A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices

This article presents a goal programming framework to solve group decision making problems where decision-makers’ judgments are provided as incomplete interval additive reciprocal comparison matrices (IARCMs). New properties of multiplicative consistent IARCMs are put forward and used to define consistent incomplete IARCMs. A two-step goal programming method is developed to estimate missing values for an incomplete IARCM. The first step minimizes the inconsistency of the completed IARCMs and controls uncertainty ratios of the estimated judgments within an acceptable threshold, and the second step finds the most appropriate estimated missing values among the optimal solutions obtained from the previous step. A weighted geometric mean approach is proposed to aggregate individual IARCMs into a group IARCM by employing the lower bounds of the interval additive reciprocal judgments. A two-step procedure consisting of two goal programming models is established to derive interval weights from the group IARCM. The first model is devised to minimize the absolute difference between the logarithm of the group preference and that of the constructed multiplicative consistent judgment. The second model is developed to generate an interval-valued priority vector by maximizing the uncertainty ratio of the constructed consistent IARCM and incorporating the optimal objective value of the first model as a constraint. Two numerical examples are furnished to demonstrate validity and applicability of the proposed approach

Study on Approaches to Interval-Valued Intuitionistic Fuzzy Multiple Attribute Decision Making with Incomplete Information

多属性决策可以描述为从有限个方案集中选择足够好的方案以获得最优目标的决策过程。可是，注意到大多数决策问题具有不确定性，并且对于不同的问题传统的决策方法通常是代价昂贵的和依赖数学上的近似方法(如非线性问题的线性化)，这样可能导致决策问题在性能方面的缺乏。因此，实用的有助决策的重要方面是提供处理不精确和模糊信息的能力。在这种情况下，模糊多属性决策方法通常比传统的多属性决策方法做得好，模糊多属性决策被Bellman和Zadeh视为目标或约束条件本质上是模糊的决策过程。从模糊数的结构来看，区间直觉模糊集作为模糊集的扩展来描述决策信息是一种非常有用的方式，因为区间直觉模糊集的隶属函数和非隶属函数是区间型...Multiple attribute decision making (MADM) may be characterised as a process of choosing or selecting 'sufficiently good' alternative(s) or course(s) of action, from a set of alternatives, to attain a goal. It should be noted, however, that much decision making involves uncertainty, and for difficult problems, conventional (nonfuzzy) methods are usually expensive and depend on mathematical approxim...学位：工学硕士院系专业：信息科学与技术学院自动化系_系统工程学号：2322006115257

Consistency test and weight generation for additive interval fuzzy preference relations

Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by Tanino (Fuzzy Sets Syst 12:117–131, 1984), a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. Then, a revised approach is proposed to obtain priority weights from a fuzzy preference relation. A revised definition is put forward for additive consistent interval fuzzy preference relations. Subsequently, linear programming models are established to generate interval priority weights for additive interval fuzzy preference relations. A practical procedure is proposed to solve group decision problems with additive interval fuzzy preference relations. Theoretic analysis and numerical examples demonstrate that the proposed methods are more accurate than those in Xu and Chen (Eur J Oper Res 184:266–280, 2008b)

A Combination of Extended Fuzzy AHP and Fuzzy GRA for Government E-Tendering in Hybrid Fuzzy Environment

The recent government tendering process being conducted in an electronic way is becoming an inevitable affair for numerous governmental agencies to further exploit the superiorities of conventional tendering. Thus, developing an effective web-based bid evaluation methodology so as to realize an efficient and effective government E-tendering (GeT) system is imperative. This paper firstly investigates the potentiality of employing fuzzy analytic hierarchy process (AHP) along with fuzzy gray relational analysis (GRA) for optimal selection of candidate tenderers in GeT process with consideration of a hybrid fuzzy environment with incomplete weight information. We proposed a novel hybrid fuzzy AHP-GRA (HFAHP-GRA) method that combines an extended fuzzy AHP with a modified fuzzy GRA. The extended fuzzy AHP which combines typical AHP with interval AHP is proposed to obtain the exact weight information, and the modified fuzzy GRA is applied to aggregate different types of evaluation information so as to identify the optimal candidate tenderers. Finally, a prototype system is built and validated with an illustrative example for GeT to confirm the feasibility of our approach

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed

Multiplicative Consistency Ascertaining, Inconsistency Repairing, and Weights Derivation of Hesitant Multiplicative Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0-1 mixed programming models and simple algebraic operations are proposed to ascertain the multiplicative consistency of HMPRs. Then, some goal programming models are developed to generate the weights from consistent HMPRs and to revise inconsistent HMPRs. An integrated procedure to manage the multiplicative consistencies of HMPRs is designed. The proposed methods are also extended to accommodate incomplete HMPRs, and to estimate missing values. Finally, some numerical examples, a comparative analysis with existent approaches, and a simulation analysis are included to illustrate the practicality and effectiveness of the developed models

An IVIF-ELECTRE outranking method for multiple criteria decision-making with interval-valued intuitionistic fuzzy sets

The method of ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing Reality, ELECTRE) is a well-known and widely used outranking method for handling decision-making problems. The purpose of this paper is to develop an interval-valued intuitionistic fuzzy ELECTRE (IVIF-ELECTRE) method and apply it to multiple criteria decision analysis (MCDA) involving the multiple criteria evaluation/selection of alternatives. Using interval-valued intuitionistic fuzzy (IVIF) sets with an inclusion comparison approach, concordance and discordance sets are identified for each pair of alternatives. Next, concordance and discordance indices are determined using an aggregate importance weight score function and a generalised distance measurement between weighted evaluative ratings, respectively. Based on the concordance and discordance dominance matrices, two IVIF-ELECTRE ranking procedures are developed for the partial and complete ranking of the alternatives. The feasibility and applicability of the proposed methods are illustrated with a multiple criteria decision-making problem of watershed site selection. A comparative analysis of other MCDA methods is conducted to demonstrate the advantages of the proposed IVIF-ELECTRE methods. Finally, an empirical study of job choices is implemented to validate the effectiveness of the current methods in the real world. First published online: 17 Sep 201