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.     

Preference‐based Learning of Ideal Solutions in TOPSIS‐like Decision Models

Combining established modelling techniques from multiple‐criteria decision aiding with recent algorithmic advances in the emerging field of preference learning, we propose a new method that can be seen as an adaptive version of TOPSIS, the technique for order preference by similarity to ideal solution decision model (or at least a simplified variant of this model). On the basis of exemplary preference information in the form of pairwise comparisons between alternatives, our method seeks to induce an ‘ideal solution’ that, in conjunction with a weight factor for each criterion, represents the preferences of the decision maker. To this end, we resort to probabilistic models of discrete choice and make use of maximum likelihood inference. First experimental results on suitable preference data suggest that our approach is not only intuitively appealing and interesting from an interpretation point of view but also competitive to state‐of‐the‐art preference learning methods in terms of prediction accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

The analytic decision‐making preference model to evaluate the disaster readiness in emergency departments: The A.D.T. model

In recent years, a series of important emergencies have been taken place worldwide in industrial plants. After the occurrence of a disaster, it is essential to activate the correct emergency procedures. Particularly, it is important to direct people injured in hospitals which are able to handle emergencies. Thus, nowadays, the emergency services require a management process starting from the disaster moment to the involvement of all actors participating in the process to provide integral, safe, and quality attention. The aim of this study is to help hospitals become better prepared for major disasters and public health emergencies and to evaluate the readiness of emergency departments for a disaster situation. A hybrid model called the “analytic decision‐making preference model” based on analytic hierarchy process, decision‐making trial and evaluation laboratory, and technique for order of preference by similarity to ideal solution methods is proposed. Analytic hierarchy process is used to determine the criteria and subcriteria weights. Then, decision‐making trial and evaluation laboratory is used to evaluate interdependence between criteria and subcriteria. After this, technique for order of preference by similarity to ideal solution is applied to rank the emergency departments from highest to lowest according to their closeness coefficient. A real‐life application in Colombia is presented.     

The Characteristic Objects Method: A New Distance‐based Approach to Multicriteria Decision‐making Problems

Multicriteria decision‐making (MCDM) methods are concerned with the ranking of alternatives based on expert judgements made using a number of criteria. In the MCDM field, the distance‐based approach is one popular method for obtaining a final ranking. The technique for order preference by similarity to the ideal solution (TOPSIS) is a commonly used example of this kind of MCDM method. The TOPSIS ranks the alternatives with respect to their geometric distance from the positive and negative ideal solutions. Unfortunately, two reference points are often insufficient, especially for nonlinear problems. As a consequence of this situation, the final result ranking is prone to errors, including the rank reversals phenomenon. This study proposes a new distance‐based MCDM method: the characteristic objects method. In this approach, the preferences of each alternative are obtained on the basis of the distance from the nearest characteristic objects and their values. For this purpose, we have determined the domain and Fuzzy number set for all the considered criteria. The characteristic objects are obtained as the combination of the crisp values of all the Fuzzy numbers. The preference values of all the characteristic object are determined on the basis of the tournament method and the principle of indifference. Finally, the Fuzzy model is constructed and is used to calculate preference values of the alternatives, making it a multicriteria model that is free of rank reversal. The numerical example is used to illustrate the efficiency of the proposed method with respect to results from the TOPSIS method. The characteristic objects method results are more realistic than the TOPSIS results. Copyright © 2014 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.     

Multiple-attribute decision making based on single-valued neutrosophic Schweizer-Sklar prioritized aggregation operator

Single-valued neutrosophic (SVN) sets can successfully describe the uncertainty problems, and Schweizer-Sklar (SS) t-norm (TN) and t-conorm (TCN) can build the information aggregation process more flexible by a parameter. To fully consider the advantages of SVNS and SS operations, in this article, we extend the SS TN and TCN to single-valued neutrosophic numbers (SVNN) and propose the SS operational laws for SVNNs. Then, we merge the prioritized aggregation (PRA) operator with SS operations, and develop the single-valued neutrosophic Schweizer-Sklar prioritized weighted averaging (SVNSSPRWA) operator, single-valued neutrosophic Schweizer-Sklar prioritized ordered weighted averaging (SVNSSPROWA) operator, single-valued neutrosophic Schweizer-Sklar prioritized weighted geometric (SVNSSPRWG) operator, and single-valued neutrosophic Schweizer-Sklar prioritized ordered weighted geometric (SVNSSPROWG) operator. Moreover, we study some useful characteristics of these proposed aggregation operators (AOs) and propose two decision making models to deal with multiple-attribute decision making (MADM) problems under SVN information based on the SVNSSPRWA and SVNSSPRWG operators. Lastly, an illustrative example about talent introduction is given to testify the effectiveness of the developed methods.     

Attribute Partitioning in Multiple Attribute Decision Making Problems for a Decision with a Purpose – a Fuzzy Approach

This work introduces a methodology to find solutions corresponding to different purposes in a multiple attribute decision‐making problem under fuzzy environment. The discernment of purpose‐based solutions becomes important when the problem is defined vaguely and solution is targeted to heterogeneous population. Depending on the purpose, for which the solution is sought, the attributes are identified and weighted in an appropriate proportion. The level of similarity between a pair of attributes plays an important role to determine the aggregated value of attributes specific to a purpose. Our work determines the similarity levels between a pair of attributes by calculating their maximum attainability in presence of each other. The achievement of an attribute in presence of another is represented as a fuzzy set in the unit interval. The crisp equivalents of the fuzzy sets in the unit interval are used to define their simultaneous satisfaction denoted as 1‐step relation. The 1‐step relation is extended to (m‐1)‐step relation to calculate the degree of attainability of the same pair of attributes in the presence of m (all) attributes. The different levels of (m‐1)‐step relations generate several partitions of the attributes corresponding to multiple purposes in the multiple attribute decision‐making problems. The degree of fulfilment of the purposes in the alternatives are numerically derived by first taking weighted average of attributes within the equivalence classes of a partition and then aggregating the values corresponding to equivalence classes through ordered weighted averaging. The methodology is illustrated with a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.     

A multiple‐method analysis of appraisal–emotion relationships: The case of the prosocial intergroup emotions

Despite its status as a prominent set of theories for explaining the elicitation and differentiation of emotions, much appraisal theory and research offer little indication of the nature of the relationship expected between appraisals and emotions. Here, we present a three‐study, multiple‐method analysis in which we examine numerous ways of testing appraisal–emotion relationships using the “prosocial” intergroup emotions—sympathy, anger, and guilt—as an example. Results show that the set of appraisal dimensions that appears strongly characteristic of an emotion varies depending on the kind of appraisal—emotion relationship hypothesised and the experimental methodology/statistical analysis used. These findings demonstrate the utility of explicit theorising about the nature of the relationship between emotions and appraisals, and show how the hypothesised appraisal–emotion relationship and choice of methodology can affect the structure of appraisal theories. We recommend an analysis across multiple methods to provide a more complete picture of a given set of appraisal–emotion relationships.     

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.     

An Examination of the Personality Constructs Underlying Dimensions of Creative Problem‐Solving Style

This study investigated the personality facets that underpin the construct of problem‐solving style, particularly when approaching more creative kinds of problem‐solving. Cattell's Sixteen Personality Factors Questionnaire and VIEW—An Assessment of Problem Solving Style were administered to 165 students from the Norwegian Business School. We explored relationships through correlational and regression analysis. Personality profiles were derived for each of VIEW's three dimensions and were in generally expected directions. Those with an Explorer preference were more imaginative and idea oriented, open to change, unconventional, freethinking, and flexible than Developers. Those with a Developer preference were more practical and solution oriented, more traditional, rule conscious, conservative, and respecting of traditional ideas. Those with an External preference were more group oriented, affiliative, socially bold, warm, and attentive to others than those with an Internal preference. Those with a more Task‐oriented preference were more impersonal, detached, utilitarian, and tough minded than those with Person‐oriented preference. We outlined implications and suggestions for further research.     

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.     

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.     

Rough approximation of pairwise comparisons described by multi‐attribute stochastic dominance

Given a finite set A of actions evaluated by a set of attributes, preferential information is considered in the form of a pairwise comparison table including pairs of actions from subset B⊂A described by stochastic dominance relations on particular attributes and a total order on the decision attribute. Using a rough sets approach for the analysis of the subset of preference relations, a set of decision rules is obtained, and these are applied to a set A\B of potential actions. The rough sets approach of looking for the reduction of the set of attributes gives us the possibility of operating on a multi‐attribute stochastic dominance for a reduced number of attributes. Copyright © 1999 John Wiley & Sons, Ltd.     

Two‐ to three‐month‐old infants prefer moving face patterns to moving top‐heavy patterns

Newborn infants prefer face‐like patterns over non‐face‐like patterns. This preference is explained by newborns' preference for a “top‐heavy” configuration, that is, for geometric patterns that have more elements in the upper part than in the lower part of the configuration (Simion, Valenza, Macchi Cassia, Turati, & Umiltà, 2002). However, for 3‐month‐old infants, face preference cannot be explained only by a preference for “top‐heaviness” because they prefer veridical face images over top‐heavy images. The present study used geometric patterns to investigate whether 2‐ to 3‐month‐old infants' preference for face patterns exceeds their preference for top‐heavy configurations. In Experiment 1, we revealed that the infants preferred the face pattern to the top‐heavy pattern only when the internal elements of the patterns were presented with face‐like movements. This facilitative effect of internal movement was observed again in Experiment 2, in which the patterns were presented with non‐face‐like movements. These results suggest that 2‐ to 3‐month‐olds' preference for geometric face patterns is greater than their preference for top‐heavy patterns only when aided by the movement of internal elements.     

An enhanced branch‐and‐bound algorithm for a partitioning problem

This paper focuses on the problem of developing a partition of n objects based on the information in a symmetric, non‐negative dissimilarity matrix. The goal is to partition the objects into a set of non‐overlapping subsets with the objective of minimizing the sum of the within‐subset dissimilarities. Optimal solutions to this problem can be obtained using dynamic programming, branch‐and‐bound and other mathematical programming methods. An improved branch‐and‐bound algorithm is shown to be particularly efficient. The improvements include better upper bounds that are obtained via a fast exchange algorithm and, more importantly, sharper lower bounds obtained through sequential solution of submatrices. A modified version of the branch‐and‐bound algorithm for minimizing the diameter of a partition is also presented. Computational results for both synthetic and empirical dissimilarity matrices reveal the effectiveness of the branch‐and‐bound methodology.     

Multivariate thurstonian models

The recent development of probabilistic Thurstonian choice models for analyzing preference data has been motivated by the need to describe both inter- and intra-individual difference, the multidimensional nature of choice objects, and the effects of similarity and comparability among choice objects. A common feature of these models is that they focus on asingle preference judgment. It is customary, however, to ask subjects not only for an overall preference judgment but also for additional paired comparison responses regarding specific attributes. This paper proposes a generalization of Thurstonian probabilistic choice models for analyzing both multiple preference responses and their relationships. The approach is illustrated by modeling data from two multivariate preference experiments.I am grateful to James, Austin, Ingo Böckenholt, and anonymous referees for helpful comments on this research. This paper is based on research presented at the Meeting of the Society for the Multivariate Analysis in the Behavioral Sciences, Groningen, The Netherlands, December 1988.     

Perceiving regulation from intimate partners: Reflected appraisal and self‐regulation processes in close relationships

Cross‐sectional (N = 202) and longitudinal analyses over a 6‐month period (N = 155) assessed the consequences of perceiving regulation attempts from romantic partners. Greater perceived regulation from the partner was associated with more negative inferences regarding how closely individuals matched their partner's ideal standards in the targeted domain (inferred ideal consistency). Lower inferred ideal consistency, in turn, was associated with poorer relationship evaluations and predicted more negative perceptions of targeted self‐attributes. Individuals also directly responded to their partner's regulation efforts with attempts to change targeted features. Finally, perceiving more negative regulation strategies produced lower inferred ideal consistency, relationship evaluations, and self‐regulation efforts, whereas perceiving more positive strategies predicted greater inferred ideal consistency across time. The operation of reflected appraisal and self‐regulation processes within romantic relationships is discussed.     

A comparison of preference‐assessment methods

In Study 1, we evaluated preference stability across 4 preference‐assessment methods for 6 individuals, 5 of whom had autism spectrum disorder and 1 of whom had traumatic brain injury. We also measured participants’ problem behavior as a corollary measure during all assessment methods. The highest mean correlation coefficients and Kendall rank coefficients of concordance across administrations were observed for the paired‐stimulus and multiple‐stimulus‐without‐replacement methods. Lower correspondence across administrations was observed for the free‐operant and response‐restriction methods. Although differentially higher levels of problem behavior did not occur with a single method, lower levels were consistently observed with the free‐operant method. During Study 2, we evaluated the implications of lower coefficients on reinforcer efficacy by comparing an initially identified and an immediately identified high‐preference stimulus in a reinforcer assessment. Initially identified and immediately identified high‐preference stimuli were equally effective reinforcers, suggesting that fluctuations in preference do not necessarily affect reinforcer efficacy in practice.     

Trade‐off ranking method for multi‐criteria decision analysis

Multi‐criteria decision analysis presumes trade‐off between different criteria. As a result, the optimal solution is not unique and can be represented by the Pareto frontier in the objective space. Each Pareto solution is a compromise between different objectives. Despite a limited number of Pareto optimal solutions, the decision‐maker eventually has to choose only one option. Such a choice has to be made with the use of additional preferences not included in the original formulation of the optimization problem. The paper represents a new approach to an automatic ranking that can help the decision‐maker. In contrast to the other methodologies, the proposed method is based on the minimization of trade‐off between different Pareto solutions. To be realized, the approach presumes the existence of a well‐distributed Pareto set representing the entire Pareto frontier. In the paper, such a set is generated with the use of the directed search domain algorithm. The method is applied to a number of test cases and compared against two existing alternative approaches.     

Cause or effect: What matters? How 12‐month‐old infants learn to categorize artifacts

This paper investigates the role of cause and effect relations for infants' learning about artifacts. Two experiments tested whether 12‐month‐olds categorized a given set of unfamiliar artifacts according to overall similarity and/or according to part similarity, depending on what kind of video demonstration was presented before the start of the categorization task. In both experiments, the actions performed with objects were accompanied by interesting effects but the causal relation between object‐structure and effects was teased apart. In one video demonstration (Expt 1), the experimenter used the object part to produce some kind of effect in a causally plausible way. In another video demonstration (Expt 2), the experimenter performed similar actions with the same objects as in Expt 1, followed by the same effects as before. Importantly, however, no plausible cause–effect relation was provided this time. Only infants participating in Expt 1 categorized the set of unfamiliar objects according to part similarity. This finding suggests that 12‐month‐olds attend to the causal relation between specific object parts and their functional use when categorizing artifacts, rather than merely associating form‐characteristics with an interesting effect.