Abstract Competitive balance is an important issue in professional sport general and European football particular. However, competitive difficult to quantify because competitiveness multi-dimensional particular sports are distinctive. We aim identify the most appropriate index for a holistic view of football. use data from eight domestic leagues over time span 60 years. The indices we consider ...

The paper is devoted to the investigation of imprecision indices, introduced in [7]. They are used for evaluation of uncertainty (or more exactly imprecision), which is contained in information given by fuzzy (nonadditive) measures, in particular, by lower or upper probabilities. We argue that there exist various types of uncertainty, for example, randomness, investigated in probability theory,...

The paper is devoted to the investigation of imprecision indices, introduced in [8]. They are used for evaluating uncertainty (namely imprecision), which is contained in information, described by fuzzy (non-additive) measures, in particular, by lower and upper probabilities. We argue that there exist various types of uncertainty, for example, randomness, investigated in probability theory, impr...

A four-hybrid information system (4HIS) is an where the dataset of object descriptions consists categorical, boolean, real-valued and missing data or attributes. This paper studies measures uncertainty for a 4HIS its application in attribute reduction. The distance function each type first provided. Then, this used to produce tolerance relation induced by given subsystem 4HIS. Next, structure p...

in this study, a new stochastic model is proposed to deal with a multi-product, multi-period, multi-stage, multi-site production and transportation supply chain planning problem under demand uncertainty. a two-stage stochastic linear programming approach is used to maximize the expected profit. decisions such as the production amount, the inventory level of finished and semi-finished product, t...

Decision support systems (DSSs) are increasingly being used in water management for the evaluation of impacts of policy measures under different scenarios. The exact impacts generally are unknown and surrounded with considerable uncertainties. These uncertainties stem from natural randomness, uncertainty in data, models and parameters, and uncertainty about measures and scenarios. It may theref...