Group decision making with incomplete fuzzy preference relations based on the additive consistency and the order consistency

In this paper, we present a new method for group decision making with incomplete fuzzy preference relations based on the additive consistency and the order consistency. We estimate unknown preference values based on the additive consistency and then construct the consistency matrix which satisfies the additive consistency and the order consistency simultaneously for aggregation. The existing group decision making methods may not satisfy the order consistency for aggregation in some situations. The proposed method can overcome the drawback of the existing methods. It provides us with a useful way for group decision making with incomplete fuzzy preference relations based on the additive consistency and the order consistency.     

Consistency techniques for continuous constraints

We consider constraint satisfaction problems with variables in continuous, numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.Our approach is based on approximating regions of feasible solutions by 2 ^k -trees, a representation commonly used in computer vision and image processing. We give simple and stable algorithms for computing labelings with arbitrary degrees of consistency. The algorithms can process constraints and solution spaces of arbitrary complexity, but with a fixed maximal resolution.Previous work has shown that when constraints are convex and binary, path-consistency is sufficient to ensure global consistency. We show that for continuous domains, this result can be generalized to ternary and in fact arbitrary n-ary constraints using the concept of (3,2)-relational consistency. This leads to polynomial-time algorithms for computing globally consistent labelings for a large class of constraint satisfaction problems with continuous variables.     

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation (IFPR) is a suitable technique to express fuzzy preference information by decision makers (DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR, by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly, a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.      

Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making

Yager (Fuzzy Sets, Syst 2003;137:59–69) extended the idea of order‐induced aggregation to the Choquet aggregation and defined induced Choquet ordered averaging operator. In this paper, an induced intuitionistic fuzzy Choquet (IFC) integral operator is proposed for the multiple criteria decision making. Some of its properties are investigated. Furthermore, an induced generalized IFC integral operator is introduced. It is worth mentioning that most of the existing intuitionistic fuzzy aggregation operators are special cases of this induced aggregation operator. A decision procedure based on the proposed induced aggregation operator is developed for solving the multicriteria decision‐making problem in which all the decision information is represented by intuitionistic fuzzy values. An illustrative example is given for demonstrating the applicability of the proposed decision procedure. © 2011 Wiley Periodicals, Inc.     

Consistency and consensus measures for linguistic preference relations based on distribution assessments

In this paper, we propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are linguistic distribution assessments. Further, we study the consistency and consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic distribution assessments in group decision making.     

Large-Scale Group Decision Making: A Systematic Review and a Critical Analysis

The society in the digital transformation era demands new decision schemes such as e-democracy or based on social media. Such novel decision schemes require the participation of many experts/decision makers/stakeholders in the decision processes. As a result, large-scale group decision making (LSGDM) has attracted the attention of many researchers in the last decade and many studies have been conducted in order to face the challenges associated with the topic. Therefore, this paper aims at reviewing the most relevant studies about LSGDM, identifying the most profitable research trends and analyzing them from a critical point of view. To do so, the Web of Science database has been consulted by using different searches. From these results a total of 241 contributions were found and a selection process regarding language, type of contribution and actual relation with the studied topic was then carried out. The 87 contributions finally selected for this review have been analyzed from four points of view that have been highly remarked in the topic, such as the preference structure in which decision-makers’ opinions are modeled, the group decision rules used to define the decision making process, the techniques applied to verify the quality of these models and their applications to real world problems solving. Afterwards, a critical analysis of the main limitations of the existing proposals is developed. Finally, taking into account these limitations, new research lines for LSGDM are proposed and the main challenges are stressed out.      

A decision support model for group decision making with intuitionistic fuzzy linguistic preferences relations

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was introduced to efficiently cope with situations in which the membership degree and non-membership degree are represented as linguistic terms. For group decision making (GDM) problems with IFLPRs, two significant and challenging issues are individual consistency and group consensus before deriving the reliable priority weights of alternatives. In this paper, a novel decision support model is investigated to simultaneously deal with the individual consistency and group consensus for GDM with IFLPRs. First, the concepts of multiplicative consistency and weak transitivity for IFLPRs are introduced and followed by a discussion of their desirable properties. Then, a transformation approach is developed to convert the normalized intuitionistic fuzzy priority weights into multiplicative consistent IFLPR. Based on the distance of IFLPRs, the consistency index, individual consensus degree and group consensus degree for IFLPRs are further defined. In addition, two convergent automatic iterative algorithms are proposed in the investigated decision support model. The first algorithm is utilized to convert an unacceptable multiplicative consistent IFLPR to an acceptable one. The second algorithm can assist the group decision makers to achieve a predefined consensus level. The main characteristic of the investigated decision support model is that it guarantees each IFLPR is still acceptable multiplicative consistent when the predefined consensus level is achieved. Finally, several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate the effectiveness and practicality of the investigated model.

     

Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology

In this paper, we propose a new fuzzy multiattribute group decision making method based on intuitionistic fuzzy sets and the evidential reasoning methodology. First, the proposed method uses the evidential reasoning methodology to aggregate each decision maker’s decision matrix and the weights of the attributes to get the aggregated decision matrix of each decision maker. Then, it uses the obtained aggregated decision matrices of the experts, the weights of the experts and the evidential reasoning methodology to get the aggregated intuitionistic fuzzy value of each alternative. Finally, it calculates the transformed value of the obtained intuitionistic fuzzy value of each alternative. The smaller the transformed value, the better the preference order of the alternative. The proposed method can overcome the drawbacks of the existing methods for fuzzy multiattribute group decision making in intuitionistic fuzzy environments.     

A vision-based method for weeds identification through the Bayesian decision theory

One of the objectives of precision agriculture is to minimize the volume of herbicides that are applied to the fields through the use of site-specific weed management systems. This paper outlines an automatic computer vision-based approach for the detection and differential spraying of weeds in corn crops. The method is designed for post-emergence herbicide applications where weeds and corn plants display similar spectral signatures and the weeds appear irregularly distributed within the crop's field. The proposed strategy involves two processes: image segmentation and decision making. Image segmentation combines basic suitable image processing techniques in order to extract cells from the image as the low level units. Each cell is described by two area-based measuring relationships between crop and weeds. The decision making determines the cells to be sprayed based on the computation of a posterior probability under a Bayesian framework. The a priori probability in this framework is computed taking into account the dynamic of the physical system (tractor) where the method is embedded. The main contributions of this paper are: (1) the combination of the image segmentation and decision making processes and (2) the decision making itself which exploits a previous knowledge which is mapped as the a priori probability. The performance of the method is illustrated by comparative analysis against some existing strategies.     

Robust Higher Order Potentials for Enforcing Label Consistency

This paper proposes a novel framework for labelling problems which is able to combine multiple segmentations in a principled manner. Our method is based on higher order conditional random fields and uses potentials defined on sets of pixels (image segments) generated using unsupervised segmentation algorithms. These potentials enforce label consistency in image regions and can be seen as a generalization of the commonly used pairwise contrast sensitive smoothness potentials. The higher order potential functions used in our framework take the form of the Robust P ⁿ model and are more general than the P ⁿ Potts model recently proposed by Kohli et al. We prove that the optimal swap and expansion moves for energy functions composed of these potentials can be computed by solving a st-mincut problem. This enables the use of powerful graph cut based move making algorithms for performing inference in the framework. We test our method on the problem of multi-class object segmentation by augmenting the conventional crf used for object segmentation with higher order potentials defined on image regions. Experiments on challenging data sets show that integration of higher order potentials quantitatively and qualitatively improves results leading to much better definition of object boundaries. We believe that this method can be used to yield similar improvements for many other labelling problems.     

NEGO — Group decision support system

There are two major frameworks for decision making: maximizing and satisficing. A combination of both may be used to describe group decision making (GDM). In the satisficing approach, decision makers (DMs) formulate aspiriation levels or demands which take the form of constraints. Choosing from among different decisions, DMs take into account their preferences or wants, which take the form of objective functions.GDM is divided into two stages: first, each DM makes a decision, and second, DMs negotiate so as to achieve a compromise decision. Negotiating is an iterative process. Negotiations are completed when all demands have been met.The group decision support system “NEGO” assists DMs in finding a compromise. It has been used for solving a GDM problem at the corporate level and is currently utilized in management courses.     

Algorithm for improving additive consistency of linguistic preference relations with an integer optimization model

Linguistic preference relation (LPR) composed by linguistic terms can well express decision makers’ (DMs’) qualitative preference opinion by comparing alternatives with each other. The investigation of its consistency becomes an important issue to guarantee the rationality of the decision making solutions. Therefore, it is significant to investigate the consistency measure and the consistency improving approach for LPRs. In this paper we present a new method for group decision making (GDM) with LPRs. First, an additive consistency index is introduced on the basis of the information of the original LPR to check whether a LPR is acceptably additive consistency. For unacceptably additively consistent LPR, an integer optimization model is further developed to obtain the acceptably additively consistent LPR. Moreover, the optimization model can guarantee the integrity of the information of the LPR with acceptably additive consistency. Then, with respect to GDM with LPRs, an entropy weight method is proposed to determine the weights of DMs. Finally, the proposed methods are implemented in two numerical examples including a GDM problem. Meanwhile, the comparative analysis with existing methods are discussed in detail to demonstrate the validity of the proposed methods.     

A type 2-hesitation fuzzy logic based multi-criteria group decision making system for intelligent shared environments

Intelligent environments aim to maximize the user comfort and safety while achieving other objectives such as energy minimization. Intelligent shared spaces (such as homes, classrooms, offices, libraries, etc.) need to consider the preferences of users from diverse backgrounds. However, there are high levels of uncertainties faced in intelligent shared spaces. Hence, there is a need to employ intelligent decision making systems which can consider the various users preferences and criteria in order to achieve the convenience of the various users while handling the faced uncertainties. Therefore, we propose a Fuzzy Logic-Multi-Criteria Group Decision Making (FL-MCGDM) system which provides a comprehensive valuation from a group of users/decision makers based on the aggregation of users’ opinions and preferences. The proposed FL-MCGDM system employs an interval type-2 fuzzy logic and hesitation index [from Intuitionistic Fuzzy Sets (IFSs)]. We have carried out experiments in the intelligent apartment (iSpace) located in the University of Essex to evaluate various approaches employing group decision making techniques for illumination selection in an intelligent shared environment. It was found that the Footprint of Uncertainty (of interval type-2 fuzzy sets) and hesitation index (of intuitionistic fuzzy sets (IFSs)) are able to provide a measure of the uncertainties present among the various decision makers. The proposed Type 2-Hesitation FL-MCGDM system better agrees with the users’ decision compared to existing fuzzy MCDM including the Fuzzy Logic based TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), type-1 FL-MCGDM and interval type-2 in FL-MCGDM.     

A Novel Approach for Linguistic Group Decision Making Based on Generalized Interval‐Valued Intuitionistic Fuzzy Linguistic Induced Hybrid Operator and TOPSIS

In the multiple attribute linguistic group decision making analysis with interval‐valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval‐valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order‐inducing variable and interval‐valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval‐valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision‐making approach based on GIVIFLIHA operator and interval‐valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility.     

混合非结构MAGDM的决策导向一致性检验方法

为有效应对现有群决策一致性检验方法的系列弊端,针对群决策的决策导向多元、决策方案众多、决策属性异构、决策信息多样等特征,在引入票权概念解析群决策一致性判定复杂性、刻画非结构多属性群决策合意信息表征假设情景的基础上,通过对常规混合非结构多属性群决策（MAGDM）问题进行公理化描述,并依据从方案层面到属性层面的整体决策信息判定策略,给出决策导向层面的整体判断信息一致性检验方法、多轮次非一致性决策信息调整策略及信息集结方法。案例应用结果表明提出的方法有效、可行。     

Revisiting the supplier selection problem: An integrated approach for group decision support

Decision support for supplier selection is a highly researched theme in procurement management literature. However applications of group decision support theories are yet to be explored extensively in this domain. This study proposes an approach for group decision support for the supplier selection problem by integrating fuzzy Analytic Hierarchy Process (AHP) for group decision making and fuzzy goal programming for discriminant analysis. In the first step, the fuzzy AHP theory with the Geometric Mean Method has been used to prioritize and aggregate the preferences of a group of decision makers. Then consensus has been developed between these aggregated priorities using the Ordinal Consensus Improvement Approach. Subsequently, the consensual priorities of this group of decision makers have been integrated with fuzzy goal programming theory for discriminant analysis to provide predictive decision support. Finally it has been shown through a case study how the integrated approach using fuzzy AHP for group decision making and fuzzy goal programming with soft constraints has been more effective as compared to an existing approach for group decision making using only AHP.     

A De Novo multi-approaches multi-criteria decision making technique with an application in performance evaluation of material handling device

Application of multiple conventional approaches to a particular multi-criteria decision making (MCDM) problem often suffers rank reversal giving rise to confusion and ambiguity in appropriate decision making. To eradicate the confusion, this paper proposes a De Novo multi-approaches multi-criteria decision making method namely Technique of Precise Order Preference (TPOP). The TPOP first examines the inconsistency in the ranking order of the alternatives of a MCDM problem by using multiple conventional approaches. If inconsistency/rank reversal in ranking order of the alternatives exists then TPOP, using advanced version of entropy weighting method introduced in this research work, measures weights of the final selection values of conventional approaches. Subsequently, TPOP based on these weights and final selection values computes precise selection indices (PSI) that determines accurate ranking order for the alternatives. The proposed technique is illustrated by two real life examples on material handling device (MHD) ranking and selection problems. The first example is initially solved using five conventional integrated fuzzy multi-criteria decision making techniques (FMCDMs) whereas the second example is taken from previous researchers’ works. The results obtained using TPOP justify the validity, applicability and requirements of the proposed technique. The study shows that the proposed multi-approaches, multi-criteria decision making technique can be a useful and effective model in MCDM.     

Multi-criteria group decision making with incomplete hesitant fuzzy preference relations

In order to simulate the hesitancy and uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of hesitant fuzzy preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. This paper defines the concept of additive consistent hesitant fuzzy preference relations. The characterizations of additive consistent hesitant fuzzy preference relations are studied in detail. Owing to the limitations of the experts’ professional knowledge and experience, the provided preferences in a hesitant fuzzy preference relation are usually incomplete. Consequently, this paper introduces the concepts of incomplete hesitant fuzzy preference relation, acceptable incomplete hesitant fuzzy preference relation, and additive consistent incomplete hesitant fuzzy preference relation. Then, two estimation procedures are developed to estimate the missing information in an expert's incomplete hesitant fuzzy preference relation. The first procedure is used to construct an additive consistent hesitant fuzzy preference relation from the lowest possible number, (n − 1), of pairwise comparisons. The second one is designed for the estimation of missing elements of the acceptable incomplete hesitant fuzzy preference relations with more known judgments. Moreover, an algorithm is given to solve the multi-criteria group decision making problem with incomplete hesitant fuzzy preference relations. Finally, a numerical example is provided to illustrate the solution processes of the developed algorithm and to verify its effectiveness and practicality.