The current research is devoted to developing methods of a novel mathematical interpretation of term-sets of linguistic variables. To the term-sets of the linguistic variables fuzzy sets are assigned. We intend to adopt the sfunctions and the π-functions to derive formulas of membership functions of these sets. The fuzzy sets are divided in three families in the case of an odd number of the ter...

Introduced here is a novel application of Satisfiability (SAT) to the set membership problem with specific focus on efficiently testing whether large sets contain a given element. Such tests can be greatly enhanced via the use of filters, probabilistic algorithms that can quickly decide whether or not a given element is in a given set. This article proposes SAT filters (i.e., filters based on S...

This paper presents a new adaptive algorithm for the linearly constrained minimum variance (LCMV) beamformer design. We incorporate the set-membership filtering (SMF) mechanism into the reduced-rank joint iterative optimization (JIO) scheme to develop a constrained recursive least squares (RLS) based algorithm called JIO-SM-RLS. The proposed algorithm inherits the positive features of reduced-r...

This paper gives comparison principles for first-order PDEs of the Hamilton-JacobiBellman type that arise in the problem of filtering under unknown disturbances with set-membership bounds on the uncertainty. The exact solutions of this problem, given in set-theoretic terms as “information sets,” are expressed as level sets to the solutions of some specific types of the HJB equation. But these s...

Set-membership estimation is in general referred in literature as the deterministic approach to state estimation, since its solution can be formulated in the context of set-valued calculus and no stochastic calculations are necessary. This turns out not to be entirely true. In this paper, we show that set-membership estimation can be equivalently formulated in the stochastic setting by employin...