An Interactive Approach to Multiple Attribute Group Decision Making with Multigranular Uncertain Linguistic Information

The multiple attribute group decision making (MAGDM) problems having multiple sources of uncertain linguistic information assessed in different linguistic label sets are investigated. The existing linguistic labels in a linguistic label set are uniformly and symmetrically distributed, but in many real-life situations, the unbalanced linguistic information appears due to the nature of the linguistic variables used in the problems (Herrera and Herrera-Viedma, Proceedings of 4th international workshop on preferences and decisions, Trento, Italy, 2003). In this paper, we first define some unbalanced linguistic label sets, and then develop some transformation functions to unify the given multigranular linguistic labels in a unique linguistic label set without loss of information. Moreover, we utilize the uncertain linguistic weighted averaging operator to aggregate all individual uncertain linguistic decision matrices into a collective one, and define two similarity measures, one for measuring the similarity degree between each pair of uncertain linguistic variables, and the other for checking the consensus degrees among the individual uncertain linguistic decision matrices and the collective uncertain linguistic decision matrix. Finally, we develop an interactive approach to MAGDM with multigranular uncertain linguistic information and illustrate the developed approach with an application example.     

Generalized Hybrid Aggregation Operators Based on the 2-Dimension Uncertain Linguistic Information for Multiple Attribute Group Decision Making

With respect to the multiple attribute decision making problems in which the attribute values take the form of the 2-dimension uncertain linguistic information, a new method based on the generalized hybrid operators is proposed. Firstly, the definition, properties, expectations and ranking method of 2-dimension uncertain linguistic information are introduced, and the operational laws the 2-dimension uncertain linguistic information are defined. Then some aggregation operators, including 2-dimension uncertain linguistic generalized weighted average operator, 2-dimension uncertain linguistic generalized ordered weighted average operator, and 2-dimension uncertain linguistic generalized hybrid weighted average operator, are developed, and some properties and special cases of them are also discussed. Finally, these operators are applied to multi-criteria decision making and an illustrative example is given to verify the developed approach and to demonstrate its effectiveness.     

A Fuzzy Stochastic Multi-Attribute Group Decision-Making Approach for Selection Problems

The purpose of this paper is to demonstrate how the fuzzy and stochastic approaches as well as multi-attribute group decision-making techniques can be effectively utilized for selection problems in different kinds of uncertainty situations. A group of the decision makers describes a value for an alternative with respect to an attribute by the use of linguistic variables. The rating of each alternative is aggregated, which can be expressed as triangular fuzzy numbers. Then Monte Carlo simulation is applied to generate the performance distribution of alternatives with respect to different attributes in an uncertain environment. Finally, a stochastic compromise ranking technique, known as the VIKOR technique, is developed to evaluate probability distributions for each alternative on each attribute and to prioritize them. The proposed fuzzy stochastic approach is suitable to compromise a solution among the conflicting tangible and intangible attributes under the group decision-making process. In addition, an application of the proposed approach is provided to solve the important risk selection problem in a highway project. The results illustrate its real-life applicability and suitability in discrete group decision-making under uncertainty.     

A Calibrated Group Decision Process

In practice most organisational decisions are made by groups that bring into the problem multiple perspectives, both complementary and contradictory. When having a group of decision makers, usually individuals’ preferences are either led to consensus or are aggregated with the use of some function like the median, the arithmetic or geometric mean. We focus in the second case, where individual’s preferences need to be aggregated. Our approach is based on the fact that when two decision makers are asked to give their preference between a pair of criteria using a specific scale, it is possible that they will give slightly different answers, even when they actually have the same opinion. This difference will not affect the case of a single decision maker, as it will be consistent throughout the whole process. However, it can affect a group decision when the values will be used as an input for the aggregation function. A novel approach is presented that enhances group decision making through a group calibration process. The proposed process adjusts individuals’ preferences based on their answers on a set of standardized questions prior to the aggregation phase. The method focuses The whole concept is applied to the group analytical network process method and it is illustrated through a telecommunications project case. The decision under examination concerns the selection of the right place for deploying a new telecom service of a multinational-based telecommunications company where a group of geographically dispersed decision makers form an ad-hoc virtual team in order to select the location for a new technical support centre.     

On Consensus of Group Decision Making with Interval Utility Values and Interval Preference Orderings

Uncertainty is a common phenomenon in our real world. Interval utility values and interval preference orderings are two of the simplest and most convenient tools to describe uncertain preferences in decision making. In this paper, we investigate consensus problems in group decision making with interval utility values and interval preference orderings. We first establish their transformation relations, and give a formula for calculating the association coefficients of individual uncertain preferences and group ones. We then develop a consensus procedure for group decision making with interval utility values and interval preference orderings, which takes interval utility values as the uniform preference representation. This procedure can be reduced to a series of processes for dealing with some special group decision making situations, such as: group decision making with utility values and preference orderings, group decision making with interval utility values, group decision making with interval preference orderings, etc. Finally, we illustrate the applications of the developed procedures with two practical examples.     

复杂信任网络群组综合评价方法及应用研究

考虑评价环境的复杂不确定性、评价专家的信任行为特征以及群组专家的共识等问题，提出了一种区间Fermatean模糊信任网络群组综合评价方法。首先，针对区间Fermatean模糊评价信息的集成问题，提出了区间Fermatean模糊信息的运算规则，并在此基础上提出了一种区间Fermatean模糊Frank集成方法。其次，考虑到评价专家间信任关系对专家权重和共识达成的影响，构建了基于语言术语的信任网络以计算专家权重，同时设计了个性化反馈机制，进而构建了信任共识交互模型以提高群组共识度。此外，针对评价指标权重未知的情形,提出了区间Fermatean模糊熵权法获取指标权重。最后，通过高校商科类本科生统计设计能力的评价问题验证所提出方法的可行性和优越性。     

Fuzzy Group Decision Making for the Selection of Facility Location

In this paper, fuzzy group decision making based on extension of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method which was proposed by Chen (Fuzzy Sets Syst, 114:1–9, 2000) is adopted for facility location selection. In this method, the ratings of various alternatives versus various subjective criteria and the weights of all criteria are assessed in linguistic variables represented by fuzzy numbers. By fuzzy numbers, it has been tried to resolve the ambiguity of concepts that are associated with human being’s judgments. To determine the order of the alternatives, closeness coefficient is defined by calculating the distances to the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS). In Chen’s approach, the distance between two fuzzy numbers is calculated with vertex method. But in this study, different distance measurement methods are used and the results are compared. Finally the proposed method has been applied to a facility location selection problem of a textile company in Turkey.     

A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information

In this paper, we propose a linguistic hybrid arithmetic averaging (LHAA) operator, which is based on linguistic weighted arithmetic averaging (LWAA) operator and extended ordered weighted averaging (EOWA) operator, and study some desirable properties of the LHAA operator. The LHAA operator can not only reflect the importance degrees of both the given argument and its ordered position, but also relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Based on the LWAA and LHAA operators, we develop a practical approach to multiple attribute group decision making under linguistic environment. The approach first aggregates the individual linguistic preference values into a collective linguistic preference value for each alternative by using the LWAA and LHAA operators (it is worth pointing out that the aggregation process does not produce any loss of linguistic information), and then orders the collective linguistic preference values to obtain the best alternative(s). Finally, an illustrative example is also given to verify the approach and to demonstrate its feasibility and practicality.     

Uncertain Power Average Operators for Aggregating Interval Fuzzy Preference Relations

In this paper, we investigate group decision making problems based on interval fuzzy preference relations. We define an uncertain power weighted average (UPWA) operator and an uncertain power ordered weighted average (UPOWA) operator, on the basis of the power average operator of Yager (IEEE Trans Syst Man Cybern A 31:724–731, 1988) and the uncertain geometric mean. In the situations where the weights of experts are known, we develop a method based on the UPWA operator for group decision making with interval fuzzy preference relations; and in the situations where the weights of experts are unknown, we develop a method based on the UPOWA operator for group decision making with interval fuzzy preference relations.     

模糊群决策方法在中间商选择中的应用研究

企业在选择中间商时往往面临着候选伙伴评价指标信息获取的困难,为了使决策科学合理,采用群决策方法集成各领域不同专家的信息,通过语言变量把专家的主观判断转化为对应模糊数,建立相应的数学模型,并计算出用模糊数表示的候选者综合评价值。     

An Extended PROMETHE II Multi-Criteria Group Decision Making Technique Based on Intuitionistic Fuzzy Logic for Sustainable Energy Planning

The implementations of Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) category to complex multi-criteria group decision making (MCGDM) scenarios have been included in thousands areas. Outranking methods such as PROMETHEE II are also greatly employed in energy planning application. In MCGDM methods if decision makers (DMs) are not able to treat precise data in order to define their preferences, the intuitionistic fuzzy set (IFS) theory enables them. IFS attributes are connected with the degree of membership and non-membership, and can be used to draw uncertainty in group decision-making situations. In this paper, a new version of the PROMETHEE II method is proposed, aiming at solving MCGDM problems. Linguistic variables are expressed in the membership function and non-membership function of IFS which are used to assess the weights of all criteria and the ratings of each alternative with respect to each criteria. Conditional normalized Euclidean distance measure is adopted to measure deviations between alternatives on intuitionistic fuzzy set. Then, a ranking algorithm is applied to indicate the order of superiority of alternatives. Finally, a practical example is given to an application of sustainable energy planning to verify our proposed method. Additionally, a comparative analysis is done among the proposed PROMETHEE II method and the intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method and elimination and choice translating reality method (IF-ELECTRE).     

Interval-Valued Intuitionistic Fuzzy WASPAS Method: Application in Reservoir Flood Control Management Policy

Interval-valued intuitionistic fuzzy sets (IVIFSs) are very flexible tool to cope with the uncertainty arises in multi-criteria decision making (MCDM) problems. In recent times, MCDM problems with interval-valued intuitionistic fuzzy information have achieved more attention from researchers in different areas and consequently, several MCDM methods have been extended for IVIFSs. In this paper, a novel approach based on WASPAS method is developed under IVIFSs. The developed method is based on the operators of IVIFSs, some amendments in the classical WASPAS method and a new process for calculation of criteria and decision experts’ weights. In process for calculating weights, new procedures is propoesd to compute the decision experts’ weights and criteria weights based on interval-valued intuitionistic fuzzy information measures (entropy, divergence and similarity measures) to achieve more realistic weights. Innovative information measures are developed based on the exponential function for IVIFSs to determine the weights of the criteria and decision experts. Since the uncertainty is an unavoidable feature of MCDM problems, the developed method can be a constructive tool for decision-making in an uncertain environment. Further, an uncertain decision making problem of reservoir flood control management policy is implemented with interval-valued intuitionistic fuzzy information, which reveals the effectiveness and reliability of the proposed IVIF-WASPAS method. To validate the result, comparative analysis with existing methods and sensitivity analysis are presented under interval-valued intuitionistic fuzzy environment.     

The Use of Ranking Veto Concept to Mitigate the Compensatory Effects of Additive Aggregation in Group Decisions on a Water Utility Automation Investment

The use of additive models for aggregating group decisions implies they have a compensatory effect in the process of aggregating all decision makers’ (DMs’) preferences. In this kind of model, the final result may produce some extremely undesirable alternatives for one or more DMs. Such alternatives may emerge with a higher ranking than desirable ones, thus generating conflicts and regrets. To overcome this problem the concept of ranking veto is introduced based on a reduction factor combined with the utility of the alternative in order to penalize conflicting alternatives and reduce disagreements in an additive model. A water utility problem was considered as a numerical application to illustrate the model. A decision group method based on MAUT, utility thresholds and a reduction factor is proposed to support group decision in selecting regions that will receive investments in automation over the next 4 years.     

Fuzzy Set Based Consensus Schemes for Multicriteria Group Decision making Applied to Strategic Planning

This paper studies three consensus schemes based on fuzzy models for dealing with the input of multiple experts in multicriteria decision making. The consensus schemes are based on different aggregation procedures for constructing a collective decision. In the paper, we propose a methodology that makes use of the three consensus schemes implemented by a coordination mode that creates an efficient manner of exploiting the capabilities of each member of the group in a cooperative work. The applicability and efficiency of the proposed methodology is demonstrated through an application related to strategic planning.     

一种基于多人决策的供应链协同决策模型

为解决供应链协同决策的有效性问题,本文分析供应链协同决策与群体决策的区别,采用构建决策流程和决策模型、基于集对理论的共识度评价等方法,建立基于模糊多目标多人决策的供应链协同决策建模,并通过算例验证模型的合理性和有效性。     

基于三阶段综合评判法的虚拟企业伙伴选择研究

选择正确的合作伙伴是组建虚拟企业的关键因素之一,而要保证伙伴选择过程中决策的正确性,就必须采用合理的合作伙伴选择方法。从虚拟企业建模角度出发,提出了基于关系理论的定性过滤、基于数据包络的定量筛选、基于综合评判的最优组合确定三阶段虚拟企业伙伴选择模型。     

A Study on Aggregation of TOPSIS Ideal Solutions for Group Decision-Making

The technique for order preference by similarity to ideal solution (TOPSIS) has become a popular multi-criteria decision making (MCDM) technique, since it has a comprehensible theoretical structure and is able to provide an exact model for decision making. For the use of TOPSIS in group decisions, the common approaches in aggregating individual decision makers’ judgments are the geometric and the arithmetic mean methods, although these are too intuitive and do not consider either preference levels or preference priorities among alternatives for individual decision makers. In this paper, a TOPSIS group decision aggregation model is proposed in which the construction consists of three stages: (1) The weight differences are calculated first as the degrees of preferences among different alternatives for each decision maker; (2) The alternative priorities are then derived, and the highest one can be denoted as the degree to which a decision maker wants his most favorite alternative to be chosen; (3) The group ideal solutions approach in TOPSIS is used for the aggregation of similarities obtained from different decision makers. A comparative analysis is performed, and the proposed aggregation model seems to be more satisfactory than the traditional aggregation model for solving compromise-oriented decision problems.     

A Decision Rule Aggregation Approach to Multiple Criteria-Multiple Participant Sorting

A system that aggregates case-based linguistic decision rules using a hybrid of the dominance-based rough set approach (DRSA) and the Dempster–Shafer (DS) theory of evidence is proposed for multiple criterion-multiple participant sorting. First, DRSA is employed to infer linguistic decision rules that estimate the preferences of a few participants by means of their evaluations of representative case sets. Next, DS theory is applied to aggregate the decision rules triggered by all participants’ evaluations of an alternative, thereby generating an overall decision recommendation for the alternative. The method is demonstrated on a numerical example.     

A family of IOWA operators with reliability measurement under interval-valued group decision-making environment

Aggregation operators play an essential role in the aggregation of various individual input arguments in group decision-making (GDM). In this paper, we have proposed a family of IOWA operators with reliability measurement to aggregate uncertain decision information represented by interval numbers in GDM problems. In particular, we introduce the reliability-induced uncertain OWA (R-IUOWA) operator and the clusters’ reliability-induced uncertain OWA (CR-IUOWA) operator. This type of operators uses the reliability measurement representing the opinion consensus of individuals as the associated order-inducing variable and considers the decision-makers’ preference in the calculation of the position weights. Thus, the aggregation results have a higher consensus level. The R-IUOWA and CR-IUOWA operators have three primary properties such as commutativity, idempotency and boundness. The generalized formulas and some special cases of the two operators are outlined. Finally, the proposed operators are applied to a GDM problem regarding the selection of an investment company. The validity of the two operators is illustrated by comparing the aggregation results with that of other operators.

     

A risk-based decision support framework for selection of appropriate safety measure system for underground coal mines

In the context of underground coal mining industry, the increased economic issues regarding implementation of additional safety measure systems, along with growing public awareness to ensure high level of workers safety, have put great pressure on the managers towards finding the best solution to ensure safe as well as economically viable alternative selection. Risk-based decision support system plays an important role in finding such solutions amongst candidate alternatives with respect to multiple decision criteria. Therefore, in this paper, a unified risk-based decision-making methodology has been proposed for selecting an appropriate safety measure system in relation to an underground coal mining industry with respect to multiple risk criteria such as financial risk, operating risk, and maintenance risk. The proposed methodology uses interval-valued fuzzy set theory for modelling vagueness and subjectivity in the estimates of fuzzy risk ratings for making appropriate decision. The methodology is based on the aggregative fuzzy risk analysis and multi-criteria decision making. The selection decisions are made within the context of understanding the total integrated risk that is likely to incur while adapting the particular safety system alternative. Effectiveness of the proposed methodology has been validated through a real-time case study. The result in the context of final priority ranking is seemed fairly consistent.