A new method for multiple criteria group decision making with incomplete weight information under linguistic environment

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method.     

A new data envelopment analysis method for priority determination and group decision making in the analytic hierarchy process

The DEAHP method for weight deviation and aggregation in the analytic hierarchy process (AHP) has been found flawed and sometimes produces counterintuitive priority vectors for inconsistent pairwise comparison matrices, which makes its application very restrictive. This paper proposes a new data envelopment analysis (DEA) method for priority determination in the AHP and extends it to the group AHP situation. In this new DEA methodology, two specially constructed DEA models that differ from the DEAHP model are used to derive the best local priorities from a pairwise comparison matrix or a group of pairwise comparison matrices no matter whether they are perfectly consistent or inconsistent. The new DEA method produces true weights for perfectly consistent pairwise comparison matrices and the best local priorities that are logical and consistent with decision makers (DMs)’ subjective judgments for inconsistent pairwise comparison matrices. In hierarchical structures, the new DEA method utilizes the simple additive weighting (SAW) method for aggregation of the best local priorities without the need of normalization. Numerical examples are examined throughout the paper to show the advantages of the new DEA methodology and its potential applications in both the AHP and group decision making.     

Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting

Multiple criteria group decision making (MCGDM) problems have become a very active research field over the last decade. Many practical problems are often characterized by MCGDM. The aim of this paper is to develop a new approach for MCGDM problems with incomplete weight information in linguistic setting based on the projection method. Firstly, to reflect the reality accurately, a method to determine the weights of decision makers in linguistic setting is proposed by calculating the degree of similarity between 2-tuple linguistic decision matrix given by each decision maker and the average 2-tuple linguistic decision matrix. By using the weights of decision makers, all individual 2-tuple linguistic decision matrices are aggregated into a collective one. Then, to determine the weight vector of criteria, we establish a non-linear optimization model based on the basic ideal of the projection method, i.e., the optimal alternative should have the largest projection on the 2-tuple linguistic positive ideal solution (TLPIS). Calculate the 2-tuple linguistic projection of each alternative on the TLPIS and rank all the alternatives according to the 2-tuple linguistic projection value. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the validity is verified by comparing the evaluation results of the proposed method with that of the technique for order preference by similarity to ideal solution (TOPSIS) method.     

Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group

Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388–393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develop a new similarity measure between intuitionistic fuzzy sets. Then we apply the developed similarity measure for consensus analysis in group decision making based on intuitionistic fuzzy preference relations, and finally further extend it to the interval-valued intuitionistic fuzzy set theory.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

Extension of VIKOR method for multi-criteria group decision making problem with linguistic information

A new method is proposed to solve multi-criteria group decision making problems in which both the criteria values and criteria weights take the form of linguistic information based on the traditional idea of VIKOR method. Firstly, the linguistic criteria weights given by all decision makers are transformed into trapezoidal fuzzy numbers, and then aggregated and defuzzified to crisp values. Secondly, the individual linguistic decision matrix given by each decision maker (DM) is transformed into 2-tuple linguistic decision matrix, and then aggregated into collective 2-tuple linguistic decision matrix by 2-tuple linguistic arithmetic mean operation. Thirdly, the 2-tuple linguistic values (_Si,_αi),$(S_i\text{,}{\alpha }_i)\text{,}$(_Ri,_αi)$(R_i\text{,}{\alpha }_i)$ and (_Qi,_αi)$(Q_i\text{,}{\alpha }_i)$ are calculated by defining the 2-tuple linguistic positive ideal solution (TL-PIS) and 2-tuple linguistic negative ideal solution (TL-NIS). Furthermore, the compromise solution can be obtained. Finally, a numerical example is used to illustrate the application of the proposed approach, and the method is verified by comparing the evaluation result with that of 2-tuple linguistic TOPSIS (TL-TOPSIS) method.     

A discrete method based on distance measure in linguistic space and its application for CMADM problem

ABSTRACT

Owing to the complexity of decision environment, not all the attributes in multiple attribute decision making are quantitative. There are also some qualitative attributes, which are related to the integration of multiple attribute decision making (MADM) and linguistic multiple attribute decision making (LMADM). The specific method for composite multiple attribute decision making (CMADM) problems is crucial for decision maker (DM) to make scientific decision. In this paper, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is extended to a Composite Technique for Order Preference by Similarity to an Ideal Solution (CTOPSIS) method to solve the CMADM problems. As the basis of the CTOPSIS method, the distance measure model in linguistic space and in n-dimension linguistic space is generated based on the non-linear mapping. Based on the distance measure in linguistic space, a standard deviation method is taken to get the attribute weight. At the same time, the distance measure models are proposed based on the distance measure in n-dimension linguistic space, which are used to calculate the distance between the alternatives and the positive and negative idea points separately. Furthermore, a CTOPSIS method is generated to solve the CMADM problems. Finally, a numerical example is illustrated to explain the process. And the result shows that the CTOPSIS method is quite practical and more approximate to the real decision making situation.     

A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment

The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method.     

Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making

In this study a generated admissible order between interval-valued intuitionistic uncertain linguistic numbers using two continuous functions is introduced. Then, two interval-valued intuitionistic uncertain linguistic operators called the interval-valued intuitionistic uncertain linguistic Choquet averaging (IVIULCA) operator and the interval-valued intuitionistic uncertain linguistic Choquet geometric mean (IVIULCGM) operator are defined, which consider the interactive characteristics among elements in a set. In order to overall reflect the correlations between them, we further define the generalized Shapley interval-valued intuitionistic uncertain linguistic Choquet averaging (GS-IVIULCA) operator and the generalized Shapley interval-valued intuitionistic uncertain linguistic Choquet geometric mean (GS-IVIULCGM) operator. Moreover, if the information about the weights of experts and attributes is incompletely known, the models for the optimal fuzzy measures on expert set and attribute set are established, respectively. Finally, a method to multi-attribute group decision making under interval-valued intuitionistic uncertain linguistic environment is developed, and an example is provided to show the specific application of the developed procedure.     

A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number

With respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, and the attribute weight is unknown, a new decision making analysis methods are developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced. Then information entropy method is used to determine the attribute weight, and the grey relational projection method combined grey relational analysis method and projection method is proposed, and to rank the alternatives are done by the relative closeness to PIS which combines grey relational projection values from the positive ideal solution and negative ideal solution to each alternative. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts

Group decision making is a type of decision problem in which multiple experts acting collectively, analyze problems, evaluate alternatives, and select a solution from a collection of alternatives. As the natural language is the standard representation of those concepts that humans use for communication, it seems natural that they use words (linguistic terms) instead of numerical values to provide their opinions. However, while linguistic information is readily available, it is not operational and thus it has to be made usable though expressing it in terms of information granules. To do so, Granular Computing, which has emerged as a unified and coherent framework of designing, processing, and interpretation of information granules, can be used. The aim of this paper is to present an information granulation of the linguistic information used in group decision making problems defined in heterogeneous contexts, i.e., where the experts have associated importance degrees reflecting their ability to handle the problem. The granulation of the linguistic terms is formulated as an optimization problem, solved by using the particle swarm optimization, in which a performance index is maximized by a suitable mapping of the linguistic terms on information granules formalized as sets. This performance index is expressed as a weighted aggregation of the individual consistency achieved by each expert.     

A goal programming method for obtaining interval weights from an interval comparison matrix

Crisp comparison matrices lead to crisp weight vectors being generated. Accordingly, an interval comparison matrix should give an interval weight estimate. In this paper, a goal programming (GP) method is proposed to obtain interval weights from an interval comparison matrix, which can be either consistent or inconsistent. The interval weights are assumed to be normalized and can be derived from a GP model at a time. The proposed GP method is also applicable to crisp comparison matrices. Comparisons with an interval regression analysis method are also made. Three numerical examples including a multiple criteria decision-making (MCDM) problem with a hierarchical structure are examined to show the potential applications of the proposed GP method.     

Range-based Multi-Actor Multi-Criteria Analysis: A combined method of Multi-Actor Multi-Criteria Analysis and Monte Carlo simulation to support participatory decision making under uncertainty

Concerns about environmental and social effects have made Multi-Criteria Decision Making (MCDM) increasingly popular. Decision making in complex contexts often – possibly always – requires addressing an aggregation of multiple issues to meet social, economic, legal, technical, and environmental objectives. These values at stake may affect different stakeholders through distributional effects characterized by a high and heterogeneous uncertainty that no social actors can completely control or understand. On this basis, we present a new process framework that aims to support participatory decision making under uncertainty: the range-based Multi-Actor Multi-Criteria Analysis (range-based MAMCA). On the one hand, the process framework explicitly considers stakeholders’ objectives at an output level of aggregation. On the other hand, by means of a Monte Carlo analysis, the method also provides an exploratory scenario approach that enables the capture of the uncertainty, which stems from the complex context evolution. Range-based MAMCA offers a unique participatory process framework that enables us (1) to identify the alternatives pros and cons for each stakeholder group; (2) to provide probabilities about the risk of supporting mistaken, or at least ill-suited, decisions because of the uncertainty regarding to the decision-making context; (3) to take the decision-makers’ limited control of the actual policy effects over the implementation of one or several options into account. The range-based MAMCA framework is illustrated by means of our first case study that aimed to assess French stakeholders’ support for different biofuel options by 2030.     

A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations

Decision makers (DMs)’ preferences on decision alternatives are often characterized by multiplicative or fuzzy preference relations. This paper proposes a chi-square method (CSM) for obtaining a priority vector from multiplicative and fuzzy preference relations. The proposed CSM can be used to obtain a priority vector from either a multiplicative preference relation (i.e. a pairwise comparison matrix) or a fuzzy preference relation or a group of multiplicative preference relations or a group of fuzzy preference relations or their mixtures. Theorems and algorithm about the CSM are developed. Three numerical examples are examined to illustrate the applications of the CSM and its advantages.     

The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making

QUALIFLEX, a generalization of Jacquet-Lagreze’s permutation method, is a useful outranking method in decision analysis because of its flexibility with respect to cardinal and ordinal information. This paper develops an extended QUALIFLEX method for handling multiple criteria decision-making problems in the context of interval type-2 fuzzy sets. Interval type-2 fuzzy sets contain membership values that are crisp intervals, which are the most widely used of the higher order fuzzy sets because of their relative simplicity. Using the linguistic rating system converted into interval type-2 trapezoidal fuzzy numbers, the extended QUALIFLEX method investigates all possible permutations of the alternatives with respect to the level of concordance of the complete preference order. Based on a signed distance-based approach, this paper proposes the concordance/discordance index, the weighted concordance/discordance index, and the comprehensive concordance/discordance index as evaluative criteria of the chosen hypothesis for ranking the alternatives. The feasibility and applicability of the proposed methods are illustrated by a medical decision-making problem concerning acute inflammatory demyelinating disease, and a comparative analysis with another outranking approach is conducted to validate the effectiveness of the proposed methodology.     

ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements

In multiple criteria decision aiding, it is common to use methods that are capable of automatically extracting a decision or evaluation model from partial information provided by the decision maker about a preference structure. In general, there is more than one possible model, leading to an indetermination which is dealt with sometimes arbitrarily in existing methods. This paper aims at filling this theoretical gap: we present a novel method, based on the computation of the analytic center of a polyhedron, for the selection of additive value functions that are compatible with holistic assessments of preferences. We demonstrate the most important characteristics of this technique with an experimental and comparative study of several existing methods belonging to the UTA family.