Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences

This paper consists of three parts: 1) some theories and an efficient algorithm for ranking and screening multicriteria alternatives when there exists partial information on the decision maker's preferences; 2) generation of partial information using variety of methods; and 3) the existence of ordinal and cardinal functions based on and strengths of preferences. We demonstrate that strengths of preference concept can be very effectively used to generate the partial information on preferences. We propose axioms for ordinal and cardinal (measurable) value functions. An algorithm is developed for ranking and screening alternatives when there exists partial information about the preferences and the ordering of alternatives. The proposed algorithm obtains the same information very efficiently while by solving one mathematical programming problem many alternatives can be ranked and screened. Several examples are discussed and results of some computational experiments are reported.