A New Method for Intuitionistic Fuzzy Multiattribute Decision Making

© 2013 IEEE. In this paper, we study the multiattribute decision-making (MADM) problem with intuitionistic fuzzy values that represent information regarding alternatives on the attributes. Assuming that the weight information of the attributes is not known completely, we use an approach that utilizes the relative comparisons based on the advantage and disadvantage scores of the alternatives obtained on each attribute. The relative comparison of the intuitionistic fuzzy values in this research use all the three parameters, namely membership degree ('the more the better'), nonmembership degree ('the less the better'), and hesitancy degree ('the less the better'), thereby leading to the tradeoff values of all the three parameters. The score functions (advantage and disadvantage scores) used for this purpose are based on the positive contributions of these parameters, wherever applicable. Furthermore, these scores are used to obtain the strength and weakness scores leading to the satisfaction degrees of the alternatives. The optimal weights of the attributes are determined using a multiobjective optimization model that simultaneously maximizes the satisfaction degree of each alternative. The optimal solution is used for ranking and selecting the best alternative on the basis of the overall attribute values. To validate the proposed methodology, we present a numerical illustration of a real-world case. The methodology is further extended to treat MADM problem with interval-valued intuitionistic fuzzy information. Finally, a thorough comparison is done to demonstrate the advantages of the solution methodology over the existing methods used for the intuitionistic fuzzy MADM problems

A chance-constrained portfolio selection model with random-rough variables

Traditional portfolio selection (PS) models are based on the restrictive assumption that the investors have precise information necessary for decision-making. However, the information available in the financial markets is often uncertain. This uncertainty is primarily the result of unquantifiable, incomplete, imprecise, or vague information. The uncertainty associated with the returns in PS problems can be addressed using random-rough (Ra-Ro) variables. We propose a new PS model where the returns are stochastic variables with rough information. More precisely, we formulate a Ra-Ro mathematical programming model where the returns are represented by Ra-Ro variables and the expected future total return maximized against a given fractile probability level. The resulting change-constrained (CC) formulation of the PS optimization problem is a non-linear programming problem. The proposed solution method transforms the CC model in an equivalent deterministic quadratic programming problem using interval parameters based on optimistic and pessimistic trust levels. As an application of the proposed method and to show its flexibility, we consider a probability maximizing version of the PS problem where the goal is to maximize the probability that the total return is higher than a given reference value. Finally, a numerical example is provided to further elucidate how the solution method works