P (Decision Matrix) = [](5)And WT (Weighing vector) = [ ](6)Using the fuzzy extent analysis, final fuzzy weighted performance matrix w.r.t. the criteria can be obtained by multiplying the Weighing vector with the decision matrix A=WT*P=[](7) Applying α-cut on Performance matrix obtained in step no. 5, determine the interval performance matrix. [ ] [ ]} (8)α-(Degree of confidence of decision maker) L and R represents the left and right values of the interval. [[ ] [ ][ ] [ ]](9)After evaluating the left and right values of the interval, these values need to be changed to their normal values using Lembda Function which reflects the attitude of the decision maker. The attitude of the decision maker can be positive, moderate or negative and accordingly they will have higher, average and less values for their fuzzy assessments. The concept of optimism index is used to calculate the normal values. [ ](10)[](11)

256Renuka Nagpal, et. al.:FAHP Approach to rank educational websites on Usability After evaluating the normal values, Normalized Performance matrix can be obtained as: √∑( )[](13) For depicting the best and the worst possible solution among the alternatives across all criteria simple fuzzy positive ideal solution and fuzzy negative ideal solution can be calculated by choosing the extreme value and the lowest value over all alternatives wr.t. criteria as ( )(14) ( ) Where, (16)) (17)Degree of Similarity between each alternative and the positive ideal solution and the negative ideal solution can be calculated respectively by: ( )( )Where, ( )is ithrow of overall performance matrix. So, larger value of and represents higher degree of similarity between each alternative and positive and negative ideal solution respectively. The overall usability score (U.S.) of each alternative and rank the alternatives according to their index. 3.EMPIRICAL STUDYIn this section we present an empirical study of a website selection problem .Selecting the best website from the available websites is a complex decision making approach in which the overall effectiveness of the website needs to be evaluated with respect to the multiple selection criteria. Various selection criteria are involved for evaluating the effectiveness of the website. In the current discussion websites of different educational institutes (W1, W2, W3, and W4) are considered as a case study. Based on comprehensive survey [1] of the relevant educational websites four parameters identified as selection criteria are Response Time (RT), Ease of use (EOU), Ease of Navigation (EON), Informative (INF).The hierarchical structure for evaluating the usability of website is given in Fig.[1].The four selection criteria’s and their corresponding fuzzy NPC matrix are given below: Figure1: Hierarchal Framework for evaluating the usability Criteria for Usability Informative (C4)Ease of Navigation(C3) Ease of Use(C2) Response Time (C1)Website (W4) Website (W3) Website (W2) Website (W1) Ranking of Websites Decision Maker

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- Fall '18
- Zia Ul Rehman
- Decision Making, Usability, Decision making software, AHP, Renuka Nagpal