A RUDN Mathematician Developed a Balanced Filter for Making Optimal Decisions
Decision making is an integral part of our daily lives. We decide what to have for dinner, which shirt to put on, or which movie to watch. These are relatively easy decisions, but some are much more difficult - for example, buying a car or making an analytical report. In this case people employ big data sets, use a number of criteria based on their preferences, and finally decide on an optimal solution. The same process but on a higher level takes place in private and state organizations when they determine a place for building a nuclear power plant or select a new drug to treat a dangerous disease. Even a minor error can cost millions of dollars and thousands of human lives. Therefore, it is important to perfect the decision-making algorithm.
Systems with multiple criteria have a peculiar feature called nonadditivity. It means that the final weight of all selection criteria is not equal to the sum of weights of each individual criterion added up together. This happens because the criteria are connected to each other. Today’s mathematical methods used to analyse such systems are unable to correctly evaluate the obtained results. RUDN mathematicians suggested a new efficient way of solving this problem.
“Multi-criteria decision analysis helps make justified decisions in complex situations involving big volumes of initial data. In the course of this process we face the phenomenon called nonadditivity of capacity. When several criteria apply, the end result may alter considerably due to their interplay. We suggest using a nonadditivity index that takes possible influence on the result into account and evaluates it,” says Gleb Belyakov, a visiting professor from RUDN.
Traditionally, the index used in multi-criteria decision analysis is the index of cooperation. However, it doesn’t always take into account the overlap of criteria or their replacement, or expression of these phenomena. It becomes difficult for a decision-making specialist to evaluate the actual value of the obtained results and to interpret them correctly. The index suggested by the RUDN mathematician is free of this disadvantage: it shows not only the type but also the level of nonadditivity.
“We suggest an alternative approach to describing the preferences set out by criteria. We showed on examples that the method could be used for developing a transparent and flexible model, a so-called decision-making filter. The values of the nonadditivity index may be limited to a certain range. This will not reduce its efficiency but will make the comparison of calculation results much easier. In our future studies we will focus on the application of the nonadditivity index to real practical tasks and on the development of support instruments for decision making based on the index,” concludes Gleb Belyakov.
The participants of the study also represented Ningbo University (China) and Deakin University (Australia).
A mathematician from RUDN University developed a matrix representation of set functions. This approach is vivid and easy to check, and it makes the calculations easier. Among other things, the new development can be applied to cooperative game theory.
A chemist from RUDN University together with colleagues created a new type of two-dimensional nanofilm from an organic material called calixarene. The invention can be used as a protective coating in electronics and as a part of molecular filters. They also suggested a way of increasing the durability of such films with UV radiation.
A biologist from RUDN University confirmed that selenium nanoparticles and garlic extract can effectively reduce the negative impact of stress on the health of grass carp in the breeding industry.