一种改进的模糊软集多参数决策方法

模糊软集多参数决策方法中经常将Zadeh交与代数积使用在数据融合方法中,在一些实际应用中会产生信息缺失,导致决策者无法做出准确的选择。针对这一问题,结合Einstein运算法则提出一种新的数据融合方法,用于解决信息缺失和对象无法排序的问题。所提出的基于模糊软集的多参数决策方法是通过Einstein积运算进行多个参数集合的整合,从而得到一个合成模糊软集,再由合成模糊软集计算得到对照矩阵与得分表,最终得到对象的全排序,为决策者提供判断依据。通过实例结果,可以验证新方法在决策问题中的正确性和有效性。     

On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods

In this paper, a kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z-soft rough fuzzy sets. As a novel Z-soft fuzzy rough set, its applications in the corresponding decision making problems are established. It is noteworthy that the underlying concepts keep the features of classical Pawlak rough sets. Moreover, this novel approach will involve fewer calculations when one applies this theory to algebraic structures. In particular, an approach for the method of decision making problem with respect to Z-soft fuzzy rough sets is proposed and the validity of the decision making methods is testified by a given example. At the same time, an overview of techniques based on some types of soft set models is investigated. Finally, the numerical experimentation algorithm is developed, in which the comparisons among three types of hybrid soft set models are analyzed.     

基于软区分矩阵的模糊软集决策方法及其应用

通过在模糊软集中引入水平软集,用软区分矩阵来处理决策问题。首先,利用模糊软集的水平软集,将模糊软集转化为经典软集。其次,在软集中引入软区分矩阵的概念,提出了一种基于软区分矩阵解决模糊软集的新算法来处理决策问题。最后,通过实例说明了该算法的可行性。     

基于软直觉multiplicative集的决策方法

针对软直觉模糊集在决策中出现的部分反直觉的现象,结合直觉multiplicative集,首先提出了一种新的软集模型——软直觉multiplicative集,推广了软集和直觉multiplicative集;然后,研究了软直觉multiplicative集的基本运算和性质,同时,给出了基于软直觉multiplicative集理论的决策算法;最后,给出软直觉multiplicative集在决策中的一个应用实例,通过实例说明了该方法的正确性和有效性。     

Group decision making in medical system: An intuitionistic fuzzy soft set approach

In medical system, there may be many critical diseases, where experts do not have sufficient knowledge to handle those problems. For these cases, experts may provide their opinion only about certain aspects of the disease and remain silent for those unknown features. Feeling the need of prioritizing different experts based on their given information, this article uses a novel concept for assigning confident weights to different experts which are mainly based on their provided information. Experts provide their opinions about various symptoms using intuitionistic fuzzy soft matrix (IFSM). In this article, we propose an algorithmic approach based on intuitionistic fuzzy soft set (IFSS) which explores a particular disease reflecting the agreement of all experts. This approach is guided by the group decision making (GDM) model and uses cardinals of IFSS as novel concept. We have used choice matrix (CM) as an important parameter which is based on choice parameters of individual expert. This article has also validated the proposed approach using distance measurements and consents of the majority of experts. The effectiveness of the proposed approach is demonstrated using a suitable case study.     

基于Vague软集的模糊群决策方法研究

运用传统的模糊集进行模糊型群决策时存在一定的困难,而Vague软集是一种处理不确定信息的重要工具。为此,给出了一种加权的Vague软集间相似度定义,并运用Vague软集对备选方案进行评判;在此基础上运用正态云模型进行群体一致性评判,将基于Vague软集的模糊群决策方法应用于供应商选择问题中,结果表明,Vague软集能极大地提高模糊群决策的科学性和有效性。     

考虑风险偏好的区间直觉模糊软集型多属性决策方法

文章针对多方参与、评价指标有差异且存在模糊性的多属性方案优选问题,提出了一种考虑风险偏好的区间直觉模糊软集决策方法.对这类区间直觉模糊软集的多属性决策问题,提出了一个三阶段的决策方法,且按照决策者三种不同风险偏好,给出了相应的决策原则.在此基础上,文章选择了其中一种情形提出了具体的决策算法.最后,文章通过数值算例验证了该方法的可行性和有效性,同时采用综合得分值对该方法的结果进行了一致性的验证和讨论.该方法不仅可以很好地解决这类多属性方案优选问题,也能进一步推广到多属性方案的排序问题中.     

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.     

Fermatean fuzzy linguistic set and its application in multicriteria decision making

In this paper, we propose the concept of Fermatean fuzzy linguistic term sets based on linguistic term sets and Fermatean fuzzy sets. The basic operational laws, the score function, and the accuracy function of Fermatean fuzzy linguistic numbers are provided. Then we propose the Fermatean fuzzy linguistic weighted aggregation operator, the Fermatean fuzzy linguistic weighted geometric operator, and the Fermatean fuzzy linguistic distance measures. Furthermore, we extend the TOPSIS method to the proposed distance measures, and the ranking of alternatives is obtained under a Fermatean fuzzy linguistic environment. An example is provided to illustrate the feasibility and effectiveness of the proposed method, and a comparison with the existing method is also analyzed. Finally, the sensitivity analysis of the parameter in the proposed distance measure is also discussed.     

The normal parameter reduction of soft sets and its algorithm

This paper is concerned with the reduction of soft sets and fuzzy soft sets. Firstly, the problems of suboptimal choice and added parameter set of soft sets are analyzed. Then, we introduce the definition of normal parameter reduction in soft sets to overcome these problems. In addition, a heuristic algorithm of normal parameter reduction is presented. Two new definitions, parameter important degree and decision partition, are proposed for analyzing the algorithm of normal parameter reduction. Furthermore, the normal parameter reduction is also investigated in fuzzy soft sets.     

A ranking function based on principal‐value Pythagorean fuzzy set in multicriteria decision making

Multicriteria decision making (MCDM) has been attracting attention in recent years. There are two essential directions in the research territory, one direction is the research of representation of evaluation information and another is the construction of ranking function. In this paper, we consider some nonstandard fuzzy sets, intuitionistic, and interval‐valued fuzzy sets. Especially, the Pythagorean membership grade and Pythagorean fuzzy set receive much attention. Then, to reflect the importance of principal value, we shall propose the principal‐value Pythagorean fuzzy number (p‐PFN) and principal‐value Pythagorean fuzzy set. Furthermore, a novel ranking function is constructed to select the ideal alternative(s) based on p‐PFNs in MCDM. Finally, an investment strategy decision‐making problem is proposed to reveal the availability and practicability of the function under the new environment.     

基于核模糊聚类的变分水平集医学图像分割方法

针对现有无须重新初始化的变分水平集分割模型, 存在对边缘模糊、对比度差等图像不是很敏感、分割效果不理想的问题, 提出了一种基于核模糊聚类的变分水平集医学图像分割方法。将原始图像进行核模糊C-均值聚类, 把得到的聚类结果带入初始化水平集函数得到初始轮廓, 最后利用李模型的分割方法实现最终的图像分割。实验结果表明, 该方法具有良好的分割质量, 适应性强, 同时可减少迭代次数。     

A review of soft consensus models in a fuzzy environment

In the consensus reaching processes developed in group decision making problems we need to measure the closeness among experts’ opinions in order to obtain a consensus degree. As it is known, to achieve a full and unanimous consensus is often not reachable in practice. An alternative approach is to use softer consensus measures, which reflect better all possible partial agreements, guiding the consensus process until high agreement is achieved among individuals. Consensus models based on soft consensus measures have been widely used because these measures represent better the human perception of the essence of consensus. This paper presents an overview of consensus models based on soft consensus measures, showing the pioneering and prominent papers, the main existing approaches and the new trends and challenges.     

A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment

Although multiple attribute decision making (MADM) problems with both individual attribute data of a single alternative and collaborative attribute data of pairwise alternatives exist in the real world, they have seldom been a focus of research. This paper proposes a MADM method using individual and collaborative attribute data in a fuzzy environment, in which experts use linguistic variables to express their opinions. In the method, first, the evaluation matrix of individual attributes date and the judgment matrix of collaborative attributes data are constructed. Then, the central dominance of one alternative outranking other all alternatives is defined for aggregating the collaborative data. From this, an integrated decision matrix incorporating individual and collaborative attribute data is constructed. Further, based on an extended TOPSIS, the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS) are determined, and the relative closeness of each alternative to the FPIS and FNIS is calculated to determine the ranking order of all alternatives. Finally, two examples are used to illustrate the applicability of the proposed method.     

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.     

A fuzzy set based solution method for multiobjective optimal design problem of mechanical and structural systems using functional-link net

The principle of solving multiobjective optimization problems with fuzzy sets theory is studied. Membership function is the key to introduce the fuzzy sets theory to multiobjective optimization. However, it is difficult to determine membership functions in engineering applications. On the basis of rapid quadratic optimization in the learning of weights, simplification in hardware as well as in computational procedures of functional-link net, discrete membership functions are used as sample training data. When the network converges, the continuous membership functions implemented with the network. Membership functions based on functional-link net have been used in multiobjective optimization. An example is given to illustrate the method.     

A robust algorithm for solution of the fuzzy clustering problem on the basis of the fuzzy joint points method

The approach called the method of Fuzzy Joint Points (FJP) is considered in which the fuzziness of clusterization lies in the detailedness of taking into account properties of elements in forming sets of similar elements. Based on this approach, a new robust variant of the FJP algorithm is proposed. The properties of this FJP algorithm are analyzed and a sufficient condition for the correct recognition of the hidden structure of clusters is proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 10–22, January–February 2008.     

Notes on “Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making”

The aim of this note is to point out and correct some errors in the definitions, notations operations and possibilistic programming model introduced by Sadi-Nezhad and Akhtari (2008) and hereby develop two correct possibilistic programming models for fuzzy multidimensional analysis of preference in the fuzzy multiattribute group decision making problems with both the fuzzy weight vector and the fuzzy positive ideal solution (PIS) unknown a priori.     

Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets

Uncertainty is an important factor in any decision-making process. Different tools and approaches have been introduced to handle the uncertain environment of group decision making. One of the latest tools in dealing with uncertainty is Pythagorean fuzzy sets (PFSs). These sets extend the concept of intuitionistic fuzzy sets. To show the advantages of these new sets, this paper offers a novel last aggregation group decision-making process for weighting and evaluating. The methodology employs a new approach in computing the weight of decision makers. Moreover, the concept of entropy is applied to address the fuzziness of weights of evaluation criteria in the process. The method develops a new index in ranking the alternatives. Finally, the proposed method is last aggregation, which means it will be more precise in situations with high variations in decision makers’ judgments. To show the applicability of the method, an example from the literature is adopted and solved for internet companies.     

A new flexible and reliable IVF-TOPSIS method based on uncertainty risk reduction in decision making process

One of the challenging and famous types of MCDM (Multiple Criteria Decision Making) problems that includes both quantitative and qualitative criteria is Facility location selection problem. For the common fuzzy MCDM problems (Type-1 fuzzy MCDM problems), the ratings of alternatives with respect to the criteria or/and the values of criteria weights, are expressed by the common fuzzy numbers. However, in the majority of cases, determining the exact membership degree for each element of the fuzzy sets which are considered for the ratings of alternatives with respect to the criteria or/and the values of criteria weights as a number in interval [0,1], is difficult. In this situation, the ratings of alternatives with respect to the criteria or/and the values of criteria weights, are expressed by the IVFNs (Interval Valued Fuzzy Numbers) and thereby the IVF-MCDM (Interval Valued Fuzzy MCDM) methods should be used. In this paper, the authors propose an IVF-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method based on uncertainty risk reduction in decision making process. By using this method, the reliability of the captured decisions in an IVF decision making problem is significantly increased. The proposed method is applied for solving a real application problem related to selecting a suitable location for digging some pits for municipal wet waste landfill in one of the largest cities in Iran. The proposed method is also compared with another IVF-TOPSIS method. As a result, the authors concluded that in addition to benefits such as simplicity and ease of use that exist in the previous IVF-TOPSIS methods, the proposed method has a significant reliability and flexibility and is practical for facility location selection problems and other IVF-MCDM problems.