Linear interpolation in a fuzzy information space

Abstract

An approach to solving a linear interpolation problem in a fuzzy information space is proposed. Two different schemes of interpolation are outlined: a heuristic one, based on the geometrical interpretation of operations, and an optimization one, based on the expansion principle. The results obtained allow performing fuzzy linear prediction.

Probability propagation in fuzzy Bayesian belief networks with nondeterministic states

“…Taking into account relationship (1), the proposed interpretation of fuzzy probability also allows one to determine nontrivial fuzzy analogues of more complicated operations, for example, fuzzy linear interpolation [16].…”

“…It is required to determine an estimate of the characteristic Y for the fuzzy inner traverse Õ as the value interpolated from the reference points if the estimates Y 1 and Y 2 are fuzzy. A procedure of fuzzy linear interpolation from two points and a fuzzy traverse is described in [16]. We now formulate the problem for N = 3 points.…”

“…The final posteriori estimate~( ) * P F is a result of fuzzy linear interpolation over the traversẽ ( ) U C from the mentioned reference estimates (in the general case, from two nearest ones) [16]. We denote the N ® 1 (Fig.…”

“…The scheme of its realization is reduced to the recursive use of operations (16) for the values of n from 1 to N, …”