ugc minor research project [mathematics] ugc minor research project [mathematics] study of decision
Post on 21-Apr-2020
Embed Size (px)
UGC MINOR RESEARCH PROJECT [MATHEMATICS]
STUDY OF DECISION MAKING PROBLEMS
USING FUZZY THEORY
UGC SANCTION NO: .F MRP – 4072/12 (/MRP/UGC-SERO) – P.No: 32
Dated 8th April, 2013
UNIVERSITY GRANTS COMMISSION
South- East Regional Office
P.BHARATHI M.Sc. M.Phil.,
Assistant Professor of Mathematics
Sri Sarada Niketan College For Women
In this chapter, we give a concise account of preliminary definitions and results required
commonly for the forthcoming chapters. We start with basic definitions from decision
making theory. All the definitions on decision making theory given here are taken from
the standard texts on this subject.
1.1 DECISION MAKING THEORY
Making decisions is undoubtedly one of the most fundamental activities of human
beings. We all face in our daily life with varieties of alternative actions available to us
and, at least in some instances, we have to decide which of the available actions to take.
In the beginning, the decisions were made by the methods of election & social choice.
Since these initial studies, decision making has evolved into a respectable and rich field
of study. The current literature on decision making based largely on theories and methods
developed in this century is enormous. Decision making is a problem solving process by
which a method is selected among various methods in order to obtain an effective and
The subject of decision making is the study of how decisions are actually made and how
they can be made better or more successfully. Much of the focus in developing the field
has been in the area of management, in which the decision making process is of key
importance for functions such as inventory control , investment, personal actions, new
product development and allocation of resources as well as many others. Decision
making itself is broadly defined to include any choice or selection of alternatives and is
therefore of importance in many sciences and engineering.
Human performance with regard to decisions has been the subject of active research from
Psychological: examining individual decisions in the context of a set of needs,
preferences and values the individual has or seeks.
Cognitive: the decision-making process regarded as a continuous process
integrated in the interaction with the environment.
Normative: the analysis of individual decisions concerned with the logic of
decision-making and rationality and the invariant choice it leads to.
Decision making can be defined as a process of specifying a problem, identifying and
evaluating criteria or alternatives and selecting a preferred alternative among possible
ones defined in common terminologies in decision making as follows:
(a) Alternatives - a set of objects, products, actions or strategies.
b) Attributes - each alternative is defined by a set of characteristic.
c) Objectives - a collection of attributes selected by the decision maker(s) to be used as a
d) Weights - the relative importance of each attribute or the relative importance of an
instance of an attribute.
A decision making problem is the problem to find the best decision in the set of feasible
alternatives with respect to several criteria functions. When dealing with practical
decision making problems we often have to take into consideration uncertainty in the
problem data. Decision-making can be regarded as the cognitive process resulting in the
selection of a belief or a course of action among several alternative possibilities. Every
decision making process produces a final choice that may or may not prompt action.
Decision making is the study of identifying and choosing alternatives based on the values
and preferences of the decision maker. Decision making is one of the central activities of
management and is a huge part of any process of implementation.
Decision analysis can be used to determine optimal strategies where a decision maker is
faced with several decision alternatives and an uncertain pattern of future events.
Decision theory comments with the assumption that regardless of the type of decision
involved, all the Decision Problems have certain common characteristics which are
1. The Decision Maker
The decision maker refers to individual or a group of individuals responsible for making the choice of an appropriate course of action amongst the available course action.
2. Courses of Action
The courses of action or Strategies are the acts that are available to the decision maker .
3. States of Nature
The events identify the occurrences which are outside the decision maker’s control and which determine the level of success for a given act. These events are often called states of nature or outcomes.
Each combination of a course of action and a state of nature is associated with a payoff, which measures the net benefit to the decision maker that accrues from a given combination of decision alternatives and events.
5. Payoff table
For a given problem, payoff table lists the states of nature which are mutually exclusive as well as collectively exhaustive and a set of given courses of action or strategies.
General form of Payoff table
States of Nature Courses of Action
A1 A2 ………….. An
S1 P11 P12 …………. P1n
S2 P21 P22 ………….. P2n
…. ………. ……… ………. …………..
Sm Pm1 Pm2 …………. Pmn
Logical decision-making is an important part of all science-based professions, where
specialists apply their knowledge in a given area to make informed decisions. For
example, medical decision-making often involves a diagnosis and the selection of
appropriate treatment. Some research using naturalistic methods shows, however, that in
situations with higher time pressure, higher stakes, or increased ambiguities, experts use
intuitive decision-making rather than structured approaches following a recognition
primed decision that fits their experience and arrives at a course of action without
weighing alternatives. Recent robust decision research has formally integrated
uncertainty into its decision-making model. Decision analysis recognized and included
uncertainties in its theorizing since its conception in 1964.
With regard to management and decision-making, each level of management is
responsible for different things. Top level managers look at and create strategic plans
where the organization's vision, goals, and values are taken into account to create a plan
that is cohesive with the mission statement. For mid-level managers, tactical plans are
created with specific steps with actions that need to be executed to meet the strategic
objective. Finally, the front-line managers are responsible for creating and executing
operational plans. These plans include the policies, processes, and procedures of the
organization. Each must take into account the overall goals and processes of the
The environment can also play a part in the decision making process. It is important to
know that environmental complexity is a factor that influences cognitive function and
well being. A complex environment is an environment with a large number of different
possible states which come and go over time. It is in different states at different times and
different in different places as opposed to the same all over. Peter Godfrey-Smith,
professor at Stamford University, states "whether a particular type of complexity is
relevant to an organism depends on what the organism is like- size, needs, habits and
Classical decision making generally deals with a set of alternative states of
nature(outcomes, results), a set of alternative actions that are available to the decision
maker , a relation indicating the state or outcome to be expected from each alternative
action, and an objective function which orders the outcomes according to their
desirability. A decision is said to be made under conditions of certainty when the
outcome for each action can be determined and ordered precisely. In this case, the
decision making problem becomes an optimization problem, the problem of maximizing
the utility function. A Decision is made under conditions of risk on the other hand when
the only available knowledge concerning the outcomes consists of their conditional
probability distributions, one for each action. In this case the decision making problem
becomes an optimization problem of maximizing the expected utility. When probabilities
of the outcomes are not known, or may not even be relevant, and outcomes for