Prioritized multi-criteria decision making based on preference relations

There may exist priority relationships among criteria in multi-criteria decision making (MCDM) problems. This kind of problems, which we focus on in this paper, are called prioritized MCDM ones. In order to aggregate the evaluation values of criteria for an alternative, we first develop some weighted prioritized aggregation operators based on triangular norms (t-norms) together with the weights of criteria by extending the prioritized aggregation operators proposed by Yager (Yager, R. R. (2004). Modeling prioritized multi-criteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 34, 2396–2404). After discussing the influence of the concentration degrees of the evaluation values with respect to each criterion to the priority relationships, we further develop a method for handling the prioritized MCDM problems. Through a simple example, we validate that this method can be used in more wide situations than the existing prioritized MCDM methods. At length, the relationships between the weights associated with criteria and the preference relations among alternatives are explored, and then two quadratic programming models for determining weights based on multiplicative and fuzzy preference relations are developed.     

Monotonic argument‐dependent OWA operators

The ordered weighted averaging (OWA) operator introduced by Yager is one of the most popular aggregation technique. In this paper, we develop two kinds of argument‐dependent OWA (DOWA) operators including the pessimistic‐dependent OWA (PE‐DOWA) operator and optimistic‐dependent OWA (OP‐DOWA) operator, that point out that the PE‐DOWA operator is decreasing and the OP‐DOWA operator is increasing, and investigate some properties of our proposed monotonic DOWA operators in detail. Furthermore, we introduce the concept of original function in which a gradient vector generates the weights of the PE‐DOWA and OP‐DOWA operators. Meanwhile, we propose two classes of original functions including summing‐type original function and multiplying‐type original function and investigate the sufficient monotonic conditions for the DOWA operators generated by the original functions. Finally, we discuss the characteristics and properties of our proposed DOWA operators in detail and use a numerical example to illustrate the flexibility of our proposed operators.     

毕达哥拉斯模糊优先集成算子及其决策应用

作为直觉模糊集的推广形式,毕达哥拉斯模糊数能更好地刻画现实中的不确定性,此外在某些问题上,方案的属性之间往往具有优先关系,针对此类信息的集成问题,将毕达哥拉斯模糊数与优先集成算子相结合,提出了毕达哥拉斯模糊优先集成算子,包括毕达哥拉斯模糊优先加权平均算子和毕达哥拉斯模糊优先加权几何算子,并讨论了这些算子的性质。在此基础上,提出了毕达哥拉斯模糊优先集成算子的多属性决策方法,最后将其应用于国内四家航空公司服务质量评价中,说明了该算子的有效性和可行性。     

Prioritized intuitionistic fuzzy aggregation operators

In some multi-attribute decision making problems, distorted conclusions will be generated due to the lack of considering various relationships among the attributes of decision making. In this paper, we investigate the prioritization relationship of attributes in multi-attribute decision making with intuitionistic fuzzy information (i.e., partial or all decision information, like attribute values and weights, etc., is represented by intuitionistic fuzzy values (IFVs)). Firstly, we develop a new method for comparing two IFVs, based on which the basic intuitionistic fuzzy operations satisfy monotonicities. In addition, we devise a method to derive the weights with intuitionistic fuzzy forms, which can indicate the importance degrees of the corresponding attributes. Then we develop a prioritized intuitionistic fuzzy aggregation operator, which is motivated by the idea of the prioritized aggregation operators [R.R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 48 (2008) 263–274]. Furthermore, we propose an intuitionistic fuzzy basic unit monotonic (IF-BUM) function to transform the derived intuitionistic fuzzy weights into the normalized weights belonging to the unit interval. Finally, we develop a prioritized intuitionistic fuzzy ordered weighted averaging operator on the basis of the IF-BUM function and the transformed weights.     

A Prioritized Information Fusion Method for Handling Fuzzy Decision-Making Problems

Although Yager has presented a prioritized operator for fuzzy subsets, called the non-monotonic operator, it can not be used to deal with multi-criteria fuzzy decision-making problems when generalized fuzzy numbers are used to represent the evaluating values of criteria. In this paper, we present a prioritized information fusion algorithm based on the similarity measure of generalized fuzzy numbers. The proposed prioritized information fusion algorithm has the following advantages: (1) It can handle prioritized multi-criteria fuzzy decision-making problems in a more flexible manner due to the fact that it allows the evaluating values of criteria to be represented by generalized fuzzy numbers or crisp values between zero and one, and (2) it can deal with prioritized information filtering problems based on generalized fuzzy numbers.     

A novel ordered weighted averaging weight determination based on ordinal dispersion

One of the most common techniques to find the adequate weights in ordered weighted averaging (OWA) operators is based on the orness concept, where the weights are determined by maximizing the entropy (variation) for a fixed orness value. But such an entropy represents a dispersion measure for nominal variables, while weights in an OWA operator are essentially ordinal rather than nominal. Hence, in this paper, we propose a novel way to determine OWA weights based upon ordinal dispersion measures instead of an standard entropy measure. From this approach, we find an explicit formula for the weights, and we illustrate differences by means some multicriteria decision-making examples.     

Scaled prioritized aggregation operators and their applications to decision making

As an extension of the prioritized aggregation operators by Yager (Int J Approx Reason 48:263–274, 2008), this paper uses the priority labels to express the prioritized relationship between criteria and presents some scaled prioritized aggregation operators, including the scaled prioritized score operator and the scaled prioritized averaging operator. Moreover, we consider the priority under uncertain environment and develop the uncertain prioritized aggregation operators, including the uncertain prioritized scoring operator and the uncertain prioritized averaging operator. We investigate the properties of these operators and build the models to derive the weights by maximizing square deviations from a possible range to distinguish the candidate alternatives mostly. Furthermore, approaches to multi-attribute decision making based on the proposed operators are given, which have benefits over the TOPSIS method (Behzadian, Expert Syst Appl 39:13051–13069, 2012) and the methods based on the OWA operator (Zhou and Chen, Fuzzy Sets Syst 168:18–34, 2011) when prioritized relationship between criteria is considered. Finally, examples are illustrated to show the feasibility and validity of the new approaches to the application of decision making.     

Intuitionistic fuzzy PRI-AND and PRI-OR aggregation operators

In this paper, we investigate the multi-attribute decision making (MADM) problem under Atanassov’s intuitionistic fuzzy environment in which the attributes are in different priority levels. We develop the intuitionistic fuzzy prioritized “and” operator and intuitionistic fuzzy prioritized “or” operator, which are motivated by the idea of Yager’s prioritized “and” operator and prioritized “or” operator. These intuitionistic fuzzy prioritized aggregation operators can be applied to aggregate intuitionistic fuzzy information when the attributes are in different priority levels. A practical example is used to illustrate the applicability and effectiveness of the proposed intuitionistic fuzzy prioritized “or” operator.     

Prioritized aggregation operators based on the priority degrees in multicriteria decision-making

We consider the multicriteria decision-making (MCDM) problems where there exists a prioritization relationship over the criteria. We introduce the concept of the priority degree. Then we give three kinds of prioritized aggregation operators based on the priority degrees: the prioritized averaging operator with the priority degrees, the prioritized scoring operator with the priority degrees, and the prioritized ordered weighted averaging operator with the priority degrees. Some desired properties of these prioritized aggregation operators are also investigated. The priority degree plays an important role in the prioritized MCDM problems. We also investigate how to select a proper priority degree according to the giving decision information. By using an illustrative example, we show that the prioritized aggregation operators based on the priority degrees provide the decision-makers more choices and they are more flexible in the process of decision-making.     

On the dispersion measure of OWA operators

We describe some basic features of the OWA operator. We turn to the problem of determining the weights associated with this operator and particularly the maximal dispersion (entropy) approach. We consider the possibility of using minimization of dispersion. After discussing concerns with both maximization and minimization of dispersion we investigate the possibility of finding an optimal solution intermediate to these extremes. We next consider alternative measures of dispersion. We introduce a fundamental requirement for a measure of dispersion called the Preference for Equal Division. A number of general classes of dispersion measures are provided notable among these are those based on t-norm and t-conorm operators.     

面向平层多房间的内墙作业移动机器人路径规划

本文针对多房间的移动机器人内墙作业的路径规划任务,提出一种两阶段路径规划方法.第1阶段针对沿墙作业过程中环境存在灰尘或雾气造成的传感器失效问题,以及房间多出口时路径规划不完整问题,我们提出起点自动选择沿墙路径规划方法,基于栅格地图离线生成沿墙规划路径.第2阶段,针对点到点路径规划过程中的动态避障问题,我们提出一种基于PSAC (prioritized experience replay soft actor critic)算法的点到点路径规划方法,在软行动者-评论家(soft actor critic, SAC)的中引入优先级经验回放策略,实现机器人的动态避障.实验部分设计了沿墙路径规划对比实验和动态避障的对比实验,验证本文所提出的方法在室内沿墙路径规划和点到点路径规划的有效性.     

基于算符优先算法的逻辑表达式合法性判断

基于字符串的逻辑表达式的合法性进行判断在很多领域和场合下是经常遇到的 ,比如 :文件检索 ,信息查询等等 .而我们常见的文件检索与信息查询软件大多仅仅支持几个简单的逻辑算符 ,例如 :与、或 ,并且逻辑表达式中的组成字符串只能做简单的与、或运算 ,使得逻辑表达式的表达能力有限 ,用户使用的灵活性小 .本文针对上述问题进行了研究 ,采用算符优先算法给出了对该问题一种非常实用而又简练的实现方法 ,不但实现了普通搜索引擎所支持的简单的逻辑表达式的合法性判断功能 ,而且扩展了所支持的逻辑表达式的逻辑表达能力 :支持非运算 ;增加了支持逻辑表达式的优先级算符“(”和“)”.这使得逻辑表达式的表达功能和表达灵活性都得到很大的增强和提高 .本文给出的算法还可用于许多其他的基于字符串的逻辑表达式的操作功能 .     

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.     

Generalized prioritized aggregation operators

This paper deals with multicriteria decision‐making problems in which the criteria are partitioned into q categories, and a prioritization relationship exists over categories. We aggregate the criteria in the same priority category by a weighted OWA (ordered weighted averaging) operator and introduce two averaging operators, a generalized prioritized averaging operator and a generalized prioritized OWA operator. In the case with one criterion in each priority category, the two operators reduce to the prioritized averaging operator and the prioritized OWA operator as proposed by Yager. © 2012 Wiley Periodicals, Inc.     

On Pythagorean fuzzy decision making using soft likelihood functions

Multicriteria decision making (MCDM) is to select the optimal candidate which has the best quality from a finite set of alternatives with multiple criteria. One important component of MCDM is to express the evaluation information, and the other one is to aggregate the evaluation results associated with different criteria. For the former, Pythagorean fuzzy set (PFS) is employed to represent uncertain information in this paper, and for the latter, the soft likelihood function developed by Yager is used. To address MCDM issues from a new perspective, the likelihood function of PFS is first proposed in this study and, to improve some of its limitations, the ordered weighted averaging (OWA)-based soft likelihood function is defined, which introduces the attitudinal characteristic to identify decision makers' subjective preferences. In addition, the defined soft likelihood function of PFS is extended by weighted OWA operator considering the importance weight of the argument. Several illustrative cases are provided based on the presented (weighted) OWA-based soft likelihood functions in Pythagorean fuzzy environment for MCDM problem.     

Multiattribute group decision-making based on Pythagorean fuzzy Einstein prioritized aggregation operators

Pythagorean fuzzy set (PFS) is a powerful tool to deal with the imprecision and vagueness. Many aggregation operators have been proposed by many researchers based on PFSs. But the existing methods are under the hypothesis that the decision-makers (DMs) and the attributes are at the same priority level. However, in real group decision-making problems, the attribute and DMs may have different priority level. Therefore, in this paper, we introduce multiattribute group decision-making (MAGDM) based on PFSs where there exists a prioritization relationship over the attributes and DMs. First we develop Pythagorean fuzzy Einstein prioritized weighted average operator and Pythagorean fuzzy Einstein prioritized weighted geometric operator. We study some of its desirable properties such as idempotency, boundary, and monotonicity in detail. Moreover we propose a MAGDM approach based on the developed operators under Pythagorean fuzzy environment. Finally, an illustrative example is provided to illustrate the practicality of the proposed approach.     

Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making

Hamacher product is a t‐norm and Hamacher sum is a t‐conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Hamacher operations to develop some Pythagorean hesitant fuzzy aggregation operators: Pythagorean hesitant fuzzy Hamacher weighted average (PHFHWA) operator, Pythagorean hesitant fuzzy Hamacher weighted geometric (PHFHWG) operator, Pythagorean hesitant fuzzy Hamacher ordered weighted average (PHFHOWA) operator, Pythagorean hesitant fuzzy Hamacher ordered weighted geometric (PHFHOWG) operator, Pythagorean hesitant fuzzy Hamacher induced ordered weighted average (PHFHIOWA) operator, Pythagorean hesitant fuzzy Hamacher induced ordered weighted geometric (PHFHIOWG) operator, Pythagorean hesitant fuzzy Hamacher induced correlated aggregation operators, Pythagorean hesitant fuzzy Hamacher prioritized aggregation operators, and Pythagorean hesitant fuzzy Hamacher power aggregation operators. The special cases of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean hesitant fuzzy multiple attribute decision making problems. Finally, a practical example for green supplier selections in green supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Nonmonotonic OWA operators

 The basic properties of the Ordered Weighted Averaging (OWA) operator are recalled. The role of these operators in the formulation of multi-criteria decision functions, using the concept of quantifier guided aggregation, is discussed. An extended class of OWA operators, one based upon a relaxation of the requirements on the OWA operators, is introduced. This relaxation allows us to consider a new branch of OWA operators, NOMOWA operators, which have negative weights and which exhibit nonmonotonicity. Some special cases of these operators are discussed and then we investigate the role of these nonmonotonic operators in the formulation of multi-criteria decision functions.     

Soft Aggregation Methods in Case Based Reasoning

Our goal is to provide some tools, based on soft computing aggregation methods, useful in the two fundamental steps in case base reasoning, matching the target and the cases and fusing the information provided by the relevant cases. To aid in the first step we introduce a methodology for matching the target and cases which uses a hierarchical representation of the target object. We also introduce a method for fusing the information provided by relevant retrieved cases. This approach is based upon the nearest neighbor principle and uses the induced ordered weighted averaging operator as the basic aggregation operator. A procedure for learning the weights is described.     

On combination rule in Dempster–Shafer theory using OWA-based soft likelihood functions and its applications in environmental impact assessment

Dempster–Shafer theory (DST) was presented as an effective mathematical tool to represent uncertainty. Its significant innovation is to allow the allocation of the belief of mass to sets or intervals, and it becomes a valuable method in the field of decision making and evaluation when accurate information is not available or when knowledge is expressed subjectively by humans. A crucial research issue in DST is the combination of multi-sources of evidence. In this paper, a novel combination rule for Dempster–Shafer structures is developed based on ordered weighted average (OWA)-based soft likelihood functions proposed by Yager. First, the belief intervals, including the belief measures and plausibility measures, of all the hypotheses in the frame of discernment (FOD) are calculated. Second, the representative value of belief interval is defined based on golden rule introduced by Yager. Third, the soft likelihood value of each hypothesis is calculated based on the proposed OWA-based soft likelihood function for belief interval, which can be considered as the combined evidence. The final evaluation results can be employed for practical applications, such as decision making and evaluation. In addition, the improved evidence combination rule is presented which takes into account the weight of evidence. Several illustrative examples are conducted to manifest the use of the developed methods. Finally, an application for environmental impact assessment is given to demonstrate the usefulness of the developed combination rule in DST.