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than that. Theoretically, all equations can be
translated into rule patches. Fuzzy systems
approximate systems in physics, communication,
physiology, etc. Fuzzy systems can be applied
wherever the brain is used.
It is hard to deny that modern-day knowledge is
fuzzy. Meanings of statements are undoubtedly
fuzzy. Knowledge has always been regarded in
terms of rules. If knowledge is fuzzy, then rules are
fuzzy as well. Fuzzy rules connect fuzzy sets. Fuzzy
knowledge comprises fuzzy rules, and “if A then B”
rule. Fuzzy patches cover the
system graph. It is the
Fuzzy Approximation Theorem and fuzzy patches
that explain the functioning of fuzzy systems.
2.1 Fuzzy Linear Programming
Operational research offers optimization models
aimed at finding an activity programme that will
yield the best possible results. The models use
precisely determined and known data. Constraints
are also precisely determined, and the goal function
is clearly defined, so that it can be formulated easily
and simply.
Reality, however, is different: very often we lack
precise information on the value of individual input
parameters, or the values of coefficients in constraint
and goal functions, and imprecise formulation of
limitations themselves is possible as well (Maier,
2008).
Fuzzy sets can be introduced into the existing
decision making models in several ways. As an
economic institution, a company bases its existence
on the environment, both from the aspect of
providing input and from the aspect of achieving and
valorising input. Miscellaneous knowledge and
experience, and also decision making in the areas of
investment, market operations, financial function,
production function or research and development,
can be considered more fully and exactly applying
fuzzy sets. Under the existing circumstances
containing fuzzy characteristics, there is a wish to
achieve radical improvements of the production
management and decision making.
The need arises for choosing an appropriate
corporate goal out of the available possible
alternative goals. When accomplishing and
executing the alternatives, the company achieves
different levels of increase in sales (because,
although the subject issue is decision making on
production, one must bear in mind that the ultimate
goal of production is sale of the produced
commodities).
In addition to many constraints under the given
conditions, one must particularly bear in mind
limitations, i.e. constraints such as:
that the selected alternative (goal) is to be
accomplished in the shortest possible period;
that investment in accomplishing the selected
alternative should not be excessive.
The goal of decision making is a large number of
sold products. The decision must best meet the goal
and constraints of the given problem.
The nature of the problem displays the
characteristics of uncertainty and vagueness. The
need for fuzzification, i.e. fuzzy decision making
systems from the fact that the decision maker is
faced with a large number of scenarios and sub-
scenarios out of which the optimum must be chosen,
and the imprecision of input data results from
subjective approach in interpreting per se vague
information.
2.2 The Mark Giving Method
The basic prerequisite to apply fuzzification for
obtaining more effective instruments for using
different kinds of uncertainty, as well as for using
the natural language in modelling decision-making,
in the field of business decision-making of
hierarchical level, faces a whole range of problems
which cannot be solved by the methods of classical
quantitative analysis.
Above all, we would point to the following
problems:
ambivalence of aims,
variability of factors,
subjectivity of sight,
linguistic description of variables.
In practice, we often meet models where multiple
criteria take part in decision-making simultaneously.
This article is an attempt to prepare a decision by the
use of the fuzzy method of ordering alternatives (i.e.
aims), and to set priorities among some alternatives
and criteria, in the decision-making situations where
there are multiple decision-makers, multiple criteria,
and in the multiple time periods. The applied method
of evaluating in this article is based on the usual
assessment, i.e. marking method used in education.
The mark-giving method, very similar to R.
Jain's ordering method, is based on the weighted
aggregation of marks. As mark processing can be
described by many rules, the method forms a fuzzy
set of extra marks by the aggregation on the basis of
rules, and it can also be programmed as a fuzzy
system. The values of criteria, which describe
DecisionSupportSystemwithMark-GivingMethod
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