A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. The interval-valued intuitionistic fuzzy soft set is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The aim of this paper is to investigate the decision making based on interval-valued intuitionistic fuzzy soft sets. By means of level soft sets, we develop an adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making and some numerical examples are provided to illustrate the developed approach. Furthermore, we also define the concept of the weighted interval-valued intuitionistic fuzzy soft set and apply it to decision making.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

An adjustable approach to fuzzy soft set based decision making

Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Recently, decision making based on (fuzzy) soft sets has found paramount importance. This paper aims to give deeper insights into decision making based on fuzzy soft sets. We discuss the validity of the Roy-Maji method and show its true limitations. We point out that the choice value designed for the crisp case is no longer fit to solve decision making problems involving fuzzy soft sets. By means of level soft sets, we present an adjustable approach to fuzzy soft set based decision making and give some illustrative examples. Moreover, the weighted fuzzy soft set is introduced and its application to decision making is also investigated.     

Group decision making methods based on intuitionistic fuzzy soft matrices

Soft set theory was originally proposed by Molodtsov as a general mathematical tool for dealing with uncertainty in 1999. Recently, researches of decision making based on soft sets have got some progress, but few people consider multi-experts situation. As such, this paper discusses multi-experts group decision making problems. Firstly, we give a concept of intuitionistic fuzzy soft matrix (IFSM) and prove some relevant properties of IFSM. Then, an adjustable approach is presented by means of median level soft set and p-quantile level soft set for dealing with decision making problems based on IFSM. Thirdly, we study aggregation methods of IFSM, give two kinds of aggregation operators and methods that how to determine experts’ weights under different situation with programming models, four corresponding algorithms have been proposed, too. Finally, a practical example has been demonstrated the reasonability and efficiency of these new algorithms.     

A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets

Soft set theory, originally proposed by Molodtsov, has become an effective mathematical tool to deal with uncertainty. A type-2 fuzzy set, which is characterized by a fuzzy membership function, can provide us with more degrees of freedom to represent the uncertainty and the vagueness of the real world. Interval type-2 fuzzy sets are the most widely used type-2 fuzzy sets. In this paper, we first introduce the concept of trapezoidal interval type-2 fuzzy numbers and present some arithmetic operations between them. As a special case of interval type-2 fuzzy sets, trapezoidal interval type-2 fuzzy numbers can express linguistic assessments by transforming them into numerical variables objectively. Then, by combining trapezoidal interval type-2 fuzzy sets with soft sets, we propose the notion of trapezoidal interval type-2 fuzzy soft sets. Furthermore, some operations on trapezoidal interval type-2 fuzzy soft sets are defined and their properties are investigated. Finally, by using trapezoidal interval type-2 fuzzy soft sets, we propose a novel approach to multi attribute group decision making under interval type-2 fuzzy environment. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

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。     

An approach to decision making based on intuitionistic fuzzy rough sets over two universes

Rough set theory has been combined with intuitionistic fuzzy sets in dealing with uncertainty decision making. This paper proposes a general decision-making framework based on the intuitionistic fuzzy rough set model over two universes. We first present the intuitionistic fuzzy rough set model over two universes with a constructive approach and discuss the basic properties of this model. We then give a new approach of decision making in uncertainty environment by using the intuitionistic fuzzy rough sets over two universes. Further, the principal steps of the decision method established in this paper are presented in detail. Finally, an example of handling medical diagnosis problem illustrates this approach.     

模糊参数软区间集及其应用

将模糊参数软集与区间集相结合,定义了模糊参数软区间集的概念,研究了模糊参数软区间集的运算及其性质.然后,给出模糊参数软区间集在决策中的应用,说明了方法的可行性.推广了软区间集的相关研究结果.     

广义多值直觉模糊软集及其在多属性决策中的应用

软集理论作为一种处理不确定问题的数学新工具弥补了传统模糊理论在参数工具上的不足。本文将广义模糊软集与多值直觉模糊集相结合,提出了广义多值直觉模糊软集的概念,给出了广义多值直觉模糊软集的交、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,还将广义多值直觉模糊软集应用到多属性决策问题中去,给出相应的算法。并进行实例分析说明该决策方法的可行性和有效性。     

Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets

This paper proposes the concept of the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets (IVIFSs) with respect to adjustable weight vectors and the Dice similarity measure based on the reduct intuitionistic fuzzy sets to explore the effects of optimism, neutralism, and pessimism in decision making. Then a decision-making method with the pessimistic, optimistic, and neutral schemes desired by the decision maker is established by combining adjustable weight vectors and the Dice similarity measure for IVIFSs. The proposed decision-making method is more flexible and adjustable in practical problems and can determine the ranking order of alternatives and the optimal one(s), so that it can overcome the difficulty of the ranking order and decision making when there exist the same measure values of some alternatives in some cases. This adjustable feature can provide the decision maker with more selecting schemes and actionable results for the decision-making analysis. Finally, two illustrative examples are employed to show the feasibility of the proposed method in practical applications.     

Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group

Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388–393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develop a new similarity measure between intuitionistic fuzzy sets. Then we apply the developed similarity measure for consensus analysis in group decision making based on intuitionistic fuzzy preference relations, and finally further extend it to the interval-valued intuitionistic fuzzy set theory.     

A Decision Making Method for the Quality Identification of Wines Based on Fuzzy Soft Sets

Quality identification of wines is a crucial one for wine industry. The paper aims to give a decision making approach based on soft fuzzy sets for it. First, based on fuzzy soft sets, calculation steps are given to solve decision making problems. The grey relative coefficient between each alternative with the ideal alternative is calculated by grey relational analysis (GRA). Then, a relative relational degree is defined to determine ranking orders of all alternatives. Finally, an application of our proposed approach demonstrates its practicality and effectiveness in the quality identification of red wines.     

Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making

Atanassov (1986) defined the notion of intuitionistic fuzzy set, which is a generalization of the notion of Zadeh’ fuzzy set. In this paper, we first develop some similarity measures of intuitionistic fuzzy sets. Then, we define the notions of positive ideal intuitionistic fuzzy set and negative ideal intuitionistic fuzzy set. Finally, we apply the similarity measures to multiple attribute decision making under intuitionistic fuzzy environment.     

A new evaluation method based on D–S generalized fuzzy soft sets and its application in medical diagnosis problem

Soft set theory, initiated by Molodtsov, is a general mathematical tool for dealing with uncertain problems. In this paper, we first point out that the similarity measure in a previous paper by Majumdar and Samanta [P. Majumdar, S.K. Samanta, Generalized fuzzy soft sets, Comput. Math. Appl. 59 (2010) 1425–1432] is limited by two counterexamples. To deal with the problems of subjective evaluation and uncertain knowledge, this paper proposes the concept of D–S generalized fuzzy soft sets by combining Dempster–Shafer theory of evidence and generalized fuzzy soft sets. We study some of its operations and basic properties, and the relationship between generalized fuzzy soft sets and D–S generalized fuzzy soft sets are introduced. Then we propose the concept of the similarity between two D–S generalized fuzzy soft sets. At last, we present a new method of evaluation based on D–S generalized fuzzy soft sets and apply it into a medical diagnosis problem.     

面向直觉模糊集排序能力提升的记分函数设计研究

直觉模糊集记分函数的排序能力是影响直觉模糊型多准则决策绩效的重要因素。本文以直觉模糊集记分函数的特性分析为切入点,较为系统地分析了现有各类记分函数的有界性、符合直觉性、排序能力、连续性等四类特征;其次,基于现有记分函数特征匹配状况,提出了新的直觉模糊集记分函数的分段函数并加以证明;最后,系统比较了现有记分函数与本文提出的记分函数在排序能力和区分度方面的差异,验证了本方法的优越性和合理性。     

基于直觉模糊集的全区间决策方法

针对属性值为直觉模糊集且属性权重已知的模糊多属性决策问题,本文基于直觉模糊算术加权平均算子,提出了一种基于直觉模糊集的全区间决策方法。全区间决策函数引入了态度指标k,从而可以反映决策者态度的变化,从0到1变化k值,可以在整个区间内挖掘决策信息的变化,与得分函数法和基于距离TOPSIS贴近度方法相比,将过去的点值判断延伸至全区间判断,避免了决策信息的丢失现象,决策更加准确合理。实例计算表明该方法的正确性、有效性和合理性,具有一定的推广借鉴价值。     

Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems

This paper investigates an approach for multi-criterion decision making (MCDM) problems with interval-valued intuitionistic fuzzy preference relations (IVIFPRs). Based on the novel interval score function, some extended concepts associated with IVIFPRs are defined, including the score matrix, the approximate optimal transfer matrix and the possibility degree matrix. By using these new matrixes, a prioritization method for IVIFPRs is proposed. Then, we investigate an interval-valued intuitionistic fuzzy AHP method for multi-criteria decision making (MCDM) problems. In the end, a numerical example is provided to illustrate the application of the proposed approach.     

Study on divergence measures for intuitionistic fuzzy sets and its application in medical diagnosis

As far as medical diagnosis problem is concerned, predicting the actual disease in complex situations has been a concerning matter for the doctors/experts. The divergence measure for intuitionistic fuzzy sets is an effective and potent tool in addressing the medical decision making problems. We define a new divergence measure for intuitionistic fuzzy sets (IFS) and its interesting properties are studied. The existing divergence measures under intuitionistic fuzzy environment are reviewed and their counter-intuitive cases has been explored. The parameter $\alpha $ is incorporated in the proposed divergence measure and it is defined as parametric intuitionistic fuzzy divergence measure (PIFDM). The different choices of the parameter $\alpha$ provide different decisions about the disease. As we increase the value of $\alpha $, the information about the disease increases and move towards the optimal solution with the reduced in the uncertainty. Finally, we compare our results with the already existing results, which illustrate the role of the parameter $\alpha $ in obtaining the optimal solution in the medical decision making application. The results demonstrate that the parametric intuitionistic fuzzy divergence measure (PIFDM) is more comprehensive and effective than the proposed intuitionistic fuzzy divergence measure and the existing intuitionistic fuzzy divergence measures for decision making in medical investigations.     

基于改进直觉模糊集成算子的多属性决策方法及其应用研究

基于直觉模糊集理论,提出了改进直觉模糊集成算子方法来研究多属性决策问题。本文定义了直觉模糊数的运算法则和比较了直觉模糊信息的一系列集成算子,然后改进了传统得分函数,并将其与直觉模糊集成算子相结合,从而得到新的直觉模糊信息的集成方式,将其运用于解决属性权重已知的直觉模糊多属性决策问题。最后,通过具体实例说明该方法的有效性和具体应用过程。