Fuzzy solution of the linear programming problem with interval coefficients in the constraints

A fuzzy concept of solving the linear programming problem with interval coefficients is proposed. For each optimism level of the decision maker (where the optimism concerns the certainty that no errors have been committed in the estimation of the interval coefficients and the belief that optimistic realisations of the interval coefficients will occur) another interval solution of the problem will be generated and the decision maker will be able to choose the final solution having a complete view of various possibilities.interval linear programming, fuzzy solution

REVIEW OF MODELING PREFERENCES FOR DECISION MODELS

A group decision problem is set in environments where there is a common issue to solve, a set of possible options to choose, and a set of individuals who are experts and express their opinions about the set of possible alternatives with the intention to reach a collective decision as the unique solution of the problem in question. The modeling of the preferences of the decision-maker is an essential stage in the construction of models used in the theory of decision, operations research, economics, etc. On decision problems experts use models of representation of preferences that are close to their disciplines or fields of work. The structures of information most commonly used for the representation of the preferences of experts are vectors of utility, orders of preference and preference relations. In decision problems, the expression of preferences domain is the domain of information used by the experts to express their preferences, the main are numerical, linguistic, and intervalar stressing the multi-granular linguistic. This paper is a review of these concepts. Its purpose is to provide a guide of bibliographic references for these concepts, which are briefly discussed in this document

A new index for bond management in an uncertain environment

Within the framework of Assets Liability Management, we understand that immunization is the main method to assure a certain yield in a future date departing from an initial portfolio. Although the objective of passive strategies is to design a portfolio that will achieve the performance of a predetermined benchmark, active bond management strategies rely on expectations of interest rate movements or changes in yield–spread relationships. However, the variation of the duration increases the risk of a portfolio, that why the decision maker will have to choose the combination of expected return and risk which provides the higher utility. Finally, the construction of a fuzzy return risk map will allow the decision maker to know the over risk and the over return as regards immunization strategy for each duration and for each risk aversion of the decision maker. The construction of a risk return map presents the results in an appropriate way. It will help the decision maker to choose the best duration for the decision maker interest rate forecast. Finally, this methodology is applied to the Spanish debt so that the decision maker can select the duration that brings him a greater preferenc