In the fuzzy setting, we define a collector of fuzzy information without probability, which allows us to consider the reliability of the observers. This problem is transformed in a system of functional equations. We give the general solution of that system for collectors which are compatible with composition law of the kind “inf”.

We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous $t$-norms to act as the weakest $t$-norm $T_W$-based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18].

In a recent paper we have introduced the fuzzy hyperbolic inequality index, to quantify the inequality associated with a fuzzy random variable in a finite population. In previous papers, we have also proven that the classical hyperbolic inequality index associated with real-valued random variables in finite populations can be unbiasedly estimated in random samplings. The aim of this paper is to analyze the problem of estimating the population fuzzy hyperbolic index associated with a fuzzy random...

The Goodman-Kruskal measure, which is a well-known measure of dependence for contingency tables, is generalized to the case when the variables of interest are categorized by linguistic terms rather than crisp sets. In addition, to test the hypothesis of independence in such contingency tables, a novel method of decision making is developed based on a concept of fuzzy $p$-value. The applicability of the proposed approach is explained using a numerical example.

In problems of testing statistical hypotheses, we may be confronted with fuzzy concepts. There are also situations in which the available data are record statistics such as weather and sports. In this paper, we consider the problem of testing fuzzy hypotheses on the basis of records. Pareto distribution is investigated in more details since it is used in applications including economic and life testing analysis. For illustrative proposes, a real data set on annual wage is analyzed using the results...

This paper presents a relaxed scheme for controller synthesis of continuous- time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions’ derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller synthesis is attainable via linear matrix inequalities, which are efficiently solved by commercially available...