A method for group decision making with multi-granularity linguistic assessment information

This paper proposes a method to solve the group decision making (GDM) problems with multi-granularity linguistic assessment information. In the method, the multi-granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers. In order to make the collective opinion close to each expert’s opinion, a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation. Then, a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers. By applying a non-dominance choice degree to this fuzzy preference relation, the ranking of alternatives is determined and the most desirable alternative(s) is selected. An example is used to illustrate the applicability of the proposed method and its advantages.     

Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making

Multiple attribute decision making (MADM) problems are the most encountered problems in decision making. Fuzziness is inherent in decision making process and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy rating. A few techniques in MADM assess the weights of attributes based on preference information on alternatives. But they are not practical any more when the set of all paired comparison judgments from decision makers (DMs) on attributes are not crisp and also we have to deal with fuzzy decision matrix. This paper investigates the generation of a possibilistic model for multidimensional analysis of preference (LINMAP). The model assesses the fuzzy weights as well as locating the ideal solution with fuzzy decision making preference on attributes and fuzzy decision matrix. All of the information is assumed as triangular fuzzy numbers (TFNs). This method is developed in group decision making environments and formulates the problem as a possibilistic programming with multiple objectives.     

A novel group decision making method with intuitionistic fuzzy preference relations for RFID technology selection

A more scientific decision making process for radio frequency identification (RFID) technology selection is important to increase success rate of RFID technology application. RFID technology selection can be formulated as a kind of group decision making (GDM) problem with intuitionistic fuzzy preference relations (IFPRs). This paper develops a novel method for solving such problems. First, A technique for order preference by similarity to ideal solution (TOPSIS) based method is presented to rank intuitionistic fuzzy values (IFVs). To achieve higher group consensus as well as possible, we construct an intuitionistic fuzzy linear programming model to derive experts’ weights. Depending on the construction of membership and non-membership functions, the constructed intuitionistic fuzzy linear programming model is solved by three kinds of approaches: optimistic approach, pessimistic approach and mixed approach. Then to derive the ranking order of alternatives from the collective IFPR, we extend quantifier guided non-dominance degree (QGNDD) and quantifier guided dominance degree (QGDD) to intuitionistic fuzzy environment. A new two-phase ranking approach is designed to generate the ordering of alternatives based on QGNDD and QGDD. Thereby, the corresponding method is proposed for the GDM problems with IFPRs. Some generalizations on the constructed intuitionistic fuzzy linear programming model are further discussed. At length, the validity of the proposed method is illustrated with a real-world RFID technology selection example.     

Linear programming method for multiattribute group decision making using IF sets

The purpose of this paper is to develop a linear programming methodology for solving multiattribute group decision making problems using intuitionistic fuzzy (IF) sets. In this methodology, IF sets are constructed to capture fuzziness in decision information and decision making process. The group consistency and inconsistency indices are defined on the basis of pairwise comparison preference relations on alternatives given by the decision makers. An IF positive ideal solution (IFPIS) and weights which are unknown a priori are estimated using a new auxiliary linear programming model, which minimizes the group inconsistency index under some constraints. The distances of alternatives from the IFPIS are calculated to determine their ranking order. Moreover, some properties of the auxiliary linear programming model and other generalizations or specializations are discussed in detail. Validity and applicability of the proposed methodology are illustrated with the extended air-fighter selection problem and the doctoral student selection problem.     

A cross-efficiency fuzzy Data Envelopment Analysis technique for performance evaluation of Decision Making Units under uncertainty

The paper presents a novel cross-efficiency fuzzy Data Envelopment Analysis (DEA) technique for evaluating different elements (Decision Making Units or DMUs) under uncertainty. In order to evaluate the performance of several DMUs while dealing with uncertain input and output data, the presented technique employs triangular fuzzy numbers. A fuzzy triangular efficiency is associated to each DMU through a cross evaluation obtained by a compromise between suitably chosen objectives. Results are then defuzzified to provide a ranking of the DMUs. The proposed method is applied to the performance evaluation of healthcare systems in a region of Southern Italy. The DMU data uncertainty derives from ongoing reforms and the reported assessment is conducted firstly in order to evaluate and rank the efficiency of the considered healthcare systems, and subsequently to assess the evolution of the performance of one of the most affected among these DMUs by the reform plans. The case study demonstrates the model ease of application, its discriminative power among DMUs when compared to a more classical fuzzy DEA approach, and the usefulness in planning and validating targeted reforms in the case of healthcare systems.     

New methods for ranking decision making units based on the dispersion of weights and Norm 1 in Data Envelopment Analysis

One of the drawbacks of Data Envelopment Analysis (DEA) is the problem of lack of discrimination among efficient Decision Making Units (DMUs) and hence, yielding large number of DMUs as efficient ones. The main purpose of this paper is to overcome this inability. One of the methods for ranking efficient DMUs is minimizing the Coefficient of Variation (CV) for inputs-outputs weights, which, was suggested by Bal et al. (2008). In this paper, we modify the model and introduce two new models for ranking efficient DMUs based on Norm 1 and using means of inputs-outputs weights. To illustrate purpose, numerical examples are given.     

An extended compromise ratio method for fuzzy group multi-attribute decision making with SWOT analysis

The technique for order preference by similarity to ideal solution (TOPSIS) is a well-known multi-attribute decision making (MADM) method that is used to identify the most attractive alternative solution among a finite set of alternatives based on the simultaneous minimization of the distance from an ideal solution (IS) and the maximization of the distance from the nadir solution (NS). We propose an alternative compromise ratio method (CRM) using an efficient and powerful distance measure for solving the group MADM problems. In the proposed CRM, similar to TOPSIS, the chosen alternative should be simultaneously as close as possible to the IS and as far away as possible from the NS. The conventional MADM problems require well-defined and precise data; however, the values associated with the parameters in the real-world are often imprecise, vague, uncertain or incomplete. Fuzzy sets provide a powerful tool for dealing with the ambiguous data. We capture the decision makers’ (DMs’) judgments with linguistic variables and represent their importance weights with fuzzy sets. The fuzzy group MADM (FGMADM) method proposed in this study improves the usability of the CRM. We integrate the FGMADM method into a strengths, weaknesses, opportunities and threats (SWOT) analysis framework to show the applicability of the proposed method in a solar panel manufacturing firm in Canada.     

Fuzzy heterogeneous multiattribute decision making method for outsourcing provider selection

One of the critical activities for outsourcing success is outsourcing provider selection, which may be regarded as a type of fuzzy heterogeneous multiattribute decision making (MADM) problems with fuzzy truth degrees and incomplete weight information. The aim of this paper is to develop a new fuzzy linear programming method for solving such MADM problems. In this method, the decision maker’s preferences are given through pair-wise alternatives’ comparisons with fuzzy truth degrees, which are expressed with trapezoidal fuzzy numbers (TrFNs). Real numbers, intervals, and TrFNs are used to express heterogeneous decision information. Giving the fuzzy positive and negative ideal solutions, we define TrFN-type fuzzy consistency and inconsistency indices based on the concept of the relative closeness degrees. The attribute weights are estimated through constructing a new fuzzy linear programming model, which is solved by using the developed fuzzy linear programming method with TrFNs. The relative closeness degrees of alternatives can be calculated to generate their ranking order. An example of the IT outsourcing provider selection problem is analyzed to demonstrate the implementation process and applicability of the method proposed in this paper.     

Estimating incomplete information in group decision making: A framework of granular computing

A general assumption in group decision making scenarios is that of all individuals possess accurate knowledge of the entire problem under study, including the abilities to make a distinction of the degree up to which an alternative is better than other one. However, in many real world scenarios, this may be unrealistic, particularly those involving numerous individuals and options to choose from conflicting and dynamics information sources. To manage such a situation, estimation methods of incomplete information, which use own assessments provided by the individuals and consistency criteria to avoid discrepancy, have been widely employed under fuzzy preference relations. In this study, we introduce the information granularity concept to estimate missing values supporting the objective of obtaining complete fuzzy preference relations with higher consistency levels. We use the concept of granular preference relations to form each missing value as a granule of information in place of a crisp number. This offers the flexibility that is required to estimate the missing information so that the consistency levels related to the complete fuzzy preference relations are as higher as possible.     

Notes on “Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making”

The aim of this note is to point out and correct some errors in the definitions, notations operations and possibilistic programming model introduced by Sadi-Nezhad and Akhtari (2008) and hereby develop two correct possibilistic programming models for fuzzy multidimensional analysis of preference in the fuzzy multiattribute group decision making problems with both the fuzzy weight vector and the fuzzy positive ideal solution (PIS) unknown a priori.     

A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making

As an extension of fuzzy set, a Pythagorean fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision‐making problems. The aim of this paper is to introduce a novel aggregation method for the Pythagorean fuzzy set and analyze possibilities for its application in solving multiple attribute decision‐making problems. More specifically, a new Pythagorean fuzzy aggregation operator called the Pythagorean fuzzy induced ordered weighted averaging‐weighted average (PFIOWAWA) operator is developed. This operator inherits main characteristics of both ordered weighted average operator and induced ordered weighted average to aggregate the Pythagorean fuzzy information. Some of main properties and particular cases of the PFIOWAWA operator are studied. A method based on the proposed operator for multiple attribute group decision making is developed. Finally, we present a numerical example of selection of research and development projects to illustrate applicability of the new approach in a multiple attribute group decision‐making problem.     

A method based on distance measure for interval-valued intuitionistic fuzzy group decision making

In this paper we introduce some relations and operations of interval-valued intuitionistic fuzzy numbers and define some types of matrices, including interval-valued intuitionistic fuzzy matrix, interval-valued intuitionistic fuzzy similarity matrix and interval-valued intuitionistic fuzzy equivalence matrix. We study their properties, develop a method based on distance measure for group decision making with interval-valued intuitionistic fuzzy matrices and, finally, provide an illustrative example.     

Sensitivity analysis on modified variable returns to scale model in Data Envelopment Analysis using facet analysis

One of the concerns in Data Envelopment Analysis (DEA) is the sensitivity and stability analysis of specific Decision Making Unit (DMU), which is under evaluation. In economical point of view, the stability region in input–output space for maintaining the efficiency score of efficient DMU is important. In this paper, a new sensitivity analysis approach based on Banker, Charnes and Cooper (BCC) model which is modified by facet analysis, is developed. An extended stability region is determined especially for DMUs that are placed on intersection of efficient and weak efficient frontier. The results are shown by numerical examples.     

Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees

As an important component of group decision making, the hybrid multi-criteria group decision making (MCGDM) is very complex and interesting in real applications. The purpose of this paper is to develop a novel interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for hybrid MCGDM considering alternative comparisons with hesitancy degrees. The subjective preference relations between alternatives given by each decision maker (DM) are formulated as an IVIF set (IVIFS). The IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers (TrFNs), linguistic variables, intervals and real numbers are used to represent the multiple types of criteria values. The information of criteria weights is incomplete. The IVIFS-type consistency and inconsistency indices are defined through considering the fuzzy positive and negative ideal solutions simultaneously. To determine the criteria weights, we construct a novel bi-objective IVIF mathematical programming of minimizing the inconsistency index and meanwhile maximizing the consistency index, which is solved by the technically developed linear goal programming approach. The individual ranking order of alternatives furnished by each DM is subsequently obtained according to the comprehensive relative closeness degrees of alternatives to the fuzzy positive ideal solution. The collective ranking order of alternatives is derived through establishing a new multi-objective assignment model. A real example of critical infrastructure evaluation is provided to demonstrate the applicability and effectiveness of this method.     

A method using weight restrictions in data envelopment analysis for ranking and validity issues in decision making

In this article we introduce a comprehensive yet efficient approach based on data envelopment analysis (DEA) with restricted multipliers for accountable and understandable multiple attribute decision making (MADM). Information system (IS) appraisals are motivated and used for illustrating the proposed methodology. Results show that the given DEA based approach can easily and significantly increase the information frame of the decision maker by identifying disparate rankings and by affirming the stability and validity of ranking outcomes. The given validity concept is contrary to the directions given in the main body of research and can also be used to question ranking outcomes of classic MADM methods.     

A consistency and consensus based decision support model for group decision making with multiplicative preference relations

In group decision making (GDM) with multiplicative preference relations (also known as pairwise comparison matrices in the Analytical Hierarchy Process), to come to a meaningful and reliable solution, it is preferable to consider individual consistency and group consensus in the decision process. This paper provides a decision support model to aid the group consensus process while keeping an acceptable individual consistency for each decision maker. The concept of an individual consistency index and a group consensus index is introduced based on the Hadamard product of two matrices. Two algorithms are presented in the designed support model. The first algorithm is utilized to convert an unacceptable preference relation to an acceptable one. The second algorithm is designed to assist the group in achieving a predefined consensus level. The main characteristics of our model are that: (1) it is independent of the prioritization method used in the consensus process; (2) it ensures that each individual multiplicative preference relation is of acceptable consistency when the predefined consensus level is achieved. Finally, some numerical examples are given to verify the effectiveness of our model.     

A consistency model for group decision making problems with interval multiplicative preference relations

The main aim of this paper is to present a consistency model for interval multiplicative preference relation (IMPR). To measure the consistency level for IMPR, a referenced consistent IMPR of a given IMPR is defined, which has the minimum logarithmic distance from the given IMPR. Based on the referenced consistent IMPR, the consistency level of an IMPR can be measured and an IMPR with unacceptable consistency can be adjusted by a proposed algorithm such that the revised IMPR is of acceptable consistency. A consistency model for group decision making (GDM) problems with IMPRs is proposed to obtain the collective IMPR with highest consistency level. Numerical examples are provided to illustrate the validity of the proposed approaches in decision making.     

An interactive method for fuzzy multiple attribute group decision making

In this paper, we develop an interactive method for multiple attribute group decision making under fuzzy environment. The method can be used in situations where the information about attribute weights is partly known, the weights of decision makers are expressed in exact numerical values or triangular fuzzy numbers, and the attribute values are triangular fuzzy numbers. The method transforms fuzzy decision matrices into their expected decision matrices, constructs the corresponding normalized expected decision matrices by two simple formulas, and then aggregates these normalized expected decision matrices into a complex decision matrix. Moreover, the decision makers are asked to provide their preferences gradually in the course of interactions. By solving linear programming models, the method diminishes the given alternative set gradually, and finally finds the most preferred alternative. By using the method, the decision makers can provide and modify their preference information gradually in the process of decision making so as to make the decision result more reasonable. The method can not only reflect the importance of the given arguments and the ordered positions of the arguments, but also relieve the influence of unfair arguments on the decision result. Finally, a practical problem is used to illustrate the developed method.     

A comparative study for consistency-based decision making with interval multiplicative preference relations

ABSTRACT

To ensure the reasonable application and perfect the theory of decision making with interval multiplicative preference relations (IMPRs), this paper continues to discuss decision making with IMPRs. After reviewing previous consistency concepts for IMPRs, we find that Krej?í’s consistency concept is more flexible and natural than others. However, it is insufficient to address IMPRs only using this concept. Considering this fact, this paper researches inconsistent and incomplete IMPRs that are usually encountered. First, programming models for addressing inconsistent and incomplete IMPRs are constructed. Then, this paper studies the consensus of individual IMPRs and defines a consensus index using the defined correlation coefficient. When the consensus requirement does not satisfy requirement, a programming model for improving consensus level is built, which can ensure the consistency. Subsequently, a procedure for group decision making with IMPRs is offered, and associated examples are provided to specifically show the application of main theoretical results.     

Ratio-based similarity analysis and consensus building for group decision making with interval reciprocal preference relations

Similarity analysis and preference information aggregation are two important issues for consensus building in group decision making with preference relations. Pairwise ratings in an interval reciprocal preference relation (IRPR) are usually regarded as interval-valued And-like representable cross ratios (i.e., interval-valued cross ratios for short) from the multiplicative perspective. In this paper, a ratio-based formula is introduced to measure similarity between a pair of interval-valued cross ratios, and its desirable properties are provided. We put forward ratio-based similarity measurements for IRPRs. An induced interval-valued cross ratio ordered weighted geometric (IIVCROWG) operator with interval additive reciprocity is developed to aggregate interval-valued cross ratio information, and some properties of the IIVCROWG operator are presented. The paper devises an importance degree induced IRPR ordered weighted geometric operator to fuse individual IRPRs into a group IRPR, and discusses the derivation of its associated weights. By employing ratio-based similarity measurements and IIVCROWG-based aggregation operators, a soft consensus model including a generation mechanism of feedback recommendation rules is further proposed to solve group decision making problems with IRPRs. Three numerical examples are examined to illustrate the applicability and effectiveness of the developed models.