A stochastic multicriteria acceptability analysis–evidential reasoning method for uncertain multiattribute decision‐making problems

Evidential reasoning (ER) is an effective approach for assessing alternatives with uncertain attribute values in the context of decision making. For the ER approach to be able to handle variations in the weights of uncertain attributes in an appropriate manner, this paper proposes a method to solve problems of uncertain multiattribute decision making that involve both uncertain attribute values and uncertain attribute weights, which this method does by combining the ER approach and stochastic multicriteria acceptability analysis‐2 (SMAA‐2). First, the uncertainty in attribute values is described by using a belief decision matrix as in the ER approach. The analytical ER algorithm is then used to create the utility function in the SMAA‐2 model, and that function is used to calculate the probability of different sorting positions of the decision units under weight‐related restrictions. Finally, the results of ranking are obtained by combining the sorting weights. An example is provided to verify the effectiveness of the proposed method.     

Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process

In this article, a new linguistic Pythagorean fuzzy set (LPFS) is presented by combining the concepts of a Pythagorean fuzzy set and linguistic fuzzy set. LPFS is a better way to deal with the uncertain and imprecise information in decision making, which is characterized by linguistic membership and nonmembership degrees. Some of the basic operational laws, score, and accuracy functions are defined to compare the two or more linguistic Pythagorean fuzzy numbers and their properties are investigated in detail. Based on the norm operations, some series of the linguistic Pythagorean weighted averaging and geometric aggregation operators, named as linguistic Pythagorean fuzzy weighted average and geometric, ordered weighted average and geometric with linguistic Pythagorean fuzzy information are proposed. Furthermore, a multiattribute decision‐making method is established based on these operators. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.     

A new DEA‐based method for fully ranking all decision‐making units

Abstract: Decision makers always lay great emphasis on performance evaluation upon a group of peer business units to pick out the best performer. Standard data envelopment analysis models can evaluate the relative efficiency of decision‐making units (DMUs) and distinguish efficient ones from inefficient ones. However, when there are more than one efficient DMU, it is impossible to rank all of them solely according to standard efficiency scores. In this paper, a new method for fully ranking all DMUs is proposed, which is based on the combination of each efficient DMU's influence on all the other DMUs and the standard efficiency scores. This method is effective in helping decision makers differentiate all units' performance thoroughly and select the best performer.     

基于信息熵与证据推理的不确定多属性决策方法

针对不确定多属性决策过程中信息特征呈多样化且属性权重完全未知时难以进行决策的问题,提出了一种基于不确定信息熵的权值计算方法。该方法首先将各种不确定信息转换到统一的信度框架下,计算出不确定信息熵从而获得属性客观权重值。该方法结合证据推理法可实现属性权重未知时不确定信息下的多属性决策。最后以应用实例验证了该方法的有效性和可行性。     

Generating Z‐number based on OWA weights using maximum entropy

In the application of Z‐number, how to generate Z‐number is a significant and open issue. In this paper, we proposed a method of generating Z‐number based on the OWA weights using maximum entropy considering the attitude (preference) of the decision maker. Some numerical examples are used to illustrate the effectiveness of the proposed method. Results show that the attitude (preference) of the decision maker can give an optimal possibility distribution of the reliability for Z‐number using maximum entropy.     

A new possibility degree measure for interval‐valued q‐rung orthopair fuzzy sets in decision‐making

As a generalization of the interval‐valued intuitionistic fuzzy sets, a consciousness of interval‐valued $q$‐rung orthopair fuzzy sets (IV $q$‐ROFSs) is a robust and trustworthy tool to fulfill the imprecise information with an adaptation of the manageable parameter $q\ge 1$. However, the ranking of any interval‐valued numbers is very valuable for interval‐valued decision‐making problems. Possibility degree measure is a worthy tool to manage the degree of possibility of one object over the other. Driven by these requisite characteristics, it is fascinating to manifest the possibility degree of comparison between two IV $q$‐ROFSs, and an innovative method is then encouraged to rank the given numbers. Few properties are checked to explain their features and exhibited the advantages of it over the existing possibility measures with some counterintuitive examples. Later on, we consider the multiattribute group decision making (MAGDM) method and embellish it with numerical examples, to rank the alternatives. Several numerical examples are implemented to test the superiority of the stated MAGDM method and to confer its more manageable and adaptable nature.     

An stochastic multiattribute acceptability analysis‐based method for the multiattribute project portfolio selection problem with rank‐level information

In many cases of practical multiattribute project portfolio selection problems, it is hard to obtain accurate measurements of attributes and precise preference information. Even after a long and costly information gathering, the attribute measurements and the preference information can still be uncertain or inaccurate. Considerable cost saving will be obtained if the selection of an optimal project portfolio can be done using rank‐level information based on some or all the attributes, without knowing the preference information. In this paper, we propose a stochastic multiattribute acceptability analysis‐based method that can deal with mixed rank and cardinal attribute measurements and uses little or no weight information. In the proposed stochastic multiattribute acceptability analysis‐based method, the decision makers need not to express their preferences explicitly or implicitly, so it is particularly useful when no weight information is available at all. A numerical example involving selection of photovoltaic plants in an industrial province in Eastern China is provided to demonstrate the proposed method.     

Quantile induced heavy ordered weighted averaging operators and its application in incentive decision making

To integrate incentives into the information aggregation process in decision making, we propose a new type of aggregation operator, denominated as the quantile induced heavy ordered weighted averaging (QI‐HOWA) operator in this paper. A primary characteristic of this type of operator is that the quantile variable can be used not only to measure the relative performance of alternatives but also to facilitate the incentive preference expression of the decision maker. We further provide a calculation technology of the QI‐HOWA weights, in which various incentive preferences of the decision maker can be considered through parameter adjustment. In addition, we discuss certain properties of the QI‐HOWA operator and note the extent to which they are effective. Finally, a numerical example regarding the selection of optimal alternatives by incentive measures is provided, and the aggregations are compared with those of ordered weighted averaging and unweighted averaging operators to illustrate the validity of the QI‐HOWA operator.     

The use of ordered weighted averaging method for decision making under uncertainty

A decision making under uncertainty (DMUU) prevails at the outset and often evolves into a decision making under partial uncertainty as information on the states of nature, for example, a probability distribution, is advanced. Many methods have emerged for solving the DMUU problems, which includes the classical decision criteria and the domain criterion. Yager (1988) introduced a new approach, the so‐called ordered weighted averaging (OWA) as a viable method for solving the DMUU problems. The OWA weights to be used in the aggregation are generated under the degree of optimism provided by a decision maker and then combined with the reordered payoffs to produce aggregated payoffs for each strategy. The reordering process, one of the characterizing features of the OWA method, enables us to perform various types of aggregations including maximax, maximin, and Hurwicz‐α index in conjunction with the generated weights. The OWA method obviously extends the Hurwicz approach by taking into account the tradeoffs among the entire payoffs while the Hurwicz approach considers a tradeoff only between the two extremes, the maximum and the minimum payoffs. In this paper, we examine the features of the OWA method in light of Milnor's set of requirements for reasonable decision criteria, thus providing a solid methodological foundation for the DMUU. The OWA method can also be used to solve a group DMUU problem by exploiting individual decision results in the situation when the use of a fuzzy majority is advocated.     

An extended COPRAS method for multiattribute group decision making based on dual hesitant fuzzy Maclaurin symmetric mean

The well-known Maclaurin symmetric mean (MSM) and the dual MSM (DMSM) are introduced as important operators to handle multiattribute group decision making (MAGDM) information. The MSM and the DMSM operators have the prominent characteristic of accurately describing the interdependence of multi-input arguments. Due to their advantage, we extend the MSM and the DMSM into the dual hesitant fuzzy environment to aggregate uncertain information. Particularly, we propose some novel aggregation operators, namely dual hesitant fuzzy MSM, weighted dual hesitant fuzzy MSM, dual hesitant fuzzy dual MSM, and weighted dual hesitant fuzzy dual MSM operators. Moreover, we study some properties and special remarks regarding different values of the parameter. With an extension of the complex proportional assessment method, we formulate a new approach for the dual hesitant fuzzy MAGDM. Finally, we test the applicability and feasibility of our proposed method by solving a mobile payment platform selection problem in Ghana.     

Partitioned Bonferroni mean based on two-dimensional uncertain linguistic variables for multiattribute group decision making

The two-dimensional uncertain linguistic variables (2DULVs) add a self-evaluation on the reliability of the assessment results given by decision makers (DMs), so they can better describe some uncertain information, and the partition Bonferroni mean (PBM) operator has the advantages, which assumes that all aggregated arguments are partitioned into several subparts, and members in the same subpart are interrelated and members in different subparts are no interrelationships. However, the traditional PBM can only deal with the crisp numbers and cannot aggregate the 2DULVs. In this paper, we extend the PBM operator to deal with the 2DULVs and propose some PBM operators for 2DULVs. First, we introduce the concepts, properties, operational laws, and comparison methods of 2DULVs, and then we propose the PBM operator for 2DULVs (2DULPBM), the weighted PBM operator for 2DULVs (2DULWPBM), the partitioned geometric Boferroni mean (PGBM) operator for 2DULVs (2DULPGBM), and weighted PGBM operator for 2DULVs (2DULWPGBM). Further, we develop a method to solve multiattribute group decision-making (MAGDM) problems with the 2DULVs. Finally, we give an example to verify that the method based on the proposed operators is effective and influential.     

Multi‐criteria group decision‐making method based on TODIM with probabilistic interval‐valued hesitant fuzzy information

Probabilistic interval‐valued hesitant fuzzy sets (PIV‐HFSs) are suitable for aggregating information from different groups because the probabilistic information of all the groups can be included by using interval values. Moreover, decision makers (DMs) prefer to use interval values to provide evaluation information. Furthermore, the traditional multi‐criteria group decision‐making (MCGDM) approach has some limitations, such as obtaining the DMs' weights with inappropriate methods and neglecting the interactions amongst the criteria and the psychological characteristics of DMs. Motivated by these research background, the main contents of this study are as follows. First, PIV‐HFSs are proposed, and the convex combination operation is extended into PIV‐HFSs. Second, a hybrid MCGDM approach with PIV‐HFSs is suggested that is based on the maximizing deviation method, fuzzy analytic network process (FANP) and TODIM (an acronym in Portuguese for interactive and multi‐criteria decision‐making model). Third, an evaluation case of health management centres based on the service‐specific failure mode and effect analysis (FMEA) is considered. The results show that the most crucial secondary factor is frequency (0.35775) and that the most serious failure mode is the inaccurate check‐in. The results demonstrate that the proposed model can evaluate service quality effectively and that it performs better than other methods.     

Multiple attribute decision making considering aspiration-levels: A method based on prospect theory

In this paper, a method based on prospect theory is proposed to solve the multiple attribute decision making (MADM) problem considering aspiration-levels of attributes, where attribute values and aspiration-levels are represented in two different formats: crisp numbers and interval numbers. According to the idea of prospect theory, aspiration-levels are firstly regarded as the reference points, and the four possible types for comparing an attribute value with an aspiration-level are described. Then, for all possible cases of the four types, the calculation formulae of gains and losses of alternatives concerning attributes are given. By calculating gain and loss of each alternative, a gain matrix and a loss matrix are constructed, respectively. Further, using the value function proposed in prospect theory and the simple additive weighting method, the overall prospect value of each alternative is calculated. Based on the obtained overall prospect values, a ranking of alternatives can be determined. Finally, a numerical example is used to illustrate the use of the proposed method.     

Multicriteria decision‐making approach based on gray linguistic weighted Bonferroni mean operator

The main purpose of this paper is to provide a multicriteria decision‐making (MCDM) approach that applies the gray linguistic Bonferroni mean (BM) operator to address the situations where the criterion values take the form of gray linguistic numbers (GLNs) and the criterion weights are known. First, the related operations and comparison method for GLNs are provided. Subsequently, a BM operator and weighted BM operator of GLNs are developed. Then, based on the gray linguistic weighted BM operator, an MCDM approach is proposed. Finally, an illustrative example is given and a comparison analysis is conducted between the proposed approach and other existing methods to demonstrate the effectiveness and feasibility of the developed approach.     

Multiple attribute decision‐making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q‐rung orthopair fuzzy environment

A Q‐rung orthopair fuzzy set (q‐ROFS) originally proposed by Yager (2017) is a new generalization of orthopair fuzzy sets, which has a larger representation space of acceptable membership grades and gives decision makers more flexibility to express their real preferences. In this paper, for multiple attribute decision‐making problems with q‐rung orthopair fuzzy information, we propose a new method for dealing with heterogeneous relationship among attributes and unknown attribute weight information. First, we present two novel q‐rung orthopair fuzzy extended Bonferroni mean (q‐ROFEBM) operator and its weighted form (q‐ROFEWEBM). A comparative example is provided to illustrate the advantages of the new operators, that is, they can effectively model the heterogeneous relationship among attributes. We prove that some existing known intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are special cases of the proposed q‐ROFEBM and q‐ROFEWEBM operators. Meanwhile, several desirable properties are also investigated. Then, a new knowledge‐based entropy measure for q‐ROFSs is also proposed to obtain the attribute weights. Based on the proposed q‐ROFWEBM and the new entropy measure, a new method is developed to solve multiple attribute decision making problems with q‐ROFSs. Finally, an illustrative example is given to demonstrate the application process of the proposed method, and a comparison analysis with other existing representative methods is also conducted to show its validity and superiority.     

Social facilitation effect in search and decision‐making components of visual inspection

This study aimed to examine the effect of social presence on the performance of the search and decision‐making components of visual inspection. A within‐subject design experiment was conducted. Participants performed easy and difficult search and decision‐making tasks in alone and audience‐present conditions with search time, decision time, decision accuracy rates, and subjective arousal level in both components measured. Results indicated that the presence of an audience shortened (lengthened) the response time in easy (difficult) search and decision‐making components but did not influence decision accuracy rates. The social facilitation intensity in the search component was stronger than that in the decision‐making component. For both components, the performance impairment in difficult tasks was stronger than the performance improvement in easy tasks, and arousal was greater in the audience‐present condition than when working alone. The findings helped clarify the influential mechanisms of the social facilitation effect in visual inspection tasks.     

Signed distance‐based ORESTE for multicriteria group decision‐making with multigranular unbalanced hesitant fuzzy linguistic information

The objective of this study is to develop an integrated approach for solving multicriteria group decision‐making problems with multigranular unbalanced hesitant fuzzy linguistic term sets (HFLTSs). Firstly, a signed distance‐based transformation function is proposed to unify multigranular unbalanced hesitant fuzzy linguistic (HFL) assessments. Secondly, a mathematical programming model based on the maximum consensus is constructed to allocate decision‐makers (DMs)' weights objectively. Thirdly, a new signed distance‐based preference score function is defined to aggregate HFL assessments and determine the weak ranking of alternatives, and a novel preference, indifference, and incomparability test framework is constructed to identify the subtle relations among alternatives. On these bases, a signed distance‐based ORESTE (Organísation, rangement et Synthèse de données relarionnelles, in French) method, in which knowledge regarding criterion values and weights are expressed as multigranular unbalanced HFLTSs, is developed to obtain the ranking of alternatives. Finally, an illustrative example, followed by sensitivity and comparative analyses, is presented to verify the feasibility and effectiveness of the proposed approach.     

基于灰关联深度系数的评价指标客观权重极大熵配置模型

在多属性决策领域中,经典评价指标客观赋权的极大熵模型主要依据指标评价值的差异度进行赋权,极易导致对评价值差异度小的指标作出不重要(权值小)的错误判断,从而产生决策偏差.对此,首先提出灰关联深度系数的概念,以表征指标客观权重包含的信息量大小;同时运用极大熵理论建立评价指标客观权重的极大熵配置模型,以确定多属性决策指标权重,较好地解决了经典模型存在的严重缺陷;最后通过实际案例的对比分析,验证了所提出解决方案的优良性能.     

基于累积前景理论的动态风险灰靶决策方法

研究信息值为区间灰数, 指标权重未知的动态风险决策问题, 提出一种基于累积前景理论和灰靶思想的决策方法. 该方法定义了区间灰数的距离测度和排序方法; 以各指标值的平均值作为参照点计算各时段的前景矩阵; 通过WAA算子将动态前景矩阵集结为静态前景矩阵; 在此基础上求解基于极大熵思想的规划模型得出各指标权重. 构造正负椭球灰靶模型, 根据各方案的正负靶心综合距对方案进行排序. 最后, 通过算例分析结果验证了该方法更加符合决策者的心理行为.

     

A new distance measure based on the weighted induced method and its application to Pythagorean fuzzy multiple attribute group decision making

This paper investigates a novel induced ordered weighted averaging (IOWA) distance operator and its application in Pythagorean fuzzy (PF) multiattribute group decision making (MAGDM). First, a new induced aggregated distance operator named the weighted IOWA distance (WIOWAD) operator is developed, which differs from the existing methods in that it considers the dual roles of the order-inducing variables at the same time. In other words, in addition to inducing the order of the arguments, the order-inducing variables of the WIOWAD operator also plays an important role in moderating the associated weight vector. Some useful properties and different families of the WIOWAD are also discussed. Then, an extension of the WIOWAD within the PF situation is presented, thus obtaining the PFWIOWAD operator. Furthermore, a MAGDM method based on the PFWIOWAD is introduced. Finally, the practicality and effectiveness of proposed approach are illustrated in a research and development project selection problem.