On recent methods for solving multi criteria decision making problems / Gamal Eldin Abdelhakim Mohamed Elemam ; Supervised Mohamed Sayed Ali Osman , Ramadan A. Zein Eldin , Hamdin Abdelwahed Khalifa

Thesis (Ph.D.) - Cairo University - Institute of Statistical Studies and Research - Department of Opertion Research

Multi-criteria decision-making (MCDM) is one of the most widely used decision methodologies in the sciences, business, and engineering worlds. In this thesis, we develop new methodologies for solving multi-criteria decision-making problems. By using hybridization between two methods, or hybridization between three methods, simple multi attribute rating technique (SMART), ELimination and choice expressing REality (ELECTRE) and technique for order preference by similarity to Ideal solution (TOPSIS). The SMART method is used here to determinate the weights for each of the criteria to reflect its relative importance. The ELECTRE method defined a partial ranking on the set of alternatives, The TOPSIS method used to rank all of the alternatives. Also we presented the hybridization between ELECTRE and TOPSIS methods to solve group decision making problem. We study the stability of MCDM problems with parameters in the decision matrix or in the weight vector of the criteria, by using the hybridization between SMART and TOPSIS methods, to explain the effect of the two parameters, parameter in the decision matrix and parameter the weight vector of criteria. Rough data expresses uncertainty, any vague concept can be represented as a pair of precise concepts based on the lower and upper approximations. An illustrative numerical example is given to solve decision-making problems with rough data, and another example applies the stability sets of the first kind using TOPSIS method

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