A Fuzzy Topsis Method for Prioritized Aggregation in Multi‐Criteria Decision Making Problems

Aggregation in a decision making environment requires the fusion of opinions of a group of decision makers. The group of decision makers are required to analyse a set of interrelated criteria that are usually measured on a linguistic scale. This process requires, in many instances, to capture experts experience, intuition and thinking that are traditionally expressed in a linguistic fashion rather than a numerical fashion. Furthermore, the necessity of considering the relationship between the criteria to the overall decision must be considered by the group of decision makers. This paper extends the application of fuzzy numbers, fuzzy relative importance scores (FRIS), fuzzy relative weights (FRW) and the fuzzy technique of order preference by similarity to ideal solution (TOPSIS) in prioritized aggregation. This extension provides a mean to systematically aggregate a group of decision makers' views for a set of interrelated criteria that are measured on a linguistic scale. First, an overview of the application of fuzzy numbers and the characteristics of aggregating fuzzy numbers in multi‐criteria decision making problems are presented. Then, the application of TOPSIS in fuzzy environments is presented. Next, past research is highlighted to present prioritized aggregation and the different aggregation operators' classes. Subsequently, a new prioritized aggregation method is presented. This method utilizes fuzzy TOPSIS with prioritized aggregation in fuzzy environments. Finally, the fuzzy prioritized aggregation method presented in this paper is applied on an actual case study. According to the results, the method presented in this paper provides a systematic approach to capture the uncertainty and imprecision associated with quantifying linguistic measurements in multi‐criteria decision making problems. Furthermore, it considers the relationship between the set of linguistically measured criteria undergoing prioritized aggregation in a fuzzy environment. Lastly, findings, conclusions and future work are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Fuzzy MCDM based on the concept of α‐cut

In a fuzzy multiple criteria decision‐making (MCDM) problem, with a hierarchical structure of more than two levels and involving multiple decision‐makers (DMs), to find the exact membership functions of the final aggregation ratings of all feasible alternatives is almost impossible. Thus, ranking methods based on exact membership functions cannot be utilized to rank the feasible alternatives and complete the optimal selection. To resolve the above‐mentioned complexity and to incorporate assessments of all DMs' viewpoints, in this paper a fuzzy MCDM method with multiple DMs, based on the concepts of fuzzy set theory and α‐cut, is developed. This method incorporates a number of perspectives on how to approach the fuzzy MCDM problem with multiple DMs, as follows: (1) combining quantitative and qualitative criteria as well as negative and positive ones; (2) using the generalized means to develop the aggregation method of multiple DMs' opinions; (3) incorporating the risk attitude index β to convey the total risk attitude of all DMs by using the estimation data obtained at the data input stage; (4) employing the algebraic operations of fuzzy numbers based on the concept of α‐cut to calculate the final aggregation ratings and develop a matching ranking method for proposed fuzzy MCDM method with multiple DMs. Furthermore, we use this method to survey the site selection for free port zone (FPZ) in Taiwan as an empirical study to demonstrate the proposed fuzzy MCDM algorithm. The result of this empirical investigation shows that the port of Kaohsiung, the largest international port of Taiwan as well as the sixth container port in the world in 2004, is optimal for the Taiwan government in enacting the plan of FPZ. Copyright © 2005 John Wiley & Sons, Ltd.     

An Approach to Multi‐Criteria Decision Problems Under Severe Uncertainty

Solving complex decision problems is a demanding task; it requires determining and evaluating the consequences of decision alternatives. To this end, uncertain factors that can only partly be influenced by the decision makers, and their interdependencies need to be considered. Scenarios focus on this part of the decision problem; they enable a systematic exploration of a multitude of possible future developments that are relevant for the decision including external events and decisions made. Scenarios are particularly useful when the problem is pervaded by severe uncertainties that cannot be quantified. For the evaluation of alternatives, multiple objectives and the potentially diverging preferences of the involved actors need to be respected. Multi‐criteria decision analysis aims at structuring the problem, evaluating the alternatives and supporting decision makers pursuing multiple goals. We propose an approach integrating scenarios and multi‐criteria decision analysis that focuses on the robustness of alternatives in complex, dynamic, uncertain and time‐bound situations. In this integrated framework, the scenarios provide the basis for evaluating a set of alternatives. Ideally, the set of scenarios considered captures all possible future developments. To appropriately explore this set, formal or analytical approaches to scenario construction generate a large number of scenarios. This challenges the decision makers' information‐processing capacity. To support them in managing the richness of information, a two‐fold approach that uses selection and aggregation is presented. By using a selection method, the scenarios that are deemed most relevant are identified, and their evaluations are presented in detail to decision makers. This approach is complemented by an aggregation of scenario evaluations on the basis of the decision makers' preferences. We present two approaches to facilitate the preference elicitation process. Copyright © 2013 John Wiley & Sons, Ltd.     

An Optimized Design of Choice Experiments: A New Approach for Studying Decision Behavior in Choice Task Experiments

In this paper, we present a new approach for the optimal experimental design problem of generating diagnostic choice tasks, where the respondent's decision strategy can be unambiguously deduced from the observed choice. In this new approach, we applied a genetic algorithm that creates a one‐to‐one correspondence between a set of predefined decision strategies and the alternatives of the choice task; it also manipulates the characteristics of the choice tasks. In addition, this new approach takes into account the measurement errors that can occur when the preferences of the decision makers are being measured. The proposed genetic algorithm is capable of generating diagnostic choice tasks even when the search space of possible choice tasks is very large. As proof‐of‐concept, we used this novel approach to generate respondent‐specific choice tasks with either low or high context‐based complexity that we operationalize by the similarity of alternatives and the conflict between alternatives. We find in an experiment that an increase in the similarity of the alternatives and an increase in the number of conflicts within the choice task lead to an increased use of non‐compensatory strategies and a decreased use of compensatory decision strategies. In contrast, the size of the choice tasks, measured by the number of attributes and alternatives, only weakly influences the strategy selection. Copyright © 2014 John Wiley & Sons, Ltd.     

A Survey on Development and Applications of the Multi‐criteria Decision Making Method MULTIMOORA

This paper focuses on the MULTIMOORA method. Specifically, it discusses its development as well as extensions alongside with an overview of their applications. Indeed, the MULTIMOORA is a relatively new multi‐criteria decision making method consisting of the three parts. Therefore, it is specific with peculiarities of both complete and partial aggregation techniques. The MULTIMOORA method consists of the three parts, namely the Ratio System, the Reference Point, and the Full Multiplicative Form. The paper discussed the extensions of MULTIMOORA into the fuzzy environment and group decision making. The carried out survey identified the two major areas of application of MOORA and MULTIMOORA, namely engineering decision support for technological development and economic researches. The economic researches can further be classified into those related to micro‐level or macro‐level analyses. Copyright © 2013 John Wiley & Sons, Ltd.     

Personality Testing in Personnel Selection: Adverse impact and differential hiring rates

Personality tests are often used in selection and have demonstrated predictive validity across a variety of occupational groups and performance criteria. Although different selection decision methods can be used to make selection decisions (e.g., compensatory top down, compensatory with sliding bands, noncompensatory) from personality test results, there is a paucity of research addressing the influence of these different selection decision methods on issues such as, adverse impact and differential hiring rates. This gap in the literature is redressed in the current study. Results from 398 bus operator candidates indicated that there may be adverse impact and differential hiring rate issues depending on the selection decision method used and the designated group being assessed. Implications and future research directions are discussed.     

A Multicriteria Decision‐Making Application to the Conceptual Design of Mechanical Components

Early design is crucial for the success of the final product. In the conceptual design phase, several constraints, criteria, objectives and disciplines have to be considered. To this aim, multidisciplinary optimization has proven effective for the solution of engineering design problems, even in the industrial every‐day practice, to improve and simplify the work of designers in a successful quest of the best compromise solution. In this paper, a multicriteria decision‐making (MCDM)‐based design platform for early optimal design of industrial components is proposed. In a group decision‐making context, the selection of the most suitable component among several possible layouts is performed by means of a group Fuzzy Technique for Order of Preference by Similarity to Ideal Solution approach. Hence, a multi‐objective optimization is performed on the selected component by applying a multi‐objective particle swarm optimization for finding optimal component dimensions. An industrial case study is presented for showing the efficiency of the multicriteria decision‐making‐based design platform, regarding an innovative and low‐cost solution to increase the duration of heel tips in women's shoes. Copyright © 2016 John Wiley & Sons, Ltd.     

Generating consensus priority interval vectors for group decision‐making in the AHP

Many practical and important decision‐making problems are complicated by at least two factors: (1) the qualitative/subjective nature of some criteria often results in uncertainty in the individual ratings; and (2) group decision‐making is involved and some means of aggregating individual ratings is required. Traditionally, both individual and group priorities have been represented as point estimates, but this approach presents severe limitations for accommodating imprecision in the decision‐making process. This paper examines the group decision‐making problem in the context where priorities are represented as numeric intervals. A set of techniques that could be used at some of the phases of an analytic hierarchy process (AHP)‐based group decision‐making process, which has the objective of generating a ‘consensus’ priority that represents the group's opinion with regards to the relative importance of a set of N objects (e.g. criteria, alternatives), is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Strategic hybrid approach for selecting suppliers of high‐density polyethylene

Supplier selection is an important process for companies in the plastic sector due to its influence on firm performance and competitiveness. For a proper selection, a number of criteria from different aspects need to be considered by decision makers. Yet, as in different fields, because there are numerous criteria and alternatives to be considered in the plastic industry, choosing an appropriate multicriteria decision‐making approach has become a critical step for selecting suppliers. Therefore, the aim of this research is to define the most suitable supplier of high‐density polyethylene through the integration of powerful multicriteria decision‐making methods. For this purpose, the fuzzy analytic hierarchy process (FAHP) is initially applied to define initial weights of factors and subfactors under uncertainty, followed by the use of decision‐making trial and evaluation laboratory (DEMATEL) to evaluate interrelations between the elements of the hierarchy. Then, after combining FAHP and DEMATEL to calculate the final contributions of both factors and subfactors on the basis of interdependence, the technique for order of preference by similarity to ideal solution is used to assess the supplier alternatives. In addition, this paper also explores the differences between the judgments of decision makers for both AHP and DEMATEL methods. To do these, a case study is presented to demonstrate the validity of the proposed approach.     

Improving an optimization‐based framework for sensitivity analysis in multi‐criteria decision‐making

The framework for sensitivity analysis in discrete multi‐criteria decision analysis developed by Rios Insua and French allows simultaneous variation of all parameters and applies to many paradigms for decision analysis. However, its computational load may inhibit use, particularly in the context of a decision conference where results are required in near real time. In order to improve on the current algorithm and its implementation, we investigate, on the one hand, an opportunistic approach aimed at reducing the number of optimization problems solved in the original framework and, on the other, an alternative framework based on distance analysis. Computational results on linear and bilinear models are reported. Copyright © 2001 John Wiley & Sons, Ltd.     

Identifying and prioritizing factors influencing the selection of the top suppliers of e‐procurement using FDEMATEL and FANP

The aim of this study is to identify, rank, and determine the importance of factors influencing the selection of the top supplier of electronic procurement in organizations using a hybrid approach. This is a case study of Irancell Telecommunication Service Company in which fuzzy decision‐making trial and evaluation (FDEMATEL) and fuzzy analytical network process (FANP) were used. FDEMATEL was employed to determine the interaction and interrelationships among the identified criteria and subcriteria, while utilizing FANP to calculate the weights of the criteria and their relevant subcriteria to determine their priorities. Therefore, the research literature was first reviewed to identify the factors influencing the selection of suppliers. For this purpose, the experts on communication networks were interviewed to select 16 final factors as the most important subcriteria that were then categorized as 5 groups (technology, environmental, services, organizational, and commercial) on which the study was based. After extracting the criteria for ranking the suppliers, codifying evaluation questionnaire, and converting the opinions in the Likert scale, 16 criteria were finally chosen with scores above the mean. FDEMATEL was used to determine the weights of subcriteria. In the final step, FANP was employed for prioritization. Results indicate that the organizational criterion is the most influential factor; however, the criterion services is the most permeable factor. The greatest weights were obtained from production capacity and provisions and geographical situation which were weighted 0.097 and 0.039, respectively. They are also regarded as the most and least important criteria for the selection of the top supplier of e‐procurement by the experts.     

A parameter analysis method for the weight‐set to satisfy preference orders of alternatives in additive multi‐criteria value models

In the context of the additive multi‐criteria value model, this paper investigates how the set of criteria weights (weight‐set hereafter) can be determined according to the preference orders of alternatives given by the decision maker. A construction method is proposed for the weight‐set for different intervals of β, where β is a differential amount of value between the preference information on two alternatives. The results of this paper are important for sensitivity analysis in multi‐criteria decision making (MCDM) problems and multi‐criteria group decision analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Unstable Interaction in Multiple Criteria Decision Problems

In this paper, we present a decision‐aid method with interacting criteria. The fuzzy measures used to aggregate the criteria depend on the considered alternatives. Pairwise comparisons on the importance of criteria and some levels of veto (or favor) degrees, specified by the decision maker, are taken into consideration. For each alternative, we search for the fuzzy measure that makes it the best. The orness degrees of the resulting fuzzy measures are compared and the alternative associated with the minimum orness degree is selected. Copyright © 2014 John Wiley & Sons, Ltd.     

Measuring logistics performance of OECD countries via fuzzy linear regression

In logistics, performance measurement has been considered as a key competency to acquire world class performance. In light of this, we presented a robust methodology to establish an analysis framework for measuring logistics performance. The proposed hybrid methodology is a combination of criteria importance through intercritera correlation (CRITIC), simple additive weighting (SAW), and Peters' fuzzy regression methods. To the best of our knowledge, country‐based logistics performance is seldom studied in the literature. Therefore, we measured the logistics performance of Organization for Economic Cooperation and Development (OECD) countries using the devised model based on the data of Logistics Performance Index 2014 provided by the World Bank. The introduced methodology, which is suitable to model imprecise relationships among system parameters, appears to be a practical alternative approach for the assessment of logistics performance. It should be noted that the evaluation framework presented in this paper is not confined to performance measurement case and can also be exploited in addressing other multiple criteria decision‐making problems incorporating uncertainty.     

Measurement scales and scale independence in the analytic hierarchy process

One approach to evaluate the relative performance of decision alternatives with respect to multiple criteria is provided by the analytic hierarchy process. The method is based on pairwise comparisons between attributes, and several numerical measurement scales for the ratio statements have been proposed. The choice of measurement scale is re‐examined, and new arguments supporting the measurement scale of geometric progression are derived. Separately from the measurement scale considerations, the effects of the scale parameter in geometric measurement scale are also studied. By using a regression model for pairwise comparisons data, it is shown that the statistical inference does not depend on the value of the scale parameter in the case of a single pairwise comparison matrix. It is also shown when the scale independence of statistical inference can be achieved in a decision hierarchy. This requires the use of the geometric‐mean aggregation rule instead of the traditional arithmetic‐mean aggregation. The results of the case study demonstrate that the measurement scale and the aggregation rule have potentially large impacts on decision support. Copyright © 2000 John Wiley & Sons, Ltd.     

Model and interactive algorithm of bi‐level multi‐objective decision‐making with multiple interconnected decision makers

Furthering a prior research on two‐person bi‐level multi‐objective decision‐making problems of the leader‐follower Stackelberg game, we present an extended model of bi‐level multi‐objective decision‐making with multiple interconnected decision makers at the lower level. In the model, the upper level decision maker acts as a leader and the lower level decision makers behave as the followers, and inter‐connections and interactions exist among these followers in decision‐making scenarios. Following the rules of leader‐follower Stackelberg game, we develop an interactive algorithm of the model for solving multi‐objective decision‐making problems and reflecting the interactive natures among the decision makers. Finally, the authors exemplify the model and algorithm, and draw a conclusion on points of contributions and the significance of this study in decision‐making and support. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessing risky public investments with MUSTARD

This paper presents a practical implementation of multicriteria methodologies based on the UTA model by Jacquet‐Lagrèze and Siskos and Quasi‐UTA model by Beuthe and Scannella, which are specified with a non‐linear, but piecewise linear, additive utility function. In contrast with the general UTA model, the Quasi‐UTA specification structures the partial utilities as recursive exponential functions of only one curvature parameter. This allows for a reduction of the quantity of information necessary to build the utility function. The software MUSTARD implements different variants of these models. Firstly, it offers the basic deterministic UTA model of disaggregation, but also its first programmed stochastic version. In both cases, the software proceeds stepwise and interactively helping the decision maker to formulate the problem and state preferences between projects; in the stochastic case, the decision maker is even helped to build the criteria distributions. The Quasi‐UTA specification can be introduced in this disaggregation model. Secondly, the software offers an aggregation model whereby the Quasi‐UTA partial utility functions are built separately through specific questioning processes. The questions relating to deterministic criteria are of the ‘direct rating type’, while those of the stochastic criteria are either of the ‘variable probability’ or the ‘variable outcome’ type. The criteria weights can be assessed by the ‘swing weight’ method or by a UTA‐II side‐program. As an example as well as a test of the Quasi‐UTA aggregation approach, the paper presents its application to a real problem of selecting road investment projects in Belgium. Several experts and civil servants were interviewed, and their individual utility functions derived. The projects are ranked according to their rate of return, which is computed on the basis of the projects certain equivalent money value. Copyright © 2002 John Wiley & Sons, Ltd.     

Prioritizing emergency shelter areas using hybrid multi‐criteria decision approach: A case study

Every year, more than 400 natural disasters affect global population. Adopting a resilient approach strengthens communities to survive and recover well from destabilizing events. Disasters destroy or damage houses and infrastructure, which calls for arrangement of temporary establishments to provide immediate evacuation and shelter to affected population. These sites are vital for an effective relief and must be strategically planned. Communities living in disaster‐prone areas should prepare themselves well in advance for any future catastrophic event. This study adopts a hybrid group decision support approach for emergency shelter site selection problem. Initially, relevant factors for locating potential sites are identified by reviewing extant literature and through consultation from a panel of disaster management experts. Next, fuzzy analytic hierarchy process theory and technique for order preference by similarity to ideal solution have been used to prioritize identified criteria and to evaluate potential locations for displacement sites. A case study of the recent Nepal earthquake has been used to illustrate the effectiveness of the proposed model. The model offers a resilience building approach to prepare communities for any future contingency by proposing and prioritizing a set of planned displacement sites.     

The relationship between indecisiveness and eye movement patterns in a decision making informational search task

Indecisiveness is a trait‐related general tendency to experience decision difficulties across a variety of situations, leading to decision delay, worry, and regret. Indecisiveness is proposed (Rassin, 2007) to be associated with an increase in desire for information acquisition and reliance on compensatory strategies—as evidenced by alternative‐based information search—during decision making. However existing studies provide conflicting findings. We conducted an information board study of indecisiveness, using eye tracking methodology, to test the hypotheses that the relationship between indecisiveness and choice strategy depends on being in the early stage of the decision making process, and that it depends on being in the presence of an opportunity to delay choice. We found strong evidence for the first hypothesis in that indecisive individuals changed shift behavior from the first to the second half of the task, consistent with a move from greater to lesser compensatory processing, while the shift behavior of decisive individuals suggested lesser compensatory processing over the whole task. Indecisiveness was also related to time spent viewing attributes of the selected course, and to time spent looking away from decision information. These findings resolve past discrepancies, suggest an interesting account of how the decision process unfolds for indecisive versus decisive individuals, and contribute to a better understanding of this tendency. Copyright © 2009 John Wiley & Sons, Ltd.