The generalized fuzzy derivative is interactive Abstract   In this article, we prove that the generalized difference between     A  ,  B  xe2x88x88   R   F  C    ,     i.e., fuzzy numbers with continuous endpoints, is given by an interactive difference. To be more precise, we construct a certain joint possibility distribution I such that the generalized difference coincides with the supI extension of the subtraction. As an immediate consequence, we have that every notion of difference between     A  ,  B  xe2x88x88   R   F  C    ,     that has so far appeared in the literature, can be derived from a supJ extension for some particular choice of J. Moreover, we show that both the generalized and the generalized Hukuhara derivative of a function     f  :  R  xe2x86x92   R   F  C       at     x  xe2x88x88  R     can be expressed as the limit for hxe2x80xafxe2x86x92xe2x80xaf0 of a difference quotient, where the difference is an interactive difference for each h. For short, we say that the generalized (as well as the generalized Hukuhara) difference is interactive.

Linguistic Pythagorean Einstein Operators and Their Application to Decision Making Linguistic Pythagorean fuzzy (LPF) set is an efficacious technique to comprehensively represent uncertain assessment information by combining the Pythagorean fuzzy numbers and linguistic variables. In this paper, we define several novel essential operations of LPF numbers based upon Einstein operations and discuss several relations between these operations. For solving the LPF numbers fusion problem, several LPF aggregation operators, including LPF Einstein weighted averaging (LPFEWA) operator, LPF Einstein weighted geometric (LPFEWG) operator and LPF Einstein hybrid operator, are propounded; the prominent characteristics of these operators are investigated as well. Furthermore, a multiattribute group decision making (MAGDM) approach is presented on the basis of the developed operators under an LPF environment. Ultimately, two application cases are utilized to demonstrate the practicality and feasibility of the developed decision approach and the comparison analysis is provided to manifest the merits of it.