In spite of the serious matters mentioned in the title this paper is a popular one. It shows how impossible it is to take a clear position to a matter on premises understood as fully determined information. On the contrary, the most logical position can be be taken based on the insufficient information, which usually is the only available one. When relying on illusively exact looking premises or information, the decision would be wrong or non-optimal. However realising that only insufficient premises are normally available and knowing how to use them, a more adequate decision can be taken or an optimal strategy can be assumed in a given situation.

1. Musical evaluations. Intuitive decisions
2. Perception of religion
3. Superstition
4. Relativity of decisions based on insufficient information
5. Disadvantages of “exact” information
6. Chess as a strategic game
7. Equilibrium situations in fuzzy cooperative decisions
8. Ethical problems
9. Outlook for the future
10. Selected references

Let us consider the indefinableness of musical opinions and taste. Due to limited possibility of evaluating by perception such musical elements like melody, harmony, way of performance, etc., a need of evaluating them using a simple logical model could appear. Let us consider a jury, which has to decide which of the two musical works W1 and W2 participating in a contest should win. The perception criteria are for example musical innovation (S1) and expressiveness (S2). The importance of these criteria or their weights is G1 for the innovation and G2 for the expressiveness, meaning that for this particular competition the expressiveness is more or less important than the innovative elements.
The personal normalised judgements in this case will be v1 in the case of evaluating the musical work W1 from the point of view of its innovative character and v2 judging its expressiveness. Further v3 will be the evaluation result of the musical work W2 from the point of view of its innovation and v4 as far as its expressiveness is concerned.
We use to insert the above set of data in the Table 1 for better and more systematic perception:

The result at this stage is a logical but uncertain conclusion of the juror, for instance:
Providing that the expressiveness is more or less important than the innovative elements (G1>G2) the verdict would be:

This verdict is however only intuitive and not transferable to clear points, marks or as we call it Perception Indices, which normally is the final expression of a neutral opinion of the jury. By using the certain process which will equip the juror with clear perception indices based on very limited information (*), he will operate with the following average table containing clear perception indices (Table 2):

The values that are weighted or in other words corrected for the importance of expressiveness and innovation are:

The E(W2) is obviously higher than the E(W1) and therefore . . .

The method described here is called Preference Analysis.

The Musical evaluations is an "appetizer" only. Similar way evaluation of the fine art works can be accomplished. The same table (Table 1) can be set up, however in this case W1 and W2 are two paintings and the evaluation criteria would be for instance the colour palette applied G1 and the composition of the paintings G2.
Also in this case verdict concerning an apparently subjective issue as the arts can be produced pretty exact using the method of the Preference Analysis.
After this simple introduction in the Preference Analysis, wouldn't it be tempting to try to test it in philosophy? For instance to take a position in so personal and intuitive an issue as religion and consider whether to believe in God or not . . .

1. Kofler, E.: Prognosen und Stabilität bei unvollständige Information, Campus Verlag 1989.
2. Kofler, E.: Linear Partial Information with Applications in “Fuzzy Sets and Systems”, North Holland, vol. 118, 1, 2001, pp. 167–177.
3. Kofler, E.: Prognosen und Optimale Strategien in unscharfen Schachsituationen, “Idee & Form“, No. 70, 2001 Zürich, pp. 2065 – 2067.
4. Kofler, E., Kofler Th.: Fuzzy Normal Distribution with Applications, in “Fuzzy Sets and Systems”, North Holland, forthcoming.
5. Kofler, E., Kofler Ch.: Musical Decisions under Fuzzy Information, forthcoming.
6. Chess as a strategic game
7. Kofler, E.: Wstep do teorii gier” (Introduction to the Game Theory), PZWS, Warszawa, 1962.
8. Kofler, E., Kofler,Th.: Forecasting Analysis of the Economical Growth under Linear Partial Information, Fuzzy Logic, ISFL, 1997.