Clustering and group selection of multiple criteria alternatives with application to space-based networks

In many real-world problems, the range of consequences of different alternatives are considerably different. In addition, sometimes, selection of a group of alternatives (instead of only one best alternative) is necessary. Traditional decision making approaches treat the set of alternatives with the same method of analysis and selection. In this paper, we propose clustering alternatives into different groups so that different methods of analysis, selection, and implementation for each group can be applied. As an example, consider the selection of a group of functions (or tasks) to be processed by a group of processors. The set of tasks can be grouped according to their similar criteria, and hence, each cluster of tasks to be processed by a processor. The selection of the best alternative for each clustered group can be performed using existing methods; however, the process of selecting groups is different than the process of selecting alternatives within a group. We develop theories and procedures for clustering discrete multiple criteria alternatives. We also demonstrate how the set of alternatives is clustered into mutually exclusive groups based on 1) similar features among alternatives; 2) ideal (or most representative) alternatives given by the decision maker; and 3) other preferential information of the decision maker. The clustering of multiple criteria alternatives also has the following advantages. 1) It decreases the set of alternatives to be considered by the decision maker (for example, different decision makers are assigned to different groups of alternatives). 2) It decreases the number of criteria. 3) It may provide a different approach for analyzing multiple decision makers problems. Each decision maker may cluster alternatives differently, and hence, clustering of alternatives may provide a basis for negotiation. The developed approach is applicable for solving a class of telecommunication networks problems where a set of objects (such as routers, processors, or intelligent autonomous vehicles) are to be clustered into similar groups. Objects are clustered based on several criteria and the decision maker's preferences.     

A two-phase case-based distance approach for multiple-group classification problems

Classification is a procedure to separate data or alternatives into two or more classes. In practice, the need to classify alternatives involving multiple criteria into distinct classes is considerable. Therefore, determining how to assist decision makers in classifying alternatives into multiple classes is an important issue in the field of multiple-criteria decision aids. This study proposes a two-phase case-based distance approach used to assist decision makers to classify alternatives into multiple groups. By incorporating the advantages of the case-based distance method, the proposed two-phase approach can classify alternatives by evaluating a set of cases selected by decision makers, reduce the number of misclassifications, improve multiple solution problems, and lessen the impact of outliers. An interactive classification procedure is also proposed to provide flexibility in such a way that decision makers can check and adjust classification results iteratively.     

Evidential reasoning‐based nonlinear programming model for MCDA under fuzzy weights and utilities

In a multiple‐criteria decision analysis (MCDA) problem, qualitative information with subjective judgments of ambiguity is often provided by people, together with quantitative data that may also be imprecise or incomplete. There are several uncertainties that may be considered in an MCDA problem, such as fuzziness and ambiguity. The evidential reasoning (ER) approach is well suited for dealing with such MCDA problems and can generate comprehensive distributed assessments for different alternatives. Many researches in dealing with imprecise or uncertain belief structures have been conducted on the ER approach. In this paper, both triangular fuzzy weights of criteria and fuzzy utilities assigned to evaluation grades are introduced to the ER approach, which may be incurred in several circumstances such as group decision‐making situation. The Hadamard multiplicative combination of judgment matrix is extended for the aggregation of triangular fuzzy judgment matrices, the result of which is applied as the fuzzy weights used in the fuzzy ER approach. The consistency of the aggregated triangular fuzzy judgment matrix is also proved. Several pairs of ER‐based programming models are designed to generate the total fuzzy belief degrees and the overall expected fuzzy utilities for the comparison of alternatives. A numerical example is conducted to show the effectiveness of the proposed approach. © 2009 Wiley Periodicals, Inc.     

Multi–criteria Classification Methods in Financial and Banking Decisions

Over the past two decades, the quantitative analysis of financial and banking decisions has gained significant interest among researchers and practitioners. A significant part of the research conducted in this field focused on the development of analytical models that can be used in evaluating the alternative ways of action in financial and banking problems. Typically, this evaluation involves the choice of the best alternative, the ranking of the alternatives from the best to the worst ones, or their classification into predefined homogenous classes. This paper is focused on the classification approach illustrating the use of multi–criteria decision aid (MCDA) classification methods in making financial and banking decisions. Three MCDA approaches (the UTADIS method, the ELECTRE TRI method, and the rough set approach) are applied in financial and banking problems, such as business failure prediction, credit–risk assessment, and portfolio selection and management. A comparison is also performed with linear and quadratic discriminant analysis, and logit analysis.     

Hierarchical semi-numeric method for pairwise fuzzy group decision making

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.     

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

The aim of this article is to develop a novel multiple criteria decision analysis (MCDA) method using a Pearson-like correlation-based Pythagorean fuzzy (PF) compromise approach under complex uncertainty based on PF sets and interval-valued Pythagorean fuzzy (IVPF) sets. Because of the complexity and ambiguity involved in real-life decision-making situations, this article utilizes the theory of Pythagorean fuzziness, which is characterized by flexible degrees of membership, nonmembership, and indeterminacy to describe uncertain information more comprehensively. PF and IVPF sets possess exceptional abilities to accurately reflect the uncertainty, fuzziness, and vagueness inherent in the decision information. However, manipulating PF and IVPF information is a complicated and difficult task for most decision makers. In this regard, this article extends the well-known and widely used concept of correlation coefficients to develop simple and effective compromise models for solving MCDA problems in PF and IVPF contexts. This article conducts an extended analysis of Pearson-like correlation coefficients for PF and IVPF sets separately and introduces new concepts of PF and IVPF correlation coefficients to furnish a solid basis for the proposed methodology. Furthermore, this article develops useful concepts of PF and IVPF correlation-based closeness coefficients to simultaneously measure the relative closeness to the positive-ideal PF/IVPF solutions and the relative remoteness from the negative-ideal PF/IVPF solutions. On the basis of the developed concepts, this article proposes a novel Pearson-like correlation-based PF/IVPF compromise approach to address uncertain MCDA problems involving PF/IVPF information and determine the ultimate priority orders among competing alternatives. Finally, this article provides an illustrative application about a financing decision of working capital management to verify the developed approach and demonstrate its feasibility and practicality.     

A modified Sobol′ sensitivity analysis method for decision-making in environmental problems

Sensitivity analysis is an important component of environmental modelling and in recent years, variance-based, global sensitivity analysis techniques, such as Sobol′, have been a preferred approach for achieving this. However, these techniques are generally only applicable to simulation models and not to models used to rank alternative options, such as multi-criteria decision analysis (MCDA) methods. In order to overcome this limitation, a modified Sobol′ method for MCDA (Sobol′-MCDA) is introduced in this paper. The method has the following features: (i) it enables the stability or robustness of the relative ranking of two alternatives to be assessed in the light of changes in assessment criteria and stakeholder preferences; and (ii) it enables the sensitivity of the ranking of two alternatives to changes in assessment criteria and stakeholder preferences to be assessed. The approach is demonstrated for a water resources case study from the literature consisting of seven alternatives and ten assessment criteria.     

An OWA-TOPSIS method for multiple criteria decision analysis

A hybrid approach integrating OWA (Ordered Weighted Averaging) aggregation into TOPSIS (technique for order performance by similarity to ideal solution) is proposed to tackle multiple criteria decision analysis (MCDA) problems. First, the setting of extreme points (ideal and anti-ideal points) in TOPSIS is redefined and extended for handling the multiple extreme points situation where a decision maker (DM) or multiple DMs can provide more than one pair of extreme points. Next, three different aggregation schemes are designed to integrate OWA into the TOPSIS analysis procedure. A numerical example is provided to demonstrate the proposed approach and the results are compared for different aggregation settings and confirm the robustness of rankings from different scenarios.     

Optimal location selection for an international distribution center by using a new hybrid method

The selection of a location for an international distribution center (IDC) is a most important decision for international logistics managers owing to the need to consider various criteria that involve a complex decision process in which multiple requirements and uncertain conditions have to be taken into consideration simultaneously. Moreover, the criteria often exist simultaneously as independent and dependent characteristics when the problems of location selection have become very complex. A new hybrid method combining the concepts of fuzzy DEMATEL and a new method of fuzzy multiple criteria decision-making (MCDM) in a fuzzy environment is proposed to solve the problems of IDC location selection. In this paper, the fuzzy DEMATEL is proposed to arrange a suitable structure between criteria, and the analytic hierarchy/network process (AHP/ANP) is used to construct weights of all criteria. The linguistic terms characterized by triangular fuzzy numbers are used to denote the evaluation values of all alternatives versus various criteria. Finally, the aggregation fuzzy assessments of different alternatives are ranked to determine the best selection. Furthermore, this paper uses an empirical case for optimal location selection for an IDC in Pacific Asia to illustrate the proposed method, and the results show that the method is an effective means for tackling fuzzy MCDM problems.     

MULTICRITERIA SORTING METHODOLOGY: APPLICATION TO FINANCIAL DECISION PROBLEMS

Abstract

The primary objective in the sorting approach is to assign a set of alternatives into predefined classes. This type of problem is often encountered in many real world decision problems. During the last two decades several new approaches have been proposed to overcome the shortcomings of traditional statistical and econometric techniques. This paper focuses on the multicriteria decision aid (MCDA) approach; it briefly reviews the main MCDA sorting techniques, and presents the multigroup hierarchical discrimination method. This new MCDA sorting technique is applied to the portfolio selection problem. A comparison with discriminant analysis is also performed. Furthermore, the efficiency of the proposal approach can be easily improved for solving large-scale problems in a multiprocessing environment.     

An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management

This paper reports on an integration of multi-criteria decision analysis (MCDA) and inexact mixed integer linear programming (IMILP) methods to support selection of an optimal landfill site and a waste-flow-allocation pattern such that the total system cost can be minimized. Selection of a landfill site involves both qualitative and quantitative criteria and heuristics. In order to select the best landfill location, it is often necessary to compromise among possibly conflicting tangible and intangible factors. Different multi-objective programming models have been proposed to solve the problem. A weakness with the different multi-objective programming models used to solve the problem is that they are basically mathematical and ignore qualitative and often subjective considerations such as the risk of groundwater pollution as well as other environmental and socio-economic factors which are important in landfill selection. The selection problem also involves a change in allocation pattern of waste-flows required by construction of a new landfill. A waste flow refers to the routine of transferring waste from one location in a city to another. In selection of landfill locations, decision makers need to consider both the potential sites that should be used as well as the allocation pattern of the waste-flow at different periods of time. This paper reports on our findings in applying an integrated IMILP/MCDA approach for solving the solid waste management problem in a prairie city. The five MCDA methods of simple weighted addition, weighted product, co-operative game theory, TOPSIS, and complementary ELECTRE are adopted to evaluate the landfill site alternatives considered in the solid waste management problem, and results from the evaluation process are presented.     

Robust ordinal regression in preference learning and ranking

Multiple Criteria Decision Aiding (MCDA) offers a diversity of approaches designed for providing the decision maker (DM) with a recommendation concerning a set of alternatives (items, actions) evaluated from multiple points of view, called criteria. This paper aims at drawing attention of the Machine Learning (ML) community upon recent advances in a representative MCDA methodology, called Robust Ordinal Regression (ROR). ROR learns by examples in order to rank a set of alternatives, thus considering a similar problem as Preference Learning (ML-PL) does. However, ROR implements the interactive preference construction paradigm, which should be perceived as a mutual learning of the model and the DM. The paper clarifies the specific interpretation of the concept of preference learning adopted in ROR and MCDA, comparing it to the usual concept of preference learning considered within ML. This comparison concerns a structure of the considered problem, types of admitted preference information, a character of the employed preference models, ways of exploiting them, and techniques to arrive at a final ranking.     

Data transformation in the evidential reasoning-based decision making process

This paper describes the application of an evidential reasoning (ER)‐based decision making process to multiple‐criteria decision making (MCDM) problems having both quantitative and qualitative criteria. The ER approach is based on the decision theory and the theory of evidence and it uses the concept of ‘degree of belief’ to assess decision alternatives on each attribute. When faced with MCDM problems, evaluation and selection or ranking of alternatives appear to be both challenging and vital to arrive at a rational and robust decision. In the presence of both qualitative and quantitative evaluations in an MCDM problem, it is necessary, when using the ER‐based decision making process, to transform or convert quantitative data into a belief structure using a number of grades so that the converted belief structure and the original quantitative data are equivalent in values or utilities. This paper suggests three scenarios for data transformation and examines how the ranking of decision alternatives is changed when different scenarios of data transformation are used. Ranking of UK universities using the ER approach is illustrated as an example.     

An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making

This paper investigates the dynamic intuitionistic fuzzy multi-attribute group decision making (DIF-MAGDM) problems, in which all the attribute values provided by multiple decision makers (DMs) at different periods take the form of intuitionistic fuzzy numbers (IFNs), and develops an interactive method to solve the DIF-MAGDM problems. The developed method first aggregates the individual intuitionistic fuzzy decision matrices at different periods into an individual collective intuitionistic fuzzy decision matrix for each decision maker by using the dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator, and then employs intuitionistic fuzzy TOPSIS method to calculate the individual relative closeness coefficient of each alternative for each decision maker and obtain the individual ranking of alternatives. After doing so, the method utilizes the hybrid weighted averaging (HWA) operator to aggregate all the individual relative closeness coefficients into the collective relative closeness coefficient of each alternative and obtain the aggregate ranking of alternatives, by which the optimal alternative can be selected. In addition, the spearman correlation coefficient for both the aggregate ranking and individual ranking of alternatives is calculated to measure the consensus level of the group preferences. Finally, a numerical example is used to illustrate the developed method.     

Fuzzy measure identification for criteria coalitions using linguistic information

Modeling interactions between criteria in multiple criteria decision analysis (MCDA) is a complex task. Such complexity arises when there are visible redundancies and synergies among criteria, which traditional MCDA methods cannot deal with. The Choquet integral is a model that has been conceived to deal with these issues, but an appropriate fuzzy measure must be defined. This article shows how to compute a fuzzy measure for criteria coalitions using linguistic information efficiently. Due to the complexity to identify an adequate fuzzy measure when the criteria set cardinality increases, the proposed model reduces the effort to determine the measure of each criteria combination by focusing on relevant interactions. Then, this fuzzy measure is used on Choquet integral to establish the best alternative in a decision-making problem. Finally, a comparison between the arithmetic mean, the OWA operator and the proposed method is presented.     

A consensus based group decision making methodology for strategic selection problems of supply chain coordination

In a supply chain (SC), the partners often make collective decisions to solve a number of problems which are characterized by various quantitative and qualitative criteria. This article presents a fuzzy TOPSIS and soft consensus based group decision making methodology to solve the multi-criteria decision making (MCDM) problems in supply chain coordination, i.e., selection problems. This methodology is proposed to improve the coordination in decentralized supply chains, i.e., supply chains that comprise several independent, legally separated entities with their own decision authorities. In order to address the imprecision of supply chain partners in formulating the preference value of various criteria, a fuzzy TOPSIS based methodology is proposed. Moreover, a soft consensus based group decision making approach is used for consensus forming among the supply chain partners, regarding the preference values of various criteria for different alternatives. Correlation coefficient and standard deviation (CCSD) based objective weight determination method is also used for enumeration of the weights of the criterion for fuzzy TOPSIS. To demonstrate the applicability of proposed methodology, an illustrative example has been presented.     

Group decision-making based on pythagorean fuzzy TOPSIS method

Group decision-making is a process wherein multiple individuals interact simultaneously, analyze problems, evaluate the possible available alternatives, characterized by multiple conflicting criteria, and choose suitable alternative solution to the problem. Technique for establishing order preference by similarity to the ideal solution (TOPSIS) is a well-known method for multiple-criteria decision-making. The purpose of this study is to extend the TOPSIS method to solve multicriteria group decision-making problems equipped with Pythagorean fuzzy data, in which the assessment information on feasible alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy numbers. A revised closeness index is utilized to obtain the ranking of alternatives and to identify the optimal alternative. The developed Pythagorean fuzzy TOPSIS (PF-TOPSIS) is illustrated by a flow chart. At length, practical examples interpreting the applicability of our proposed PF-TOPSIS are solved.     

A Bayesian network for recurrent multi-criteria and multi-attribute decision problems: Choosing a manual wheelchair

This paper discusses recurrent multi-criteria, multi-attribute decision problems. Because of the possibility of decision-maker ignorance or low decision-maker involvement the decision problem structuring is done once for all by a group of experts and does not involve the implication of the decision makers. We propose an original model based on Bayesian networks, which provides a decision process that helps the decision-maker to select an appropriate alternative among a set of alternatives, taking into account multiple criteria that are often conflicting. Our model makes it possible to represent in the same model the decision case (i.e., the decision-maker characteristics, contextual characteristics, their needs and preferences), the set of alternatives with the different attributes, and the choice criteria. The model allows us to compute the value of three essential elements: the importance of each criterion, which is based on the decision-case characteristics; each criterion’s evaluation index in terms of the alternative; and each criterion’s satisfaction index. The recurrent problem of choosing a manual wheelchair (MWC) illustrates the construction and use of our model.     

A case-based distance model for multiple criteria ABC analysis

In ABC analysis, a well-known inventory planning and control technique, stock-keeping units (SKUs) are sorted into three categories. Traditionally, the sorting is based solely on annual dollar usage. The aim of this paper is to introduce a case-based multiple-criteria ABC analysis that improves on this approach by accounting for additional criteria, such as lead time and criticality of SKUs, thereby providing more managerial flexibility. Using decisions from cases as input, preferences over alternatives are represented intuitively using weighted Euclidean distances which can be easily understood by a decision maker. Then a quadratic optimization program finds optimal classification thresholds. This system of multiple criteria decision aid is demonstrated using an illustrative case study.