Preference Structures and Co-comparability Graphs

In reliability allocation, certain reliability values are assigned to subsystems and components to achieve the required system reliability. One big challenge in solving such reliability‐based design problems is how to handle the uncertain preferences of a decision maker on multiple attributes of interest. In this paper, we propose a new ordered weighted averaging (OWA) method based on an analytic hierarchy process to address the decision maker's uncertain preferences in reliability allocation. In the proposed OWA operator, a bi‐objective mathematical programming model considering both maximal entropy and minimal variance is transformed into a single‐objective mathematical programming model using an ideal‐point method. The maximum entropy minimal variance OWA operator takes full advantage of available information and avoids overestimating the decision maker's preferences. A detailed computational procedure is presented to facilitate the implementation of the proposed method in practice. An illustrative example about the powertrain of fuel cell vehicles is provided to demonstrate the effectiveness of this method in handling multiple attributes with uncertain preferences in reliability allocation. Copyright © 2015 John Wiley & Sons, Ltd.

The decision maker's preference information on the importance and interaction of decision criteria can be explicitly described by the probabilistic interaction indices in the framework of the capacity based multicriteria decision analysis. In this paper, we first investigate some properties of the probabilistic interaction indices of the empty set, and propose the maximum and minimum empty set interaction principles based capacity identification methods, which can be considered as the comprehensive interaction trend preference information oriented capacity identification methods. Then, by introducing the deviation variables, the goal constraints, as well as the goal objective function, we give a new and more flexible approach to representing the decision maker's explicit preference information on the kind and degree of the interaction of any given combination of decision criteria as well as on the degree of the importance of any decision criterion, and construct the nonempty set interaction indices based capacity identification method, which can be considered as the detailed explicit preference information oriented identification method. Finally, two illustrative examples are respectively given to show the feasibility and applicability of the two kinds of methods. In addition, the comparison analysis between these two kinds of methods and some existing capacity identification methods are also mentioned.

Data envelopment analysis (DEA) model has been applied for evaluating bank branches and recognizing efficient and inefficient branches can help bank managers to provide appropriate strategies to improve the inefficient branches' performance. Conventional DEA models are based on the ‘black box’ approach. However, the process of providing services in banks is made up of interactive and interdependent processes. Additionally, some managers tend to incorporate their preferences in evaluation process. In this paper, best worst method (BWM) is used for incorporating decision maker (DM) preferences in two‐stage DEA model. First, BWM model is applied to obtain the weights of inputs, intermediate measures and outputs based on DM's judgement. Second, generated weights are imposed on two‐stage DEA model as additional constraints and a novel bi‐objective BWM‐two stage DEA model is introduced. Finally, the proposed bi‐objective BWM‐two stage DEA model is solved using min‐max approach. To illustrate the capability of proposed model, 45 Agricultural Bank (Agribank) branches in West Azerbaijan province of Iran are evaluated. The branches' processes are considered as two stages ‘production’ and ‘profitability’ and efficiency of branches are calculated in each stage. According to the efficiencies of each sub‐stage, branches are divided to four groups and recommendations are made for each group.

Primary facets of order polytopes

In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Procedure. In the procedure, the decision maker articulates preference information over representative samples from the nondominated set either by assigning preference “values” to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Choo [Steuer, R. E., E.-U. Choo. 1983. An interactive weighted Tchebycheff procedure for multiple objective programming. Math. Programming 26(1) 326–344.]). The computational results indicate that the Interactive FFANN Procedure produces good solutions and is robust with regard to the neural network architecture.

Multi-objective analysis of hospital delivery systems

Let n stimuli be linearly ordered by a physical attribute. Consider an individual's “more than” relation based on perceived attribute values. Assuming that the individual's relation agrees with the linear order and is an interval order, the paper examines the extent to which ordered pairs in the linear order but not in the interval order (due to nondetection of “small” differences) can be correctly identified on the basis of the interval order alone. Different methods of constructing strict weak orders from interval orders are compared by the degree of agreement with the underlying linear order.

A novel interactive preferential evolutionary method for controller tuning in chemical processes

To address problems with multiple conflicting objective functions while incorporating preference information from a decision maker (a domain expert), interactive evolutionary multiobjective optimization methods have been proposed and widely adopted. To systematically assess the performance of these methods, it is desirable to have indicators that not only rely on the Pareto dominance relation, where solutions with better objective function values are preferred, but also take the decision maker's preferences into account. In this way, indicator values can meaningfully reflect the decision maker's preferences and the quality of the solutions obtained. In this paper, we propose the first performance indicator that incorporates preference information in the form of two reference points, specifically, an aspiration point, consisting of aspiration levels that represent the decision maker's full satisfaction, and a reservation point, consisting of reservation levels that represent dissatisfaction. The new indicator, termed D-PHI, translates information about reservation and aspiration points into a transformed hypervolume measure that assesses the performance of a solution set. We introduce D-PHI with an extended set of guidelines for preference-based performance evaluation, discuss its theoretical properties, and demonstrate its behavior through empirical examples. Moreover, we define a complementary indicator (CI) based on a so-called achievement scalarizing function. CI offers additional insight into whether aspiration and reservation levels have been achieved, and its usefulness is demonstrated through examples.

A new neural network‐based multiobjective optimization of water quality management for water pollution control and river basin planning is presented. Past research on water quality management problems has shown that traditional multiobjective decision making does not provide an adequate solution since it depends directly on the decision maker's (DM's) preferences, which may not be clearly defined. In order to overcome the DM's preferences problem this study uses a neural network algorithm to form a model for the solution of the multiobjective problems of water quality management in a river basin. Using the backpropagation algorithm of feedforward neural networks, a multiobjective programming model can simulate the DM's preferences, providing direct help to the analysts involved in real applications. Before describing the details of the multiobjective optimization problem, neural networks are proposed which can be used to predict the DM's preference structures. To demonstrate the procedures and the performance of the neural network‐based approach, the case of the Tou‐Chen River Basin in Taiwan is selected for analysis and discussion.

Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations

Outranking-based approaches for multiple criteria partially ordered clustering: A review of existing algorithms, new proposals, and experimental comparison

Integrated, multi-scale and multi-objective design of batch food processing plants. Part 2: Application to a mobile fruit and vegetable processing unit

In Chapter 3, we have seen how averaged heights of objects hav(x) can be calculated. Thus partial order provides a method to obtain a linear order without the need of making additional assumptions like weights for indicators. The main computational problem, however, is the huge number of linear extensions, which sometimes makes the calculation of averaged heights and from them the linear order difficult. This chapter discusses different procedures to rank objects.

We find out suitable conditions on a To-principal topology, under which the associated partial order is a partial order with nontransitive incomparability, that is an interval order, a partial semiorder or a semiorder. In order to perform these characterizations, only a T 1 separation axiom is needed. The settheoretical approach allows us to give a simple proof of a fundamental theorem due to Fish burn, concerning the numerical representation of interval orders. We also introduce a class of planar interval orders, called strong interval orders. Although planar posets, as well as interval orders, have arbitrary finite dimension, we prove that a strong interval order is the intersection of at most two linear orders.