“I would never tell them that an elephant
has a trunk. I would just show
them the elephant if I had a chance…”
(Sellinger “Teddy»)

In this article I am going to share with you my ideas regarding quantitative criteria of condition changes of the “problem - > purpose - > task” management system. Besides, I will touch upon the problems of risk monitoring and decision-making algorithms, as many of you asked me to do.
 
First of all, it is necessary to understand, that the considered system consists of two objects, the phenomenon under analysis and the researcher himself. We can speak about the possibility of describing quantitative changes of system globally (i.e. irrespective of the researchers) only in case when the changes are obvious for most researches. For example, on the one hand, a light earthquake is an obvious fact for the main population; however some skeptics may assert that nothing is going on. While on the other, absolutely weak pushes of the earth’s crust can be felt only by very sensitive people or determined by experts with the help of special devices. Thus, one should understand that the accuracy of description of system condition depends on both the system (or phenomenon) condition and the qualitative characteristics of observers. Our knowledge constantly develops, thus increasing our abilities to observe and distinguish more specific details of systems and phenomena. The purchasing capacity of dollar is constantly falling, while the knowledge quality is increasing. Things that we did not know and thus could not see a hundred years ago become reality today. Nowadays, a school pupil knows and understands more than some academicians knew one or two centuries ago. One may draw many reasons confirming the thesis that research results depend on both the phenomenon and the researcher.
 
I would like to draw your attention to one more factor, i.e. the factor of risk. Disregarding risk, it is quite impossible to create a security system and to determine any quantitative criterion of decision-making. It is quite reasonable, given that we do not know how to determine the line between dangerous and safe earthquakes. If the chandelier in my house starts shaking and the furniture begins to move, how can I guess the moment when I should cry for help and jump out of the window with the bed sheet instead of a parachute? Obviously, it depends on both the earthquake power and my ability to run risks. I am quite sure that most people will leave their homes even after weak pushes of earth, at the same time I am quite confident that some fans of extreme situations will sit still in their homes even when the walls almost fall down. It is all subjective.     Each of us creates his own characteristic function of risk estimation, which reflects the degree of his ability to run risks depending on results of analysis of specific initial conditions. For example, the most simple is as follows: risk = earthquake force * my weight multiplier. Certainly, I will cry for help at various levels of risk in different situations and conditions. Let us assume that my weight multiplier is 1. Then, if optimistically-minded, I will cry for help when the risk exceeds 5. Otherwise, I will leave home in panic when risk hardly exceeds 3. The weight multiplier is determined by seismic stability of my house. I trust the builders who set up my house, thus supposing that the seismic stability of my house corresponds to the standard earthquake scale, so I take 1 as coefficient. If I did not trust the builders, I would rather take the coefficient of 1.5~3 depending both on the degree of mistrust and the deterioration of the building (however, in this case the threshold values of decision-making would remain unchanged). So, on the one hand we have algorithm of risk estimation and, on the other, we have criteria of decision-making, both sides being absolutely independent. Thus characteristic functions and criteria of decision-making are built, depending on the values of similar functions at certain initial data (here Richter seismic scale).
 
Using the above-mentioned reasoning, we can create analytical tables reflecting the research of some system or phenomenon (see the picture). Our everyday experience allows analyzing systems by more than one criterion (as described above). Moreover, the lion’s share of our initial analytical data has likelihood structure, which can be estimated with certain accuracy. It would all be quite perfect if only we could actually estimate the probability of all factors. But sometimes we cannot even imagine what may happen if this or that event occurs – a complete uncertainty. Now let us take a look at the tables. We have the phenomenon itself, the factors by which we try to analyze the phenomenon with the corresponding weight multipliers of factors’ importance. It gets more interesting further on as we have to consider not just the positive impact of a certain factor, but its negative influence as well. Actually, this is what made me create the rarified sets. (“Go there noone knows where and bring that no one knows what”.) A thoughtful researcher is likely to analyze both factors which can bring him success and factors which can ruin his success.
 
So, in case we analyze some problem we are likely to get two clearly-divided characteristic functions, one of them reflecting a successful realization of our plans and research and the other one - the failure. It is impossible to create a function with one of its components having no value at all. What will we actually get if we add nothing to 1 (I guess, the result will be “nothing”, and is it possible to analyze “nothing”?)? Thus, as a result we get two phenomenon characteristics, given the strict requirement that the characteristic function should not be equal to emptiness (or to nothing). This is a vivid example of a rarified set, so this is a qualitative view on the problem. Thus, on the first table we try to analyze the problem. One should take account of the fact that weight indexes tend to change in time, but we shall assume their behavior as extremely conservative. The example with the earthquake makes me understand that such indexes tend to grow in time. However, in some 20-30 years, there will come a certain moment when my house undergoes capital reconstruction, and the index will fall again. But I suppose that the index will hardly change within a year.
 
Let us proceed with our research. We have come to a conclusion that we do not have all the necessary data (it is so called rarified field of data). Then our company pays money to some third parties for getting the required information, and finally we get it. After that our table seems to be more complete. Now we have all the necessary figures. On this stage we can narrow up the data (build a characteristic function) at the vertical level as well (for example, by subtraction one index from another and by division on their average index) at a complete absence of the empty indexes. However, our description of the phenomenon still has a very vague structure depending on the initial factors. Though some risk is still possible, we have already put the criteria for analysis together. This situation is perfectly described by fuzzy logic. According to my ideas, the phenomenon under analysis has been transformed from the state of a problem into the state of purposes analysis. Actually, we are already able to make real planning, while we may still run some risk. (I guess that life would have been boring if we did actually achieve all our aims…).
 
Further on we are going to change our table until it is possible to give orders to direct executors. To achieve this we should believe in success of our plans. Hence, the probability of realization of orders (factor realization) should almost equal to one. At some stage we get the third table. How we have achieved it remains our personal secret – either we are so acute or it was time that helped us. It does not actually matter now. The important thing is that the probability of initial data in characteristic functions has almost achieved the absolute indexes of their execution probability. This is a common and classical set, like “go to the stable, harness the horses and bring up the carriage to the porch” (though on the way one can break his leg, or the stable can burn out, or the carriage can get broken, etc…). So, we have come up to the notion of tasks, to the point of direct executors.   
 
Thus, we have determined criteria of transition from one notion to another. In order to find a proof to my ideas let us compare the given criteria and the decision-making systems. Consensus is on top of it. Actually, two ways are possible – “yes” and “no” – and the decision should be taken by a member of the top management who has a deeper understanding of the problem. The next point for discussion is compromise. The higher the reasonable risk, the higher the income of the direct executor. The last level is the level of ordinary executors, who run minimal risk and get stable income. (In this paragraph I have also provided the conformity of public goods distribution system depending on the risk level at decision-making).
 
Now that we have discussed this system (along with characteristic functions), we can pay attention to a very important factor, namely the time factor. In the course of time, these tables can naturally change. However, the changes can be reversible or they can even skip one level. Let us take for example fairy tales on Ivan the fool. Here we deal with the level of ordinary executor with minimal risk and low income. Just imagine that the system he is living in changes upward skipping one level. In this case the executor supporting a similar functional, starts to solve problems. Just a bit of luck can help Ivan get prosperity. However, it is possible to move in another direction, i.e. to think what a failure is and how to fight it (maybe a change of position in the system may be helpful).
     
I have mentioned my ideas on the time factor in order to draw your attention to another important point – risk monitoring. (Success – failure, rise – fall and so on in the course of time…). What do people mean saying that someone knows how to live? It simply means that he skillfully uses (though intuitionally) his own risk monitoring system and is able to change his position in any system. And what if we apply this reasoning to a company or some other public organization? Why do some of them prosper and the others decay? These are the different sides of the same coin. On the one hand, we obtain technologies which help us estimate the external impact (as described above), and, on the other, we have some kind of an inside system of risk estimation and getting welfare (self-knowledge). Actually, risk monitoring reflects their periodical mutual matching. In case they are equal (if all the required decisions are taken timely – it is the third whale of success), a company develop progressively. Otherwise, a company starts to decay. We will come back to this problem in my article on the business strategy and tactics. And now let us get back to the problem of risk monitoring.
 
Just imagine yourself at the brink of Niagara Falls, where you will admire the sights instead of crying for help. Now imagine that in the morning you look through the window to see something similar to Niagara Falls in the streets of your city. Possibly you will not cry for help, but it is quite obvious that you will try to turn on the radio and TV, or call your friends or relatives, or talk with your neighbors in order to guess what has happened and how soon it will be over. The situation can be even worse, if you do not have enough food to last you until a raging flood is over. In this case you run the risk of either starving to death or getting drowned trying to get some bread. When the flood occurs, the first thing to do is to wait until it starts to decrease. We are constantly estimating the risks of getting drowned or starving to death. These risks depend on some initial data, like food supply and consumption speed, water rise, speed of water streams in the streets, remoteness from places where you can replenish the edibles, your ability to swim and your general ability of finding solutions in critical situations. However, we do not take quick decisions, as we need some time to estimate the situation (only in case the water has not yet got into our beds). I mean that we do not just “wait in vain”, but expect risk changes: either the risk of starving to death reaches its critical point or the risk of getting drowned gets lower. This is risk monitoring. We build characteristic functions according to several initial factors, like: food and water edibles, remoteness from some product depots, depth of water, speed of floods, water and air temperature, etc… From time to time we estimate our chances to survive or get drowned (for example, listening to the weather forecasts on the radio each half-an-hour). Moreover, each of us has his own view on the maximum risk (a kind of a threshold function of decision-making), when it is easier to make decisions. Thus, we determine a decision-making criterion according to which we put on boots and start seeking for bread in case our food edibles can last us just for two days and the water depth does not exceed 1 meter. However, if our edibles are enough to last us for the whole month, then is it worth running risk at all? (See the picture).
 
Now we have briefly covered risk monitoring and threshold function. Naturally, in any situation we put all the initial data into some characteristic functions (for example, the probability of swimming as far as the depots and its dependence on the water temperature, depth and speed) enabling us to make decisions. However, we should never forget that this process requires periodical getting of initial data (weather forecast) and putting them together into some system (based on my tables), i.e. their systemizing. Thus, from time to time we make analysis calculating the characteristic functions (whether we will get drowned or not) on the one hand and applying the threshold function of decision-making on the other. We can make decisions as soon as their indexes start intersecting or belonging to each other)(see the picture). Any risk depends on as far as our image of danger exceeds our risk threshold, and on the reasons for risk. For example, during the flood it is quite dangerous to go out if the water depth exceeds 1 meter. However, our neighbors can turn out to be more courageous people and empty the nearest product depots, while we sit still waiting until the water falls down to 10 centimeters. Here is the essence of making risky decisions. Now let us sum up all the above-mentioned. Consensus – we think of possible solutions (having good edibles, maybe we should not run risk but wait until the water level gets down, in the meanwhile we should better decide what depots we will visit afterwards). Compromise – we go out to get some food, when the water level has got sufficiently lower, however still we run risk of getting drowned, though we can easily get food from the nearest depots, so it raises our safety. Authoritarianism – the government allowed us to go out and advised us what bases we should visit in order to get food, and we followed the call. Meanwhile, you can always get fresh weather forecast, which enables you to monitor your risk and make proper decisions (if the forecasts expect new strikes of hurricane, maybe you should better get back home immediately).
 
I do not provide some specific types of characteristic functions, I do not show threshold functions of risk and my tables are just demonstrative. And I do it intentionally, as in any field, management system, or company all these factors may have specific features and should be determined according to the initial factors. The initial data can be and should be derived from any automation systems (accounting, business transactions, trade, production or other systems) as well as from the experts’ estimations. Before applying the proposed technologies, we should create a model of the situations and determine whether we can actually survive at the water depth of 1 meter and the air temperature of 15 degrees (otherwise, we will run a risk of getting drowned, while we can perform the experiment in a swimming pool and apply our life experience). I would like to pay special attention to the life experience as it gives us a clearer vision on characteristic functions and on own weight multipliers as well (negates our experience). Therefore it should not be neglected. Sometimes, life experience substitutes several higher educations, as universities teach us how to build characteristic functions, while the life experience helps realize them and apply to everyday’s life.

Last modified: 21.09.2003
Translation by Elena Polyanskaya