In this paper, a new method for estimating the linear regression coefficients approximation is presented based on Z-numbers. In this model, observations are real numbers, regression coefficients and dependent variables (y) have values ​​for Z-numbers. To estimate the coefficients of this model, we first convert the linear regression model based on Z-numbers into two fuzzy linear regression mode...

Envisaging a futuristic environment of man–machine and machine–machine synergy, this article documents our research on the augmented Z-numbers, the Z∗-numbers, for machineperception encapsulation. The Z∗-numbers have been envisioned as operands of endogenous machine-mind processes underlying bespoke comprehension of the real world. Besides information-certainty, as in a Z-number, a Z∗-number in...

Usually, in real-world engineering problems, there are different types of uncertainties about the studied variables, which can be due to the specific variables under investigation or interaction between them. Fuzzy cognitive maps, which addresses the cause-effect relation between variables, is one of the most common models for better understanding of the problems, especially when the quantitati...

In this paper we propose a new method for ranking Z- numbers and generalizations. This method is based on the internal structure of the artificial neural network, which suggests that the structure of this network consists of inputs weights and the transfer function linear, nonlinear and sometimes linear and nonlinear. It is shown that the proposed method while possessing the ranking properties ...

Decisions are based on information. To be useful, information must be reliable. Basically, the concept of a Z-number relates to the issue of reliability of information. A Z-number, Z, has two components, Z = (A,B). The first component, A, is a restriction (constraint) on the values which a real-valued uncertain variable, X, is allowed to take. The second component, B, is a measure of reliabilit...

Let p/q be a rational noninteger number with p > q ≥ 2. A real number λ > 0 is a Zp/q-number if {λ(p/q)n} < 1/q for every nonnegative integer n, where {x} denotes the fractional part of x. We develop several algorithms to search for Zp/q-numbers, and use them to determine lower bounds on such numbers for several p and q. It is shown, for instance, that if there is a Z3/2-number, then it is grea...