A fuzzy multi-criteria group decision making framework for evaluating health-care waste disposal alternatives

Nowadays, as in all other organizations, the amount of waste generated in the health-care institutions is rising due to their extent of service. Medical waste management is a common problem of developing countries including Turkey, which are becoming increasingly conscious that health-care wastes require special treatment. Accordingly, one of the most important problems encountered in Istanbul, the most crowded metropolis of Turkey, is the disposal of health-care waste (HCW) from health-care institutions. Evaluating HCW disposal alternatives, which considers the need to trade-off multiple conflicting criteria with the involvement of a group of experts, is a highly important multi-criteria group decision making problem. The inherent imprecision and vagueness in criteria values concerning HCW disposal alternatives justify the use of fuzzy set theory. This paper presents a fuzzy multi-criteria group decision making framework based on the principles of fuzzy measure and fuzzy integral for evaluating HCW treatment alternatives for Istanbul. In group decision making problems, aggregation of expert opinions is essential for properly conducting the evaluation process. In this study, the ordered weighted averaging (OWA) operator is used to aggregate decision makers’ opinions. Economic, technical, environmental and social criteria and their related sub-criteria are employed to assess HCW treatment alternatives, namely “incineration”, “steam sterilization”, “microwave”, and “landfill”. A comparative analysis is presented using another classical operator to aggregate decision makers’ preferences.     

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.     

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 new consensus model for group decision making using fuzzy ontology

Involving many people in decision making does not guarantee success. In practice, there are always individuals who try to exert pressure in order to persuade others who could easily be influenced. In these situations, classical group decision making models fail. Thus, there is still the necessity of developing tools to help users reach collective decisions as if they participated in a real face to face meeting. In such a way, a proper negotiation process can lead to successful solutions. Therefore, we propose a new consensus model to deal with the psychology of negotiation by using the power of a fuzzy ontology as weapon of influence in order to improve group decision scenarios making them more precise and realistic. In addition, the use of a fuzzy ontology gives us the possibility to take into account large sets of alternatives.     

A discrete consensus support model for multiple attribute group decision making

In multiple attribute group decision making (MAGDM), it is preferable that the set of experts reach a high degree of consensus amongst their opinions before applying a selection process. In this paper, we present a discrete model to support the consensus reaching process for MAGDM problems. Firstly, a consensus scheme for a set of arguments is provided, where the basic idea is to tighten the range of opinions amongst experts. Based on the well-defined scheme, a convergent algorithm is presented to autocratically guide experts to reach a predefined consensus level. In the selection process, the maximizing deviation method is applied to determine the attribute weights. Then, the choice of the best alternative(s) from the group decision matrix is obtained by the simple additive weighting method. Finally, one example is presented to show the application and effectiveness of the proposed model.     

Adaptive consensus support model for group decision making systems

In this paper, we present an adaptive consensus support model for group decision making systems based on intervals of linguistic 2-tuples. The proposed method has the following advantages: (1) the evaluating values can either be represented by linguistic terms or intervals of linguistic terms, (2) if the required consensus degree is too high, then the proposed adaptive consensus support model can modify experts’ preferences to improve convergence toward a higher consensus degree or a sufficient agreement for group decision making and (3) the proposed method is an interactive method, where each expert can modify the adjustments made by the system during the consensus reaching process if he/she does not agree with the adjustments made by the system. The proposed adaptive consensus support model can overcome the drawback of Mata et al.’s method (2009). It provides us with a useful way for adaptive consensus support for group decision making based on intervals of linguistic 2-tuples.     

A consensus model for group decision making problems with linguistic interval fuzzy preference relations

Sometimes, we find decision situations in which it is difficult to express some preferences by means of concrete preference degrees. In this paper, we present a consensus model for group decision making problems in which the experts use linguistic interval fuzzy preference relations to represent their preferences. This model is based on two consensus criteria, a consensus measure and a proximity measure, and on the concept of coincidence among preferences. We compute both consensus criteria in the three representation levels of a preference relation and design an automatic feedback mechanism to guide experts in the consensus reaching process.     

An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives

This article proposes a framework to handle multiattribute group decision making problems with incomplete pairwise comparison preference over decision alternatives where qualitative and quantitative attribute values are furnished as linguistic variables and crisp numbers, respectively. Attribute assessments are then converted to interval-valued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in the evaluation process. Group consistency and inconsistency indices are introduced for incomplete pairwise comparison preference relations on alternatives provided by the decision-makers (DMs). By minimizing the group inconsistency index under certain constraints, an auxiliary linear programming model is developed to obtain unified attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS). Attribute weights are subsequently employed to calculate distances between alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method.     

A consensus model for group decision making under trapezoidal fuzzy numbers environment

Natural linguistic terms can preferably express the opinions of decision makers in complicated decision environment. Group decision making with multiplicative trapezoidal fuzzy preference relations transforming from natural linguistic terms attracts the attention of researchers for its important research significant. The developed approach is based on consensus improving process by using a new similarity measure and a trapezoidal fuzzy power ordered weighted geometric averaging (TFPOWGA) operator. In order to introduce this approach, firstly, trapezoidal fuzzy power geometric averaging operator and TFPOWGA operator are presented to aggregate trapezoidal fuzzy numbers (TFNs). Secondly, a new similarity measure for TFNs is introduced by combining centroids and areas of TFNs. We further propose a new consensus improving algorithm that consists of consensus measure and a dynamic feedback mechanism containing a multi-objective optimization model and some indirect rules. And then a selection stage is described to rank the alternatives. At last, an example is implemented to demonstrate effectiveness of the approach.

     

Dynamic fuzzy OWA model for group multiple criteria decision making

Obtaining relative weights in MCDM problems is a very important issue. The Ordered Weighted Averaging (OWA) aggregation operators have been extensively adopted to assign the relative weights of numerous criteria. However, previous aggregation operators (including OWA) are independent of aggregation situations. To solve the problem, this study proposes a new aggregation model – dynamic fuzzy OWA based on situation model, which can modify the associated dynamic weight based on the aggregation situation and can work like a “magnifying lens” to enlarge the most important attribute dependent on minimal information, or can obtain equal attribute weights based on maximal information. Two examples are adopted in this paper for comparison and showing the effects under different weights.     

A simulation based multi-attribute group decision making technique with decision constraints

The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a useful technique for solving Multi Attribute Group Decision Making (MAGDM) problems. In MAGDM, the performance scores of the alternatives and the weights of assessment attributes are mostly vague. Therefore, using of deterministic data throughout decision making process may lead to inaccurate results. In order to overcome inherent vagueness and uncertainty, various fuzzy MAGDM techniques were presented in the literature. However, these fuzzy MAGDM techniques are focused on expected and extreme values, which are sometimes insufficient for the precise determination of alternatives’ preference structure. In this paper, in order to eliminate the limitations of deterministic and fuzzy MAGDM methods, we present a probabilistic methodology, which is based on TOPSIS and Monte-Carlo simulation of triangular data. In addition to its straightforward application and thanks to its versatility, simulation enables decision makers to incorporate some decision constraints into decision-making process. Two illustrative examples are also given to show the effectiveness of the proposed methodology. The method is also compared with a fuzzy TOPSIS technique from the literature.     

A consensus model for group decision making under interval type-2 fuzzy environment

We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.     

Consensus-based decision support for multicriteria group decision making

Consensus decision making is complex and challenging in multicriteria group decision making due to the involvement of several decision makers, the presence of multiple, and often conflicting criteria, and the existence of subjectiveness and imprecision in the decision making process. To ensure effective decisions being made, the interest of all the decision makers usually represented by the degree of consensus in the decision making process has to be adequately considered. This paper presents a consensus-based approach for effectively solving the multicriteria group decision making problem. The subjectiveness and imprecision of the decision making process is adequately handled by using intuitionistic fuzzy numbers. An interactive algorithm is developed for consensus building in the group decision making process. A decision support system framework is presented for improving the effectiveness of the consensus building process. An example is presented for demonstrating the applicability of the proposed approach for solving the multicriteria group decision making problem in real world situations.     

Selecting the most preferable alternatives in a group decision making problem using DEA

Group decision making is the study of identifying and selecting alternatives based on the values and preferences of the decision maker. Making a decision implies that there are several alternative choices to be considered. This paper uses the concept of Data Envelopment Analysis to introduce a new mathematical method for selecting the best alternative in a group decision making environment. The introduced model is a multi-objective function which is converted into a multi-objective linear programming model from which the optimal solution is obtained.A numerical example shows how the new model can be applied to rank the alternatives or to choose a subset of the most promising alternatives.     

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.     

Adaptive model for decision making

Learning of an adaptive model in terms of the creation of n-dimensional bodies is presented. N-dimensional bodies are used to partition the space Rⁿ of measurable pattern parameters in order to separate patterns of one answer, e.g. class or type of disease, from those of other ones.

The model, when applied medically in the prognosis of acute pancreatitis and in the diagnosis of disseminated cancer of unknown origin, showed good results.     

A multi-objective model for environmental investment decision making

Investment in landscapes to achieve outcomes that have multiple environmental benefits has become a major priority in many countries. This gives rise to opportunities for mathematical programming methods to provide solutions on where investments could be made on the landscape, to maximise multiple environmental benefits. The problem was formulated as a multi-objective integer programming model, with objective functions representing biodiversity, water run-off and carbon sequestration. We applied a multi-objective Greedy Randomised Adaptive Search Procedure (GRASP) as an evolutionary programming method to find solutions along the Pareto front. This allows the decision maker to explore trade-off's between the objectives. A 142,000 ha case study catchment in eastern Australia was used to test the methodology and assess the sensitivity of the different and often competing environmental benefits.     

A distance-based aggregation approach for group decision making with interval preference orderings

Xu (2013) proposed a nonlinear programming model to derive an exact formula to determine the experts’ relative importance weights for the group decision making (GDM) with interval preference orderings. However, in this study, we show that the exact formula to determine the weight vector which always equals to w = (1/m, 1/m, … , 1/m)^T (m is the number of experts). In this paper, we propose a distance-based aggregation approach to assess the relative importance weights for GDM with interval preference orderings. Relevant theorems are offered to support the proposed approach. After that, by using the weighted arithmetic averaging operator, we obtain the aggregated virtual interval preference orderings. We propose a possibility degree formula to compare two virtual interval preference orderings, then rank and select the alternatives. The proposed method is tested by two numerical examples. Comparative analysis are provided to show the advantages and effectiveness of the proposed method.     

A consensus reaching model for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

The aim of this paper is to put forward a consensus reaching method for multi-attribute group decision-making (MAGDM) problems with linguistic information, in which the weight information of experts and attributes is unknown. First, some basic concepts and operational laws of 2-tuple linguistic label are introduced. Then, a grey relational analysis method and a maximising deviation method are proposed to calculate the incomplete weight information of experts and attributes respectively. To eliminate the conflict in the group, a weight-updating model is employed to derive the weights of experts based on their contribution to the consensus reaching process. After conflict elimination, the final group preference can be obtained which will give the ranking of the alternatives. The model can effectively avoid information distortion which is occurred regularly in the linguistic information processing. Finally, an illustrative example is given to illustrate the application of the proposed method and comparative analysis with the existing methods are offered to show the advantages of the proposed method.     

Consensus-reaching methods for hesitant fuzzy multiple criteria group decision making with hesitant fuzzy decision making matrices

Group decision making plays an important role in various fields of management decision and economics. In this paper, we develop two methods for hesitant fuzzy multiple criteria group decision making with group consensus in which all the experts use hesitant fuzzy decision matrices (HFDMs) to express their preferences. The aim of this paper is to present two novel consensus models applied in different group decision making situations, which are composed of consensus checking processes, consensus-reaching processes, and selection processes. All the experts make their own judgments on each alternative over multiple criteria by hesitant fuzzy sets, and then the aggregation of each hesitant fuzzy set under each criterion is calculated by the aggregation operators. Furthermore, we can calculate the distance between any two aggregations of hesitant fuzzy sets, based on which the deviation between any two experts is yielded. After introducing the consensus measure, we develop two kinds of consensus-reaching procedures and then propose two step-by-step algorithms for hesitant fuzzy multiple criteria group decision making. A numerical example concerning the selection of selling ways about ‘Trade-Ins’ for Apple Inc. is provided to illustrate and verify the developed approaches. In this example, the methods which aim to reach a high consensus of all the experts before the selection process can avoid some experts’ preference values being too high or too low. After modifying the previous preference information by using our consensus measures, the result of the selection process is much more reasonable.