We propose a learning-oriented interactive algorithm for solving multicriteria linear integer programming (MCLIP) problems, considered as multicriteria decision making problems. At each iteration, the DM may partition the criteria set into at most seven classes, namely: improvement, improvement by a desired amount, deterioration, deterioration by at most a certain amount, nondeterioration, chan...

Multiple criteria decision making (MCDM) literature concentrates on the concept of conflicting objectives, which is related to focusing on the need of trading off. Most approaches to eliciting preferences of the decision maker (DM) are built accordingly on contradistinguishing different attainable levels of objectives. We propose to pay attention to the non-conflicting aspects of decision makin...

We consider multiple criteria decision-making problems where a group of decision-makers wants to find the most preferred solution from a discrete set of alternatives. We develop a method that uses achievement scalarizing functions for charting subsets of reference points that would support a certain alternative to be the most preferred one. The resulting descriptive information is provided to t...

In this paper, an integration of Analytic Network Process (ANP) and achievement scalarizing functions is proposed to choose the best suppliers and define the optimum quantities among the selected suppliers by considering tangible–intangible criteria and time horizon. To reflect the decision maker’s (DM’s) preferences more accurate, an additive achievement function is defined consist of several ...

In this paper we investigate a vector optimization problem (P) where objective and constraints are given by set-valued maps. We show that by mean of marginal functions and suitable scalarizing functions one can characterize certain solutions of (P) as solutions of a scalar optimization problem (SP) with single-valued objective and constraint functions. Then applying some classical or recent res...

In recent years, the paradigm of ‘soft glassy matter’ has been used to describe diverse nonergodic materials exhibiting strong local disorder and slow mesoscopic rearrangement. As so far formulated, however, the resulting ‘soft glassy rheology’ (SGR) model treats the shear stress in isolation, effectively ‘scalarizing’ the stress and strain rate tensors. Here we offer generalizations of the SGR...

In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the -constraint method, the Benson method, the hybrid method and the elastic -constrai...

Currently, stochastic optimization on the one hand and multi-objective optimization on the other hand are rich and well-established special fields of Operations Research. Much less developed, however, is their intersection: the analysis of decision problems involving multiple objectives and stochastically represented uncertainty simultaneously. This is amazing, since in economic and managerial ...