A Soft Set based Group Decision Making Method with Criteria Weight

Authors: Samsiah Abdul Razak, Daud Mohamad

Abstract:

Molodstov-s soft sets theory was originally proposed as general mathematical tool for dealing with uncertainty problems. The matrix form has been introduced in soft set and some of its properties have been discussed. However, the formulation of soft matrix in group decision making problem only with equal importance weights of criteria, which does not show the true opinion of decision maker on each criteria. The aim of this paper is to propose a method for solving group decision making problem incorporating the importance of criteria by using soft matrices in a more objective manner. The weight of each criterion is calculated by using the Analytic Hierarchy Process (AHP) method. An example of house selection process is given to illustrate the effectiveness of the proposed method.

Keywords: Soft set, Soft Matrix, Soft max-min decision making (SMmDM), Analytic hierarchy process (AHP)

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062538

References:

[1] D. Molodstov, "Soft Set Theory-First Result," An International Journal of Computers and Mathematics with Applications, vol. 37, pp. 19-31,1999.
[2] P.K. Maji, R. Biswas, and A.R. Roy, "Soft Set Theory," An International Journal of Computers and Mathematics with Applications, vol. 45, pp. 555-562, 2003.
[3] H. Aktas, and N. Cagman, "Soft sets and soft groups," An International Journal of information sciences, vol. 177, pp. 2726-2735,2007.
[4] N.Cagman, and S.Enginoglu, "Soft Set Theory and Uni-Int Decision Making," European Journal of Computers and Mathematics with Applications, vol. 207, pp. 848-855 , 2010.
[5] T. Herawan, and M. M. Deris, "Soft Decision making for patient suspected influenza," Springer-Verlag Berlin Heidelberg, 2010.
[6] P.K. Maji, and A.R. Roy, "An Applications of Soft Sets in A Decision Making Problem," An International Journal of Computers and Mathematics with Applications, vol. 44, pp.1077-1083, 2002.
[7] N. Cagman, and S. Enginoglu, "Soft matrix theory and its decision making," An International Journal of Computers and Mathematics with Applications, vol. 59, pp. 3308-3314 , 2010.
[8] Kunz, J. (2010). The Analytic Hierarchy Process (AHP), Eagle City Hall Location Option Task Force, February/March, 2010.
[9] Y. Wen Liu, Y. Jik Kwon, and B. Do Kang, "A fuzzy AHP approach to evaluating e-commerce websites" Fifth International Conference on Software Engineering Research, Management and Applications,pp. 114-122, 2007.
[10] T. L. Saaty, and L. G. Vargus, "Model, Methods, Concepts, & Applications of the Analytic Hierarchy Process," United Stated of America: Kluwer Academic Publishers, 2001, pp. 27-43.
[11] S. Razak, D. Mohamad, "An Application of Soft Matrices in Group Decision Making Problems" unpublished.