This paper presents new results concerning the effective practical computation of the membership function of the infinite sum (defined via the supHamacher-norm convolution) of triangular fuzzy numbers. Namely, we shall calculate the limit distribution of the Hγ-sum ã1 ⊕ ã2 ⊕ · · · ⊕ ãn ⊕ · · · of triangular fuzzy numbers ãi, i ∈ N, for γ = 0, 1, 2.

This paper reveals the analytical structure of a fuzzy twoterm (PI/PD) controller which employs N1 (≥3) number of symmetric fuzzy sets for the input variable ‘displacement’, N2 (≥3) number of symmetric fuzzy sets for the input variable ‘velocity’ and N1+N2-1 number of symmetric fuzzy sets for the output variable ‘controller output’. The analytical structures are derived via triangular membershi...

This paper presents a variety of cardinality concepts offered by cardinality theory of triangular norm-based fuzzy sets, including the scalar and the "fuzzy" streams.

The goal of this paper is to give a functional relationship between the membership functions of fuzzy intervals M1⊕...⊕Mn and M1 ... Mn, where Mi are positive LR fuzzy intervals of the same form Mi = M = (a, b, α, β)LR and the extended addition ⊕ and multiplication are defined in the sense of a triangular norm (i.e. via sup–t–norm convolution).

Let L n be a lower triangular matrix of dimension n each of whose nonzero entries is an independent N(0; 1) variable, i.e., a random normal variable of mean 0 and variance 1. It is shown that n , the 2-norm condition number of L n , satisses n p n ! 2 almost surely as n ! 1. This exponential growth of n with n is in striking contrast to the linear growth of the condition numbers of random dense...

Min-independence has been proved to be a sufficient condition of a vector of fuzzy random variables to be a fuzzy random vector. The objective of this paper is to study further on the independence condition for fuzzy random vector based on continuous triangular norms. We first discuss measurability criteria for fuzzy random vector, and present two more new equivalent formulations of the measura...

This paper is concerned with the problem of finding bounds for the norm of lower triangular matrix operators from [Formula: see text] into [Formula: see text], where [Formula: see text] is the Cesàro weighted sequence space and [Formula: see text] is a non-negative sequence. Also this problem is considered for lower triangular matrix operators from [Formula: see text] into [Formula: see text], ...