Design and Development of Decision Making System Using Fuzzy Analytic Hierarchy Process

: This article aims to develop a fuzzy Multicriteria Decision Making (MCDM) tool that equips with Analytic Hierarchy Process (AHP) framework to help users in semi-structured and unstructured decision making tasks. The tool provides portability and adaptability features by deploying the software on web platform. In addition, this system provides an integrated domain reference channel via a database connection to assist the user obtains relevant information regarding the problem domain before constructing the AHP hierarchy attributes. Our decision making tool combines the characteristics of real time information retrieval through Internet and MCDM problem analytical processing logic.


INTRODUCTION
Decision making analysis aims to realize conflicts that occur due to various different opinions, fluctuating environment conditions, subjective assessments, etc. In real world, decision often been made under various alternatives with their associated criteria. Improper final selection may cause unpleasant outcome with undesired results of misuse in resources, manpower as well as precious time. Hence, it is important to achieve an optimal decision in real world problems which involve multiple alternatives and criteria in qualitative and quantitative domains.
One of the important procedures in AHP is the pair-by-pair comparison values for a set of predefined objects (alternatives). The AHP requires the decision makers furnish with complete information and ample knowledge of all aspects of the problem statements during their judgments under a predefined semantic scale. However, the nature of the real-world problems often relates to fuzziness and ambiguousness which initiates by the unprecedented environment conditions, human factors, incomplete information and etc. Numerous studies [10][11][12] implement the fuzzy set theory in the AHP problem to tolerate the vagueness conditions.
In this study, we develop an AHP multicriteria decision making tool which equips with fuzzy set theory [13] to tolerate the fuzziness in decision maker's judgements. Most of the current AHP decision support commercial software is largely bases on the local machine executable format where user needs to setup the software prior to use. In our system design, we provide portability and adaptability features by deploying the software on web platform. In addition, this tool provides an integrated domain reference channel via a database connection to assist the end user obtain relevant information regarding the problem domain before constructing the AHP hierarchy tree. Hence, our decision making tool combines the characteristic of real time information retrieval through internet and MCDM problem analytical processing logic.   where i = 1,2,3…… r, j = 1,2,3……s and k = r, or k = s. After that, a fuzzy weighted performance matrix (W) % can thus be obtained by multiplying the weight vector with the decision matrix.

MATERIALS AND METHODS
Step 3: Fuzzy number ranking evaluation: In order to make a crisp choice among the alternatives, we need to check and compare the ranking of the fuzzy numbers. We apply the alpha-cuts-based method 1 [14] to the total weighted performance matrices for each alternative and check the ranking consistency for each alternative under different alpha level. The alpha-cuts-based method 1 states that if let A % and B % be fuzzy numbers with α-cuts, . It say A is smaller than B, denotes by A % ≤ B % , if a α -< b α and a α + < b α + for all α ∈ (0.1]. The advantage of this method is the conclusion is less controversial. Step 4: Confidence level fuzzy number: A level threshold (0,α,1) of the fuzzy set is defines to show the decision-makers' confidence to their judgements. The confidence value ranges between 0 and 1, from the least confidence to the most confidence. The definition of the symmetrical triangle fuzzy number (f = (l,m,u)) with the interval confidence at level, α, can be determined by: and respectively.
Step 5: Optimistic level evaluations: The nature optimistic level of the decision maker can be optimistic, moderate or pessimistic. The decision maker's optimistic level with fixed α is denotes as: where λ∈ [0,1]. This crisp performance matrix is represents by: Finally, we normalize the α λ C (i) to evaluate the highest degree of suitability among the selection with respect to i-alternatives using the following formula: Problem formulation: Consider a fresh graduate student would like to choose a job that can provide overall satisfactions in term of benefits, colleagues, location and reputation. Says, the available jobs are job A, B and C. The problem formulation process involves the goal, criteria and alternatives (three level hierarchy) as indicates in Fig. 1. When the user has a clear picture in mind regarding the problem, one can start by inserting the values for each level in the main page. Else, the system provides a domain information repository (DIR) and Google search to assist the user in problem determination. Pairwise comparison: After the problem formulation (goal, criteria and alternatives), the system moves to the state of accepting pairwise judgment from the user. The scoring scale is according to the Saaty's original scale [1,2] .
Consistency checking: Before viewing the result of the AHP operation, user can select PCM Consistency Check (Fig. 3) button to check whether the evaluations are consistent (Fig. 4) enough to be useful. If the evaluation is inconsistent, the system will alert the user to redefine the pairwise comparison for the PCM. Result visualization: Finally, the results are indicated in Fig. 6.

CONCLUSION
This program achieves simplicity and abstraction with fuzzy AHP algorithm that works behind the scene. The Web bases feature enhances the accessibility and portability of this tool. In addition, we also integrate the domain information repository to assist the user with the information (criteria and alternatives) for certain common problem domains.