Associated Probabilities in Insufficient Expert Data Analysis

Abstract

Problems of modeling uncertainty and imprecision for the analysis of insufficient expert data (IED) are considered in the environment of interactive multi-group decision-making (MGDM). Based on the Choquet finite integral, a moments’ method for the IED is developed for the evaluation of the associated probabilities class (APC) of Choquet’s second-order capacity based on the informational entropy maximum principle. Based on the IED new approach of the lower and upper Choquet’s second-order capacities, identification is developed. The second pole of insufficient expert data, the data imprecision indicator, is presented in the form of a fuzzy subset and image on the alternatives set. In the environment of the Dempster–Shafer belief structure, connections between an associated possibilities class (APosC), with the APC, and an associated focal probabilities class (AFPC) are constructed. In the approach of A. Kaufman’s theory of expertons, based on the APosC and the AFPC unique fuzzy subset, the IED image on the alternatives set is constructed. Based on Sugeno’s finite integral most typical value (MTV), as a prediction on possible alternatives set, the IED is constructed. In the example, a sensitive and comparative analysis is provided for the evaluation of the new approach’s stability and reliability.

Keywords

• fuzzy measure
• Choquet’s capacity
• imprecise probabilities
• insufficient expert data
• associated and focal probabilities
• expertons