In this paper, we derive new neuro-fuzzy structures called flexible neuro-fuzzy inference systems or FLEXNFIS. Based on the input-output data, we learn not only the parameters of the membership functions but also the type of the systems (Mamdani or logical). Moreover, we introduce: 1) softness to fuzzy implication operators, to aggregation of rules and to connectives of antecedents; 2) certaint...

A finite element method with numerical quadrature is considered for the solution of a class of second-order quasilinear elliptic problems of nonmonotone type. Optimal a priori error estimates for the H and the L norms are derived. The uniqueness of the finite element solution is established for a sufficiently fine mesh. Application to numerical homogenization methods is considered.

In this paper we introduce and describe two classes of aggregation functions with members that are migrative. First continuous triangular norms are studied that own the migrative property with respect to another fixed t-norm, in particular to the three prototypes minimum, product, and the Łukasiewicz t-norm. For classes of nilpotent and strict migrative t-norms the characterization and construc...

A new knowledge representation language, called QDLP, which extends DLP to deal with uncertain values is introduced. Each (quantitative) rule is assigned a certainty degree interval (a subinterval of [0; 1℄). The propagation of uncertainty information from the premises to the conclusion of a quantitative rule is achieved by means of triangular norms (T -norms). Different T -norms induce differe...

This paper is an improving of the work from [6], in which the upper and lower bounds for the spectral norms of the matrices An = Circ(F (k,h) 0 , F (k,h) 1 , · · · , F (k,h) n−1 ) and Bn = Circ(L (k,h) 0 , L (k,h) 1 , · · · , L (k,h) n−1 ) are established. In this new paper, we compute the spectral norms of these matrices. Mathematics Subject Classification: 15A45, 15A60

Ordinal sums have been introduced in many different contexts, e.g., for posets, semigroups, t-norms, copulas, aggregation operators, or quite recently for hoops. In this contribution, we focus on ordinal sums of t-norms acting on some bounded lattice which is not necessarily a chain or an ordinal sum of posets. Necessary and sufficient conditions are provided for an ordinal sum operation yieldi...

This paper deals with the unique continuation problems for variable coefficient elliptic differential equations of second order. We will prove that the unique continuation property holds when the variable coefficients of the leading term are Lipschitz continuous and the coefficients of the lower order terms have small weak type Lorentz norms. This will improve an earlier result of T. Wolff in t...

In the present paper, considering differential equations on smooth closed manifolds, we investigate and establish well-posedness of boundary value problems nonlocal type for parabolic also hyperbolic in H?lder spaces. Furthermore, various norms new coercivity estimates solutions such manifolds as well.

The possible application of fuzzy sets theory in strategic management to the problem of portfolio matrices analysis, used for strategy alternative(s) formulation and selection is described. The values of membership functions of input variables into portfolio matrices are combined with di erent t-norms: (a) TM (x; y) = min(x; y); (b) TP(x; y) = xy; (c) Sugeno’s t-norms; (d) Hamacher’s t-norm fam...