A class of fuzzy numbers induced by probability density functions and their arithmetic operations

In this paper we are interested in a class of fuzzy numbers which is uniquely identified by their membership functions. The function space, denoted Xh,p, will be constructed combining nonlinear mappings h (subjective perception) and probability density functions (PDF) p (objective entity), respectively. Under our assumptions, prove that there always exists to fulfill the observed outcome for given p. Especially, common triangular number can interpreted pair (h,p). As an example, consider sample space Xh,p where tangent chosen as Gaussian kernel with free variable μ. By means μ (which also expectation p(x;μ)), define addition, scalar multiplication subtraction on Xh,p. We claim that, under definitions, has linear algebra. Some numerical examples provided illustrate proposed approach.