Choquet-integral-based evaluation models are proposed. The evaluation parameters – fuzzy measures – are assigned from a fuzzy rule table. There are three variations in this model: TF-, BP-, and AV-type models. The TF-type model is a natural extension of ordinal Choquet integrals. The BP-type model involves an evaluation using a reference point. The AV-type model involves a neutral evaluation me...

Based on a set of criteria and a measuring lattice, we introduce relational measures as generalizations of fuzzy measures. The latter have recently made their way from the interval [0, 1] ⊆ IR to the ordinal or even to the qualitative level. We proceed further and introduce relational measures and relational integration. First ideas of this kind, but for the real-valued linear orderings stem fr...

The concepts of the Choquet and Sugeno integrals, based on a fuzzy measure, can be adopted as useful tools in estimation of the total effectiveness of a drug when appreciating its positive influence on a collection of symptoms typical of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting ...

When there are interactions among the independent variables, the performances of the most often used multiple regression models and ridge regression model are not well enough. In contrast, the Choquet integral takes into account the interactions among independent variables, the discrete Choquet integral regression models based on some non-negative valued fuzzy measures or monotonic measure can ...

In [3] we introduced a “monotone-type” (that is, Choquet-type) integral for realvalued functions, with respect to finitely additive positive set functions, with values in a Dedekind complete Riesz space. A “Lebesgue-type” integral for such kind of functions was investigated in [7]. In [4] we gave some comparison results for these types of integrals. In [10], a Choquet-type integral for real-val...

The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. We focus on the notion of quantile of a lattice-valued function which have several properties of its real-valued counterpart and we study a class of aggregation functionals that generalizes Sugeno integrals to the setting of complete lattices. Then we introduce in the r...

In this paper, we propose new methods to represent interdependence among alternative attributes and experts’ opinions by constructing Choquet integral using interval-valued intuitionistic fuzzy numbers. In the sequel, we apply these methods to solve the multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. First, the concept of interva...