A Probability-Based Approach to Comparison of Fuzzy Numbers and Applications to Target-Oriented Decision Making

In this paper, we introduce a new comparison relation on fuzzy numbers based on their alpha-cut representation and comparison probabilities of interval values. Basically, this comparison process combines a widely accepted interpretation of fuzzy sets together with the uncertain characteristics inherent in the representation of fuzzy numbers. The proposed comparison relation is then applied to the issue of ranking fuzzy numbers using fuzzy targets in terms of target-based evaluations. Some numerical examples are used to illuminate the proposed ranking technique as well as to compare with previous methods. More interestingly, according to the interpretation of the new comparison relation on fuzzy numbers, we provide a fuzzy target-based decision model as a solution to the problem of decision making under uncertainty, with which an interesting link between the decision maker's different attitudes about target and different risk attitudes in terms of utility functions can be established. Moreover, an application of the proposed comparison relation to the fuzzy target-based decision model for the problem of fuzzy decision making with uncertainty is provided. Numerical examples are also given for illustration.     

Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives

The aim of this study is to employ the main structure of LINMAP (LINear programming technique for Multidimensional Analysis of Preference) to propose an interval programming method for solving multi-attribute group decision making (MAGDM) problems in which the ratings of alternatives are taken as hesitant fuzzy elements (HFEs) and all pair-wise comparison judgments over alternatives are represented by interval numbers. The contribution of this study is fivefold: (1) we define the new consistency and inconsistency indices; (2) we construct an interval programming model to determine the hesitant fuzzy positive ideal solution and the optimal weights of attributes, and at the same time present a decision algorithm; (3) we discuss several special cases of the proposed model in detail; (4) we show that compared with intuitionistic fuzzy LINMAP method (Li et al., 2010), the proposed approach reveals more useful information including the interval preference information, and does not need to transform HFEs into intuitionistic fuzzy numbers but directly deals with MAGDM problems and thus obtains better final decision results; and (5) we demonstrate the applicability and implementation process of the proposed approach by using an energy project selection example.     

属性值为三角模糊数的决策对象可能度关系模型

对于属性值是三角模糊数的不确定多属性决策问题,首先研究几组三角模糊数比较可能度公式之间的等价关系,提出三角模糊数比较优势关系理论,并得到一些优良性质关系和结论;然后借鉴离差最大化思想构建一种确定属性权重向量的三角模糊数型比较可能度关系模型,通过集结所有决策对象比较的可能度值,并对方案对象集进行优劣筛选和次序排定,得到一种新的三角模糊数多属性决策对象的可能度关系模型算法;最后通过算例分析验证所提出模型算法的可行性和实用性.     

一种结合主客观信息的多属性决策方法

研究了具有模糊偏好信息的模糊多属性决策问题．提出一种结合主观偏好信息与客观信息的综合特征向量方法．主观偏好信息由决策方案的模糊偏好互补矩阵和属性权重的两两比较互反矩阵组成，客观信息由客观决策矩阵组成．给出了求解模糊多属性决策问题的最小二乘偏差估计方法．通过建立二次规划模型决定属性权重向量，并对方案进行排序．最后，给出了使用该方法的数值例子．     

A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information

The aim of this study is to introduce a novel generalized distance measure for interval valued intuitionistic fuzzy sets and to illustrate the applicability of the proposed distance measure to group decision making problems. Firstly, a generalized distance measure is proposed along with proofs satisfying its axioms. Then, a comparison between the proposed distance measure and well-known distance measures is performed in terms of counter-intuitive cases. Subsequently, the extension of TOPSIS method, in which the proposed distance measure is used to calculate separation measures, to an interval valued intuitionistic fuzzy (IVIF) environment is demonstrated to solve multi-criteria group decision making (MCGDM) problems using optimal criteria weights determined with linear programming model based on the concept of maximizing relative closeness coefficient. Finally, two illustrative examples are provided for proof-of-concept purposes and to demonstrate benefits of using the proposed distance measure over the existing ones in IVIF TOPSIS method for MCGDM problems.     

Applying fuzzy hierarchy multiple attributes to construct an expert decision making process

The main objective of this paper is to propose an approach within the AHP framework for tackling the uncertainty and imprecision of service evaluations during pre-negotiation stages, where the expert’s comparison judgments are represented as fuzzy triangular numbers. A fuzzy prioritization method, which derives crisp priorities from consistent and inconsistent fuzzy comparison matrices, is described. The fuzzy analytic hierarchy process (FAHP)-based decision-making method can provide decision makers or buyer a valuable reference for evaluating software quality. A case study demonstrates the effectiveness of the proposed scheme. Importantly, the proposed scheme can assist decision makers in assessing the feasibility of digital video recorder system to management public space, making it highly applicable for academic and commercial purposes.     

加型Pythagorean模糊偏好关系的多属性决策方法

考虑Pythagorean模糊偏好关系的多属性决策问题,提出了加性Pythagorean模糊偏好关系的多属性决策方法。基于加性一致性Pythagorean模糊偏好关系提出一种新的Pythagorean模糊权重确定模型。给出了可接受加性一致性Pythagorean模糊偏好关系的定义,并针对不满足可接受加性一致性的Pythagorean模糊偏好关系,提出一种加性一致性调整算法。给出基于Pythagorean模糊偏好关系加性一致性的多属性决策方法,并通过实例分析提出的新方法的可行性和合理性。     

Fuzzy rough set based attribute reduction for information systems with fuzzy decisions

Fuzzy rough set is a generalization of crisp rough set to deal with data sets with real value attributes. A primary use of fuzzy rough set theory is to perform attribute reduction for decision systems with numerical conditional attribute values and crisp (symbolic) decision attributes. In this paper we define inconsistent fuzzy decision system and their reductions, and develop discernibility matrix-based algorithms to find reducts. Finally, two heuristic algorithms are developed and comparison study is provided with the existing algorithms of attribute reduction with fuzzy rough sets. The proposed method in this paper can deal with decision systems with numerical conditional attribute values and fuzzy decision attributes rather than crisp ones. Experimental results imply that our algorithm of attribute reduction with general fuzzy rough sets is feasible and valid.     

Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP

The lack of consistency in decision making can lead to inconsistent conclusions. In fuzzy analytic hierarchy process (fuzzy AHP) method, it is difficult to ensure a consistent pairwise comparison. Furthermore, establishing a pairwise comparison matrix requires judgments for a level with n criteria (alternatives). The number of comparisons increases as the number of criteria increases. Therefore, the decision makers judgments will most likely be inconsistent. To alleviate inconsistencies, this study applies fuzzy linguistic preference relations (Fuzzy LinPreRa) to construct a pairwise comparison matrix with additive reciprocal property and consistency. In this study, the fuzzy AHP method is reviewed, and then the Fuzzy LinPreRa method is proposed. Finally, the presented method is applied to the example addressed by Kahraman et al. [C. Kahraman, D. Ruan, I. Do?an, Fuzzy group decision making for facility location selection, Information Sciences 157 (2003) 135-153]. This study reveals that the proposed method yields consistent decision rankings from only n − 1 pairwise comparisons, which is the same result as in Kahraman et al. research. The presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy AHP method.     

Some interesting properties of the fuzzy linguistic model based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information

The management of hesitant fuzzy information is a topic of special interest in fuzzy decision making. In this paper, we focus on the use and properties of the fuzzy linguistic modelling based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information. Among these properties, we can highlight the existence of aggregation functions with no need of transformations or the possibility of a greater flexibilization of the opinions of the experts, even using different linguistic chains (multigranularity). Furthermore, based on these properties we perform a comparison between this model and the one based on hesitant fuzzy linguistic term sets, showing the advantages of the former with respect to the latter. Finally, a fuzzy decision making model based on discrete fuzzy numbers is proposed.     

An integrated fuzzy MCDM approach for supplier evaluation and selection

A fuzzy multi-criteria group decision making approach that makes use of quality function deployment (QFD), fusion of fuzzy information and 2-tuple linguistic representation model is developed for supplier selection. The proposed methodology seeks to establish the relevant supplier assessment criteria while also considering the impacts of inner dependence among them. Two interrelated house of quality matrices are constructed, and fusion of fuzzy information and 2-tuple linguistic representation model are employed to compute the weights of supplier selection criteria and subsequently the ratings of suppliers. The proposed method is apt to manage non-homogeneous information in a decision setting with multiple information sources. The decision framework presented in this paper employs ordered weighted averaging (OWA) operator, and the aggregation process is based on combining information by means of fuzzy sets on a basic linguistic term set. The proposed framework is illustrated through a case study conducted in a private hospital in Istanbul.     

Development of an interval type-2 fuzzy sets based hierarchical MADM model by combining DEMATEL and TOPSIS

In this study, a new interval type-2 fuzzy multiple-attribute decision making model is developed by integrating Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Decision Making Trial and Evaluation Laboratory (DEMATEL). The proposed model utilizes hierarchical decomposition approach for reducing inherent complexity of the decision making problems. Additionally, interdependencies among problem attributes are taken into consideration by using interval type-2 fuzzy DEMATEL method. Finally, ranking orders of the alternatives are obtained by hierarchical interval type-2 fuzzy TOPSIS method. As there are several forms of interactions among criteria in real life settings, decision makers should be provided with the expert and intelligent systems which can overcome the preferential independence assumption. The proposed method is able to model causal dependencies by using interval type-2 trapezoidal fuzzy sets. The proposed method is implemented in a Strengths, Weaknesses, Opportunities, and Threats (SWOT)-based strategy selection problem.     

An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem

The consideration of this paper is given to address the straight and U-shaped assembly line balancing problem. Although many attempts in the literature have been made to develop deterministic version of the assembly line model, the attention is not considerably given to those in uncertain environment. In this paper, a novel bi-objective fuzzy mixed-integer linear programming model (BOFMILP) is developed so that triangular fuzzy numbers (TFNs) are employed in order to represent uncertainty and vagueness associated with the task processing times in the real production systems. In this proposed model, two conflicting objectives (minimizing the number of stations as well as cycle time) are considered simultaneously with respect to set of constraints. For this purpose, an appropriate strategy in which new two-phase interactive fuzzy programming approach is proposed as a solution method to find an efficient compromise solution. Finally, validity of the proposed model as well as its solution approach are evaluated though numerical examples. In addition, a comparison study is conducted over some test problems in order to assess the performance of the proposed solution approach. The results demonstrate that our proposed interactive fuzzy approach not only can be applied in ALBPs but also is capable to handle any practical MOLP models. Moreover, in light of these results, the proposed model may constitute a framework aiming to assist the decision maker (DM) to deal with uncertainty in assembly line problem.     

A new fuzzy linear assignment method for multi-attribute decision making with an application to spare parts inventory classification

In this paper, a novel fuzzy linear assignment method is developed for multi-attribute group decision making problems. Since uncertain nature of many decision problems, the proposed method incorporates various concepts from fuzzy set theory such as fuzzy arithmetic and aggregation, fuzzy ranking and fuzzy mathematical programming into a fuzzy concordance based group decision making process. Fuzziness in the group hierarchy and quantitative type criteria are also taken into account. In order to present the validity and practicality of the proposed method, it is applied to a real life multi-criteria spare part inventory classification problem. The case study has demonstrated that the proposed method is easy to apply and able to provide effective spare parts inventory classes under uncertain environments. In addition to the practical verification by the company experts, the proposed method is also compared with some of the commonly used fuzzy multi-attribute decision making methods from the literature. According to the comparison of the results, there is an association between classes of spare parts obtained by the proposed method and the benchmarked methods.     

Development of a fuzzy decision model for manufacturability evaluation

A manufacturability evaluation decision model is formulated and analyzed based on fuzzy logic and multiple attribute decision-making under the concurrent engineering environment. The study emphasizes on the treatment of the linguistic and vagueness at the early product development stage. The study also considers the function integration of the total life cycle of a product. Hence, the integrated decision model covers the multi-level, multi-goal requirements of the products. Multiple criteria such as the goal space, the decision space, the function space, the development (i.e., product & process design) space, and the activity space, are then applied under different analysis of decision-making methods. For instances, the fuzzy multiple attribute decision-making (FMADM) combined with activity-based costing (ABC) can be used in the activity decision space. The fuzzy logic decision model can be applied in the goal decision space. The results of this study point out the importance of early decision making capability. An example of a high-pressure vessel is provided to demonstrate the proposed model for evaluating the manufacturability.     

An α-Fuzzy Goal Approximate Algorithm for Solving Fuzzy Multiple Objective Linear Programming Problems

Multiple conflicting objectives in many decision making problems can be well described by multiple objective linear programming (MOLP) models. This paper deals with the vague and imprecise information in a multiple objective problem by fuzzy numbers to represent parameters of an MOLP model. This so-called fuzzy MOLP (or FMOLP) model will reflect some uncertainty in the problem solution process since most decision makers often have imprecise goals for their decision objectives. This study proposes an approximate algorithm based on a fuzzy goal optimization under the satisfactory degree α to handle both fuzzy and imprecise issues. The concept of a general fuzzy number is used in the proposed algorithm for an FMOLP problem with fuzzy parameters. As a result, this algorithm will allow decision makers to provide fuzzy goals in any form of membership functions.     

Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information

In the classical Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), the decision maker (DM) gives the pair-wise comparisons of alternatives with crisp truth degree 0 or 1. However, in the real world, DM is not sure enough in all comparisons and can express his/her opinion with some fuzzy truth degree. Thus, DM's preferences are given through pair-wise comparisons of alternatives with fuzzy truth degrees, which may be represented as trapezoidal fuzzy numbers (TrFNs). Considered such fuzzy truth degrees, the aim of this paper is to develop a new fuzzy linear programming technique for solving multiattribute decision making (MADM) problems with multiple types of attribute values and incomplete weight information. In this method, TrFNs, real numbers, and intervals are used to represent the multiple types of decision information. The fuzzy consistency and inconsistency indices are defined as TrFNs due to the alternatives’ comparisons with fuzzy truth degrees. Hereby a new fuzzy linear programming model is constructed and solved by the possibility linear programming method with TrFNs developed in this paper. The fuzzy ideal solution (IS) and the attribute weights are then obtained. The distances of alternatives from the fuzzy IS can be calculated to determine their ranking order. The implementation process of the method proposed in this paper is illustrated with a strategy partner selection example. The comparison analyzes show that the method proposed in this paper generalizes the classical LINMAP, fuzzy LINMAP and possibility LINMAP.     

Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making

Multiple attribute decision making (MADM) problems are the most encountered problems in decision making. Fuzziness is inherent in decision making process and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy rating. A few techniques in MADM assess the weights of attributes based on preference information on alternatives. But they are not practical any more when the set of all paired comparison judgments from decision makers (DMs) on attributes are not crisp and also we have to deal with fuzzy decision matrix. This paper investigates the generation of a possibilistic model for multidimensional analysis of preference (LINMAP). The model assesses the fuzzy weights as well as locating the ideal solution with fuzzy decision making preference on attributes and fuzzy decision matrix. All of the information is assumed as triangular fuzzy numbers (TFNs). This method is developed in group decision making environments and formulates the problem as a possibilistic programming with multiple objectives.     

Multiattribute decision making based on intuitionistic fuzzy interaction average operators: a comparison

This paper proposes a new family of intuitionistic fuzzy information aggregation operators for multiattribute decision making. Such aggregate operators provide an excellent complement to the existing ones. In this study, comparison with existing intuitionistic fuzzy aggregation operators is presented in detail. Properties and special cases of the proposed operators are investigated. Finally, we introduce an approach to intuitionistic fuzzy multiattribute decision making. An example of the recruitment of intern candidates is illustrated to show the feasibility and superiority of the proposed method.     

Multiple attribute decision‐making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q‐rung orthopair fuzzy environment

A Q‐rung orthopair fuzzy set (q‐ROFS) originally proposed by Yager (2017) is a new generalization of orthopair fuzzy sets, which has a larger representation space of acceptable membership grades and gives decision makers more flexibility to express their real preferences. In this paper, for multiple attribute decision‐making problems with q‐rung orthopair fuzzy information, we propose a new method for dealing with heterogeneous relationship among attributes and unknown attribute weight information. First, we present two novel q‐rung orthopair fuzzy extended Bonferroni mean (q‐ROFEBM) operator and its weighted form (q‐ROFEWEBM). A comparative example is provided to illustrate the advantages of the new operators, that is, they can effectively model the heterogeneous relationship among attributes. We prove that some existing known intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are special cases of the proposed q‐ROFEBM and q‐ROFEWEBM operators. Meanwhile, several desirable properties are also investigated. Then, a new knowledge‐based entropy measure for q‐ROFSs is also proposed to obtain the attribute weights. Based on the proposed q‐ROFWEBM and the new entropy measure, a new method is developed to solve multiple attribute decision making problems with q‐ROFSs. Finally, an illustrative example is given to demonstrate the application process of the proposed method, and a comparison analysis with other existing representative methods is also conducted to show its validity and superiority.