Table 1. Example of an extended decision matrix for Table 3. The j-E matrix evaluation of three different learning objects pc(Lo) pc(LO) ec(LO) ec( LO) d(Lo) d(LO) IEEE LOM Path Units or Factor .498 0.66 0.553 LOn (LO2) (L03) 0.219 0.32 5 he relative closeness indexed of the three LOM/General (2) Finally, objects are generated by equations(17)is (2,2=31m LOn)(LO2)0LO2)了=0606023801561 So the recommendation order over the specifie Interactivity Level(3) learner preference iS LO,>LO,>LO3. In this case, LOMEducatiorall wUO5 learning object LO, is ranked to be the most suitable fo Semanic Density (13) S10 L0.5) Difticulty (3) s(0.6) 4. Conclusion Learning Resource Type (13) The evidential reasoning approach proposed in this VU(an-wery ttsmitable, U(a)-unsanitable, A(oj-amerage, s(aj-statable, S(ej-rery statable work provides an alternative way to treat uncertain ecision the evaluation grades is defined by ng in learning object recommendation From problem. The presented decision making procedure S=S S4 S5=/rery umsuitable umsuitable composed of this approach and the CODASId method can be used to deal with multiple feature decision making problems with uncertainty. The demonstrated examples S is transformed into the preference degree have presented the implementation process of treat using the following scale uncertainty in multiple features decision making P(S)=[p(S1)P(S2) P(S,)P(S4) P(S)] oblems. This system provides personalized guidance fitters out unsuitable course concept to reduce cognitive load, recommend the most suitable learning object to th Each of the preference degrees for quantifying the learner by the raking method states of the qualitative features at all learning objects is 5. References generate following the same process demonstrated in the previous section. The global suitability assignments are [I P Dodds, Advanced Distributed Learning Sharable Content Object generated using the global combination algorithm. The Reference Model Version 1. 2, online], available at example of results is listed in Table 2 http://www.adlnet.org(2001) Cognition, Revised December 12, 2006.(2006) Table 2. Suitability assignments for f(LO) [2]J. Novak and A Canas"The Theory Underlying Concept Maps and Basic Suitability Suitable grades How to Construct them, Technical Report IHMC STools 2006-01, Florida Institute for Human and Machine (B×A2) vU(p) U() ↓S( nition, Revised December 12, 2006.(2006 IEEE Standard for Learning Object Metadata, 1484.12.1 [4N. Pukkhem, M.W. Evens, and w. Vatanawood, " The Concept lobal Suitability Path Combination model for St ting a personalized learni 0.000 Path in Adaptive Educational Systems, In Proceedings of th Then, the preference degrees of the two qualitative (EEE06),, Las Vegas, USA,(2006) features at the three learning objects are calculated using (13). For example, Attribute Decision Models'", Journal of multi Criteria Decision Analysis, vol. Il, pp291-303 (2002) 2=2pS)+32n(S)+1S)+,)+82S)+pS Case-Based Reasoning Applications", Knowledge's Engineering vie,203),pp.325-328(2006 =0.0×(-1)+0.072×(-04)+087×(0)+00×(0.4)+0.041×(1)+0017×0 [7 K. Sentz and S Ferson, Combination of evidence in Demper- =0.012 Shafer theory", SAND Report, SAND2002-0835, (2002) [8 D. Dubois, H. Fargier, P Pemy and H. Prade, A Characterization Using equations(15)-(16),we obtain the riteria Decision ollowing judgment and evaluation matrix (Table 3) Making, International Journal of Intelligent Systems, vol 18, pp.751-774(1998)Table 1. Example of an extended decision matrix for evaluation of three different learning objects Features or IEEE LOM Path of Features Units or Factor Learning Object (LO1) (LO2) (LO3) Size ( 1 f ) Mb 5 8 2 LOM/General/ ( 2f ) Structure ( 1 2v ) VS(0.9) S(1.0) A(1.0) Aggregation Level ( 2 2v ) A(0.5) S(0.5) S(1.0) S(0.8) VS(0.1) LOM/Educational/ ( 3f ) Interactivity Type ( 1 3v ) A(1.0) VS(0.9) U(1.0) Interactivity Level ( 2 3v ) VS(1.0) S(1.0) S(1.0) Semantic Density ( 3 3v ) VS(1.0) S(1.0) VU(0.5) U(0.5) Difficulty ( 4 3v ) S(1.0) S(0.5) VS(0.5) S(0.6) Learning Resource Type ( 5 3v ) S(1.0) A(1.0) VS(1.0) VU very unsuitable U unsuitable A average S suitable VS very suitable ( ) , ( ) , ( ) , ( ) , ( ) ω ω ωω ω − − −− − From (3), the evaluation grades is defined by S SSS S S = { 1 23 4 5 } = {very unsuitable unsuitable average suitable very suitable } S is transformed into the preference degree space using the following scale: 12345 { } [ ( ) ( ) ( ) ( ) ( )]T pS pS pS pS pS pS = = [-1 -0.4 0 0.4 1] T Each of the preference degrees for quantifying the states of the qualitative features at all learning objects is generate following the same process demonstrated in the previous section. The global suitability assignments are generated using the global combination algorithm. The example of results is listed in Table 2. Table 2. Suitability assignments for 2 1 f ( ) LO Basic Suitability ( 2 β × λ ) Suitable Grades VU ( ) β U ( ) β A( ) β S( ) β VS( ) β Factors 1 2v 0.9 0.72 2 2v 0.45 0.45 Global Suitability (2) n C Sb 0.000 0.072 0.870 0.000 0.041 Then, the preference degrees of the two qualitative features at the three learning objects are calculated using (13). For example, 12 3 4 5 (2) (2) (2) (2) (2) (2) 12 1 2 3 4 5 ( ) ( ) ( ) ( ) ( ) () CC CC C C SS SS S S p b pS b pS b pS b pS b pS b pS =+++++ = 0.0 ( 1) 0.072 ( 0.4) 0.87 (0) 0.0 (0.4) 0.041 (1) 0.017 0 ×− + ×− + × + × + × + × = 0.012. Using equations(15)-(16), we can obtain the following judgment and evaluation matrix (Table 3). Table 3. The J-E matrix pc LO ( ) pc LO ( ) ec LO ( ) ec LO ( ) d LO ( ) d LO ( ) 1 LO 0.769 0.876 1.006 0.703 0.728 0.464 2 LO 0.436 0.498 0.566 0.396 0.867 0.553 3 LO 0.308 0.352 0.313 0.219 0.536 0.342 Finally, the relative closeness indexed of the three learning objects are generated by equations (17) is: 12 3 ( ) ( ) ( ) T ⎡u LO u LO u LO ⎤ ⎣ ⎦ = [0.606 0.238 0.156] T . So the recommendation order over the specific learner preference is LO LO LO 123 > > . In this case, learning object LO1 is ranked to be the most suitable for specific learner. 4. Conclusion The evidential reasoning approach proposed in this work provides an alternative way to treat uncertain decision making in learning object recommendation problem. The presented decision making procedure composed of this approach and the CODASID method can be used to deal with multiple feature decision making problems with uncertainty. The demonstrated examples have presented the implementation process of treat uncertainty in multiple features decision making problems. This system provides personalized guidance, fitters out unsuitable course concept to reduce cognitive load, recommend the most suitable learning object to the learner by the raking method. 5. References [1] P. Dodds, Advanced Distributed Learning Sharable Content Object Reference Model Version 1.2, [online], available at: http://www.adlnet.org (2001). Cognition, Revised December 12, 2006. (2006). [2] J. Novak and A. Caňas “The Theory Underlying Concept Maps and How to Construct them, Technical Report IHMC CmapTools 2006-01”, Florida Institute for Human and Machine Cognition, Revised December 12, 2006. (2006). [3] IEEE, IEEE Standard for Learning Object Metadata, 1484.12.1- 2002, 2002. (2002). [4] N. Pukkhem, M.W. Evens, and W. Vatanawood, "The Concept Path Combination Model for Supporting a Personalized Learning Path in Adaptive Educational Systems", In Proceedings of the 2006 International Conference on e-Learning, e-Business, Enterprise Information Systems, e-Government, and Outsourcing (EEE'06), , Las Vegas, USA, (2006). [5] R. Roberts and P.Goodwin, “Weight Approximations in Multi- Attribute Decision Models”, Journal of Multi Criteria Decision Analysis, vol. 11, pp291-303 (2002). [6] R. Lopez de Mantarus, P. Perner and P. Conningnam, “Emergent Case-Based Reasoning Applications”, Knowledge’s Engineering Review, 20(3), pp. 325-328 (2006). [7] K. Sentz and S. Ferson, “Combination of evidence in Demper- Shafer theory”, SAND Report, SAND2002-0835, (2002). [8] D. Dubois, H. Fargier, P. Perny and H. Prade, A Characterization of Generalized Concordance Rules in Multi-Criteria Decision Making, International Journal of Intelligent Systems, vol.18, pp. 751-774 (1998). 265