In this paper, an optimization problem with uncertain objective function coefficients is considered. The uncertainty is specified by providing a discrete scenario set containing possible realizations of the objective function coefficients. The concept of belief function in the traditional and possibilistic setting is applied to define a set of admissible probability distributions over the scenario set. The generalized Hurwicz criterion is then used to compute a solution. In this paper, the complexity of the resulting problem is explored. Some exact and approximation methods of solving it are proposed.

In this paper a class of optimization problems with uncertain constraint coefficients is discussed. Namely, for each ill-known coefficient a possibility distribution, being a membership function of a fuzzy interval, is specified. In a possibilistic interpretation, the induced possibility distribution in the set of constraint coefficient realizations encodes a family of probability distributions in this set. The distributionally robust approach is then used to transform imprecise constraints into crisp counterparts. An extension of the model is proposed, in which individual risk aversion of decision makers is taken into account.

In this paper a robust optimization problem with uncertain objective function is considered. The uncertainty is modeled by specifying a scenario set, containing a finite number of objective function coefficients, called scenarios. Additional knowledge in scenario set can be represented by using a mass function defined on the power set of scenarios. This mass function defines a belief function, which in turn induces a family of probability distributions in scenario set. One can then use a generalized Hurwicz criterion, i.e. a convex combination of the upper and lower expectations, to solve the uncertain problem. Recently, possibility theory has been applied to extend the model of uncertainty based on belief functions. Namely, belief function can be induced by a random fuzzy set. In this paper we show how this generalized model can be applied to robust optimization.

This paper deals with a linear optimization problem with uncertain objective function coefficients modeled by possibility distributions. The fuzzy robust optimization framework is applied to compute a solution. Namely, the necessity degree that the objective value is lower than a given threshold is maximized. The aim of this paper is to take the knowledge on dependencies between the objective coefficients into account by means of a family of copula functions. It is shown that this new approach limits the conservatism of fuzzy robust optimization, better evaluates possibility distributions for the values of the objective function and do not increase the complexity of the problem.

A bipolar structure called BLF expresses knowledge about decisions in terms of decision principles that are ranked and polarized according to the utility of the consequences of these decisions. A BLF allows us to compare decisions under incomplete knowledge. For a given decision, the BLF returns a vector of utility/dis-utility in terms of achievement of positive/negative goals. Decisions are compared thanks to these vectors. In this paper we focus on the link between the uncertain knowledge aggregation made by the BLF and classical aggregation functions used in decision under uncertainty and multi-criteria approaches. The main benefit of a BLF is that thanks to the bipolar scale, positive and negative goals can be dealt with independently under their own point of view (each of them being either pessimistic or optimistic).

The paper deals with a production planning problem, that is a version of the capacitated single-item lot sizing problem with backordering, under uncertain cumulative demands, modeled by fuzzy intervals centered around the cumulative demand nominal values. Their membership functions are regarded as possibility distributions for the values of the unknown cumulative demands. Furthermore, the budgeted uncertainty model is assumed, in which at most a specified number of cumulative demands can deviate from their nominal values at the same time. In order to choose a robust production plan that optimizes against plausible cumulative demand scenarios, under the model assumed, possibilistic criteria are adopted. Polynomial linear programming based methods for finding such robust production plans are proposed, showing in this way that the problem under consideration is not much computationally harder than its deterministic counterpart. Some results of computational tests are presented.

Our research concerns the problem of explainable decision in a context of incomplete knowledge. We define a framework called Bipolar Layered Framework with Support and Weights (BLFSW) that represents the set of argument graphs that can be used in the domain, enabling us to compute what results can be obtained in the different decision situations. This framework also contains information about the utilities/disutilities of these tangible results. This paper extends Bipolar Layered Frameworks defined in [1] by enabling the expression of supports for decision principles and by giving the user the possibility to fix the strength of inhibitors and supports with weights. This increased expressiveness of the framework is important both for refining the evaluation of alternatives and to improve the compactness of the representation. The main result of this paper is to provide an automatic way to explain a possibilistic decision setting in terms of a BLFSW which makes explicit the principles that govern the decision.

The paper deals with a single-item production planning problem with uncertain demands modeled by fuzzy intervals whose membership functions are possibility distributions for the values of the uncertain demands. Optimization criteria, in the setting of possibility theory, that lead to choose robust production plans under fuzzy demands are given. Algorithms for determining optimal robust production plans with respect to the proposed criteria are provided and some computational experiments are presented.