Intuitionistic Fuzzy Hybrid Weighted Aggregation Operators

Intuitionistic fuzzy sets (IFSs) have attracted more and more scholars’ attention due to their powerfulness in expressing vagueness and uncertainty. In the course of decision making with IFSs, aggregation operators play a very important role since they can be used to synthesize multidimensional evaluation values represented as intuitionistic fuzzy values into collective values. This paper proposes a family of intuitionistic fuzzy hybrid weighted aggregation operators, such as the intuitionistic fuzzy hybrid weighted averaging operator, the intuitionistic fuzzy hybrid weighted geometric operator, the generalized intuitionistic fuzzy hybrid weighted averaging operator, and the generalized intuitionistic fuzzy hybrid weighted geometric operator. All these newly developed operators not only can weight both the arguments and their ordered positions simultaneously but also have some desirable properties, such as idempotency, boundedness, and monotonicity. To show the applications of our proposed intuitionistic fuzzy hybrid weighted aggregation operators, a simple schema for decision making with intuitionistic fuzzy information is developed. An example concerning the human resource management is given to illustrate the validity and applicability of the proposed method and also the hybrid weighted aggregation operators.     

直觉模糊逻辑算子研究’

模糊逻辑算子是模糊信息融合、模糊推理及模糊决策的重要工具。针对作为模糊逻辑算子重要扩展的直觉模糊逻辑算子,首先引入了直觉模糊集在特殊格上的等价定义。其次,验证了直觉模糊t-模与s-模的若干重要性质。在此基础上,对两种常用的蕴涵算子：直觉模糊孓蕴涵与直觉模糊R-蕴涵所具有的新性质进行讨论和证明,从而便于直觉模糊逻辑算子的进一步应用。     

语言区间直觉模糊Frank算子

针对语言区间直觉模糊信息的集结问题,文中提出Frank集结算子,并构建解决供应商选择问题的群决策方法.首先引入拓展Frank t-模与s-模定义语言区间直觉模糊集的Frank运算法则,提出语言区间直觉模糊Frank加权平均(LIVIFFWA)算子与几何(LIVIFFWG)算子,证明算子的幂等性、封闭性、单调性等基本性质,剖析算子关于参数的退化性.然后,基于LIVIFFWA算子与LIVIFFWG算子构建语言区间直觉模糊多属性群决策方法,用于解决供应商决策问题.最后,通过共享单车回收供应商选择的案例分析验证文中决策方法的可行性和灵活性,讨论参数变化对决策结果的影响,并验证参数具有表征和反馈决策者态度的能力.     

直觉模糊逻辑的语义算子研究

首先引用Atanassov直觉模糊集的基本概念和运算。在阐明直觉模糊集的集中、扩张、归一化算子之后,新定义了强化算子。通过考察Atanassov直觉模糊集与Zadeh模糊集之间的关系,给出了直觉模糊语言、结构化直觉模糊语言和直觉模糊语义的数学描述,重点对基于直觉模糊集和直觉模糊关系的模糊语言的语义算子,如语气算子、模糊化算子、判定化算子及连接与否定算子等进行了研究,并举例阐明其应用,使直觉模糊逻辑的语义算子得到进一步的拓广。     

加权模糊聚集算子研究

在数据挖掘、模糊专家系统和多Agent协同决策过程中,要经常面对信息聚集技术和对多个模糊数据来源进行聚集运算,一般用得最多的是合取、析取及加权平均等算子,但是不同的领域有着不同的需求,本文着重对加权聚集算子进行研究。首先,提出了加权平均关系与析取关系结合后的析取-加权平均算子,该算子解决了加权平均算子不能区分析取与合取的关系。然后,提出了一种最大加权平均算子和最小加权平均算子,该算子将最大最小值算子与加权平均算子进行了泛化,解决了同时考虑信息局部性特征与信息整体性特征的问题。理论分析表明,本文提出的加权模糊聚集算子对于模糊信息源的聚集运算起到了很好的补充和完善的功能。     

模糊聚合算子在医疗诊断中的应用

模糊性是客观世界的固有属性。该文用Dubois的平均聚合算子M和Yager的有序权平均算子OWA来改进Sanchez和Umeyama的诊断模型,使结果更稳定。     

An Intuitionistic 2‐Tuple Linguistic Information Model and Aggregation Operators

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Fuzzy sets was presented to manage situations in which experts have some membership value to assess an alternative. The fuzzy linguistic approach has been applied successfully to many problems. The linguistic information expressed by means of 2‐tuples, which were composed by a linguistic term and a numeric value assessed in [ ? 0.5, 0.5). Linguistic values was used to assess an alternative and variable in qualitative settings. Intuitionistic fuzzy sets were presented to manage situations in which experts have some membership and nonmembership value to assess an alternative. In this paper, the concept of an I2LI model is developed to provide a linguistic and computational basis to manage the situations in which experts assess an alternative in possible and impossible linguistic variable and their translation parameter. A method to solve the group decision making problem based on intuitionistic 2‐tuple linguistic information (I2LI) by the group of experts is formulated. Some operational laws on I2LI are introduced. Based on these laws, new aggregation operators are introduced to aggregate the collective opinion of decision makers. An illustrative example is given to show the practicality and feasibility of our proposed aggregation operators and group decision making method.     

A Probabilistic and Decision Attitude Aggregation Operator for Intuitionistic Fuzzy Environment

In this paper, a new operator for aggregation of uncertain information under intuitionistic fuzzy environment is proposed. A novel approach is proposed for the selection of best alternative action in the face of the imprecise probabilities and the complex attitudinal character of the decision makers (DMs). This approach is distinguished with its capacity to accommodate the linguistic specification of probabilities as provided by human experts directly without the need to determine the fuzzy membership grades. The focus is to compute the net payoff for each alternative in the face of uncertain states of nature and DM's attitude. The proposed operator and the approach are illustrated through two real case studies.     

直觉模糊集时态逻辑算子及扩展运算性质

首先在考察Atanassov直觉模糊集的基本运算的基础上．引入两个典型的作用于直觉模糊集的时态逻辑算子“□(always)”和“◇(sometimes)”,重点研究了直觉模糊集在直觉模糊时态逻辑算子作用下的若干扩展运算及其性质。最后,将这些运算性质归结为一组定理,并给出详细的证明过程。     

MIN and MAX Operators for Fuzzy Intervals and Their Potential Use in Aggregation Operators

This paper aims at expressing MIN and MAX operations when triangular fuzzy intervals are taken as inputs, that is when Zadeh's extension principle is considered. First presented approach consists in representing fuzzy intervals by means of their profiles. In this context, a computation algorithm can be easily derived for implementing the MIN and MAX operations. Another methodology based on interval relations is then proposed for determining a general analytical expression of the MIN and MAX operations. The potential use of these expressions in the framework of uncertain aggregation operators is illustrated with the two-additive Choquet integral.     

Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation Operators

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with interval‐valued Pythagorean fuzzy sets (IVPFSs). First, the concept, operational laws, score function, and accuracy function of IVPFSs are defined. Then, based on the operational laws, two interval‐valued Pythagorean fuzzy aggregation operators are developed for aggregating the interval‐valued Pythagorean fuzzy information, such as interval‐valued Pythagorean fuzzy weighted average (IVPFWA) operator and interval‐valued Pythagorean fuzzy weighted geometric (IVPFWG) operator. A series of inequalities of aggregation operators are studied. Later, we develop some interval‐valued Pythagorean fuzzy point operators. Moreover, combining the interval‐valued Pythagorean fuzzy point operators with IVPFWA operator, we present some interval‐valued Pythagorean fuzzy point weighted averaging (IVPFPWA) operators, which can adjust the degree of the aggregated arguments with some parameters. Then, we propose an interval‐valued Pythagorean fuzzy ELECTRE method to solve uncertainty MAGDM problem. Finally, an illustrative example for evaluating the software developments is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Some Hesitant Fuzzy Information Aggregation Operators Based on Einstein Operational Laws

The performance and development review (PADR) evaluation in a company is a complex group decision‐making problem that is influenced by multiple and conflicting objectives. The complexity of the PADR evaluation problem is often due to the difficulties in determining the degrees of an alternative that satisfies the criteria. In this paper, we present a hesitant fuzzy multiple criteria group decision‐making methods for PADR evaluation. We first develop some operations based on Einstein operations. Then, we proposed some aggregation operators to aggregate hesitant fuzzy elements and the relationship between our proposed operators and the existing ones are discussed in detail. Furthermore, the procedure of multicriteria group decision making based on the proposed operators is given under hesitant fuzzy environment. Finally, a practical example about PADR evaluation in a company is provided to illustrate the developed method.     

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。     

Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making

Atanassov's intuitionistic fuzzy set (IFS) is a generalization of a fuzzy set that can express and process uncertainty much better. There are various averaging operators defined for IFSs. In this paper, a new type of operator called an intuitionistic fuzzy entropy weighted power average ggregation operator is proposed. The entropy among IFSs is taken into consideration to determine the weights. What's more, the similarity is considered to measure the support degree between two elements of the IFS. Compared with other classical power average operators, the proposed operator is completely driven by data and fully takes into account the relationship among values. Finally, an illustrative example of multiple attribute group decision making is presented to show that the proposed operator is effective and practical.     

直觉模糊S-粗集时态逻辑算子及扩展运算性质

首先给出直觉模糊S-粗集的基本概念,在直觉模糊S-粗集基本运算的基础上,引入两个典型的作用于直觉模糊S-粗集的时态逻辑算子"□(always)"和"◇(sometimes)",重点研究了直觉模糊S-粗集在时态逻辑算子作用下的若干扩展运算及其性质.最后将这些性质归结为定理,并给出详细的证明过程.     

Pythagorean模糊幂Bonferroni集成算子及其决策应用

结合幂平均与Bonferroni平均集成算子的优点,定义了毕达哥拉斯模糊幂Bonferroni平均和毕达哥拉斯模糊加权幂Bonferroni平均集成算子,其不仅考虑了数据信息之间的整体均衡性,还考虑了属性之间可能存在的相互关联关系。研究了这些集成算子的优良性质和特殊情形,并在此基础上提出了一种属性间存在相关性的毕达哥拉斯模糊多属性决策方法。将其应用于国内航空公司的服务质量评价中,并与现有方法进行分析比较,验证了所提方法的有效性和可行性。     

Support-intuitionistic模糊集集成算子及其决策应用

介绍Support-intuitionistic模糊集(SIFS)的概念,定义SIFS运算法则和客观权重,在此基础上提出SIFS加权算术平均算子和加权几何平均算子并证明相关定理。建立基于SIFS模糊信息的决策方法及定义SIFS得分函数和精确函数,利用SIFS支持度确定目标属性的权重使得属性权重成为客观值,加强集成结果的客观性。通过实例验证了该决策方法适用于处理基于SIFS模糊信息环境的决策问题。     

Aggregation Operators and Commuting

Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. We investigate the property of commuting for aggregation operators in connection with their relationship to bisymmetry. In case of bisymmetric aggregation operators we show a sufficient condition ensuring that two operators commute, while for bisymmetric aggregation operators with neutral element we even provide a full characterization of commuting n-ary operators by means of unary distributive functions. The case of associative operations, especially uninorms, is considered in detail.     

多值直觉模糊集定义

基于直觉模糊集的基本概念,考虑其隶属度与非隶属度两个因素的影响,定义了一种多值直觉模糊集,并给出了五种多值直觉模糊集的隶属度与非隶属度的综合评判准则,即算术平均法、几何平均法、去掉最大最小值算术平均法、隶属度中值法、非隶属度中值法,从而使直觉模糊得到了拓广和应用.