Fuzzy Multiple Objective Decision Making

At the turn of the century, reducing complex real-world systems into precise mathematical models was the main trend in science and engineering. In the middle of this century, Operations Research (OR) began to be applied to real-world decision-making problems and thus became one of the most important fields in science and engineering. Unfortunately, real-world situations are often not so deterministic. Thus precise mathematical models are not enough to tackle all practical problems.

Decision making is the process of selecting a possible course of action from all available alternatives. In many cases, multiplicity of criteria for judging the alternatives is pervasive. Often the decision maker wants to attain more than one objective or goal in selecting a course of action, while satisfying constraints dictated by environment, processes, and resources.

In the previous chapter, we have discussed a variety of computationally efficient approaches for solving crisp multiple objective decision making problems. However, the input data, such as the unit profit/cost, goals, available resources and/or technological coefficients, may not be precisely determined because of incomplete or non-obtainable information. For instance, the unit profit and cost (C) of new products may be expected to be “near $2.3” and “above $7.5.” Available labor hours and available material (b) may be “around 1220” hours and “about 1550” units, respectively, and the estimates of technological coefficients (A) may be “around 3” units per labor hour. In this chapter, we use preference-based membership functions, μ(·), to resolve this fuzzy nature and obtain fuzzy multiple objective decision making problems (FMODM). FMODM problems are then transferred into crisp auxiliary MODM problems which can be solved by techniques discussed in Chapter 2 or by any prevailing MODM methodologies. If the imprecise nature of input data is modelled by possibility distributions, π(·), of possibility theory, then we would have possibilistic multiple objective decision making (PMODM) problems, which will be discussed in the following chapter.

Stochastic programming has been used since the late 1950s for decision models where input data (coefficients in LP problems) have been given probability distributions. Pioneer works were done by Dantzig, Beale, Tintner, Simon, Charnes, Cooper and Symonds. Since then, a number of stochastic programming models have been formulated in inventory theory, system maintenance, micro-economics, and banking and finance. The most recent summaries of the development of stochastic programming methods are Stancu-Minasian and Wets (see Appendix).

During the last 25 years, fuzzy set theory has been applied in many disciplines such as operations research, management and decision science, artificial intelligence/expert systems, control theory, statistics, etc. In this study, we concentrate on (fuzzy) multiple objective decision making which is one of the most important fields in operations research, and management and decision science. This study provides readers and researchers with a capsule look into existing methods, their characteristics and their applicability to multiple objective decision analysis under crispness, fuzziness and imprecision.