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    UGC MINOR RESEARCH PROJECT [MATHEMATICS]

    STUDY OF DECISION MAKING PROBLEMS

    USING FUZZY THEORY

    FINAL REPORT

    UGC SANCTION NO: .F MRP – 4072/12 (/MRP/UGC-SERO) – P.No: 32

    Dated 8th April, 2013

    Submitted to

    UNIVERSITY GRANTS COMMISSION

    South- East Regional Office

    Hyderabad.

    Principal Investigator

    P.BHARATHI M.Sc. M.Phil.,

    Assistant Professor of Mathematics

    Sri Sarada Niketan College For Women

    Amaravathipudur,Sivagangai District

    Tamilnadu.

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    CHAPTER 1

    INTRODUCTION

    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

    applicable result.

    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

    several perspectives:

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     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

    goal.

    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.

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    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

    enumerated below.

    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.

    4. Payoff

    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.

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    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

    organization.

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    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

    physiology."

    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

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