that possess the same assumptions—these complex operators so developed can then be viewed as compatible and consistent with the commonly used fuzzy set and arithmetic operators.