On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights

In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig’s method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented.     

New Classification Method for Independent Data Sources Using Pawlak Conflict Model and Decision Trees

The research concerns data collected in independent sets—more specifically, in local decision tables. A possible approach to managing these data is to build local classifiers based on each table individually. In the literature, many approaches toward combining the final prediction results of independent classifiers can be found, but insufficient efforts have been made on the study of tables’ cooperation and coalitions’ formation. The importance of such an approach was expected on two levels. First, the impact on the quality of classification—the ability to build combined classifiers for coalitions of tables should allow for the learning of more generalized concepts. In turn, this should have an impact on the quality of classification of new objects. Second, combining tables into coalitions will result in reduced computational complexity—a reduced number of classifiers will be built. The paper proposes a new method for creating coalitions of local tables and generating an aggregated classifier for each coalition. Coalitions are generated by determining certain characteristics of attribute values occurring in local tables and applying the Pawlak conflict analysis model. In the study, the classification and regression trees with Gini index are built based on the aggregated table for one coalition. The system bears a hierarchical structure, as in the next stage the decisions generated by the classifiers for coalitions are aggregated using majority voting. The classification quality of the proposed system was compared with an approach that does not use local data cooperation and coalition creation. The structure of the system is parallel and decision trees are built independently for local tables. In the paper, it was shown that the proposed approach provides a significant improvement in classification quality and execution time. The Wilcoxon test confirmed that differences in accuracy rate of the results obtained for the proposed method and results obtained without coalitions are significant, with a p level = 0.005. The average accuracy rate values obtained for the proposed approach and the approach without coalitions are, respectively: 0.847 and 0.812; so the difference is quite large. Moreover, the algorithm implementing the proposed approach performed up to 21-times faster than the algorithm implementing the approach without using coalitions.     

Pruning Decision Rules by Reduct-Based Weighting and Ranking of Features

Methods and techniques of feature selection support expert domain knowledge in the search for attributes, which are the most important for a task. These approaches can also be used in the process of closer tailoring of the obtained solutions when dimensionality reduction is aimed not only at variables but also at learners. The paper reports on research where attribute rankings were employed to filter induced decision rules. The rankings were constructed through the proposed weighting factor based on the concept of decision reducts—a feature reduction mechanism embedded in the rough set theory. Classical rough sets operate only in discrete input space by indiscernibility relation. Replacing it with dominance enables processing real-valued data. Decision reducts were found for both numeric and discrete attributes, transformed by selected discretisation approaches. The calculated ranking scores were used to control the selection of decision rules. The performance of the resulting rule classifiers was observed for the entire range of rejected variables, for decision rules with conditions on continuous values, discretised conditions, and also inferred from discrete data. The predictive powers were analysed and compared to detect existing trends. The experiments show that for all variants of the rule sets, not only was dimensionality reduction possible, but also predictions were improved, which validated the proposed methodology.     

GK可能C均值模糊聚类的白菜红外光谱分析

红外光谱分析是基于分子振动与跃迁理论的鉴别物质化学组成的技术.得到的光谱数据常常具有较高的维数和重叠度,这给后续的数据处理带来困难.为此提出一种GK可能C均值聚类算法(GKIPCM),引入了GK聚类算法的马氏距离测度与改进的可能C均值聚类算法(IPCM)的模糊隶属度与聚类中心更新方程,使样本的距离测度具有自适应性且避免...     

模糊子坡代数、模糊等价关系及模糊同余关系的序方面

证明了坡代数(X,+,*)上所有模糊子坡代数构成的集合(SI[0.1](X,+,*),≤),所有模糊理想构成的集合(Id[0.1](X,+,*),≤),所有模糊滤子构成的集合(Fil[0.1](X,+,*),≤)都是([0,1]x,≤)的子完备格,所有模糊等价关系构成的集合(Equ[0.1](X,+,*),≤),所有模...     

基于FEAHP法和模糊理想点法的B2R低碳物流决策方法

在对B2R低碳物流服务商选择决策过程中,构建低碳经济发展下的评价指标体系,建立模糊拓展层次分析法(FEAHP)模型对计算各个指标权重,然后根据模糊理想点法(FTOPSIS)的思想,获得各备择方案与理想解的靠近程度对B2R低碳物流服务商进行排序,选择出最佳的合作伙伴。最后,通过算例证明FEAHP和FTOPSIS具有可靠性和实用性。     

广义对偶犹豫模糊软集及其在决策中的应用

犹豫模糊软集作为一种处理不确定问题的工具受到了广泛关注。本文将广义模糊软集与对偶犹豫模糊集相结合,提出了广义对偶犹豫模糊软集的概念,给出了广义对偶犹豫模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,定义了广义对偶犹豫模糊软集的信息能量、相关性和相关系数的概念并讨论了它的性质。最后,给出了基于广义对偶犹豫模糊软集的多属性决策方法,并通过实例说明了该方法的的可行性和有效性。     

基于区间数的直觉模糊多属性决策研究

研究一类属性权重未知的直觉模糊多属性决策问题.将直觉模糊数的属性值转由双区间数表示,根据决策方案属性值间的离差确定属性权重.根据各方案属性加权综合值及区间直觉模糊数的得分函数,对2套方案分别进行排序和比较,并通过实例说明了该方法的有效性.     

Eliciting Electre Tri category limits for a group of decision makers

Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.