16-04-2013, 02:17 PM
Multiple Attributes Decision Making Approach for Project Selection by TOPSIS Technique
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Abstract:
Under the many conditions, crisp data are inadequate to model real-life situations. Human judgments include preferences, which are often vague and cannot be expressed as an exact numerical value. Decision making problem is the process of finding the best option from all of the feasible alternatives. In this paper, from among multi-criteria models in making complex decisions and multiple attributes for most preferable choice, technique for order preference by similarity to ideal solution (TOPSIS) approach has been dealt with. Finally, implementing TOPSIS algorithm, assessment of projects has been done. The results have been tested in numerical example.
Introduction:
In the last two decades, fuzzy set theory has been applied in many disciplines such as operations research, management and decision sciences, artificial intelligence/expert system, control theory, statistics, etc. Fuzzy set theory has provided a new research direction of both concepts and methodologies to formulate and solve mathematical programming and objective decision making problems. The evaluations of alternatives with respect to some attributes are uncertain and vague, fuzzy set theory has theory has been used. By merging fuzzy set theory and multiple-attribute decision making a new decision support system (DSS), namely fuzzy decision method (FDM), has been developed to compare different alternatives with respect to the attributes as crisp variables, and linguistic variables. FDM embodies an expert system whose duty is to choose an appropriate method among the SAW, fuzzy SAW, TOPSIS or fuzzy TOPSIS based on the characteristics of the problem.
Bellman and Zadeh [1] provide the first fuzzy set theory in decision making. Chen and Hwang [6] gave a comprehensive state-of-the-art in fuzzy multiple attribute decision making (FMADM). Triantaphyllou and Lin [18] evaluated five FMADM methods: fuzzy SAW model, fuzzy weighted product model, fuzzy AHP, revised fuzzy AHP and fuzzy TOPSIS. There are many works in the literature on application of FMADM methods in various fields. For example, Bender and Simonovic [2] developed a fuzzy compromise planning approach for a water management problem. Prokash [16] has used FMADM methods in an analysis of Land suitability for agricultural crops. Chen [4] has used the FTOPSIS method in a group decision making problem, when the evaluations of the alternatives versus the criteria are linguistic variables.
Multiple Attribute Decision Making:
Decisions making is part of our daily lives. Almost all decision problems have multiple, usually conflicting, criteria. How to solve such problems has been enomous. Methodologies as well as their applications, appear in professional journals of different disciplines. The problems may be classified into two categories: (i) Multiple Attribute Decision Making (MADM) and (ii) Multiple Objective Decision Making (MODM).
MADM refers to making selections among some courses of action in the presence of multiple, usually conflicting, attributes. For example, one may choose a job depending on salary, work location, promotion opportunity, colleagues, etc. Water resources development plans for a community should be evaluated in terms of cost, possibility of water shortage, energy, flood protection, water quality, etc. Selection criteria for an assistant professor can be based on research ability, teaching ability, communication skills, and maturity. We can go forever: individuals, organizations, societies, and even whole nations face many problems of this type.
Fuzzy Multiple Attribute Decision Making:
Fuzzy MADM methods basically consist of two phases: (i) aggregation of performance scores with respect to all attributes for each alternative, and (ii) rank ordering of alternatives according to aggregated scores. We will refer to results of the first and second phases using the terms “final rating” and “ranking order” respectively. For a crisp MADM problem, final ratings are expressed as real numbers and ranking order can be easily obtained by comparing these real numbers. The main focus of MADM problem solving is the first phase. In a fuzzy MADM problem, performance scores of an alternative with respect to all attributes may be expressed by linguistic data or fuzzy sets. As a result, the final ratings are expressed by linguistic data or fuzzy sets. Obtaining a ranking order of these fuzzy sets is not a trivial task. In this case, both phase one and phase two are important in solving a fuzzy MADM problem.
TOPSIS Method:
TOPSIS is based upon the concept that the chosen alternative should have the shortest distance from the ideal solution and farthest from the negative ideal solution [9]. Assume that each alternative takes the monotonically increasing (or decreasing) utility. It is then easy to locate the ideal solution, which is a combination of all the best attribute value attainable, while the negative ideal solution is a combination of all the worst attribute values attainable.
Numerical Example:
The economic and financial analysis of the project is based on the comparison of the case flow of all costs and benefit resulting from the activities. There are four methods of comparing alternative investments i.e. net present value (NPV), rate of return (ROR), benefit cost analysis and payback period (PBP). Each of these is dependent on a selected interest rate or discount rate to adjust cash flows at different points in time [10]. Assume that the management wants to choose the best project amongst all proposed projects.
Conclusion:
The evaluation and selection of industrial projects before investment decision is customarily done using technical and financial information. In this paper, Author proposed a new methodology to provide a simple approach to assess alternative projects and help decision maker to select the best one. In this approach, we considering the distance of an alternative from the positive ideal solution its distance from the negative ideal solution is also considered. The less distance of the alternative under evaluation from positive ideal solution and more its distance from the negative ideal solution, the better its ranking.