Multi-attribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers

In this paper, we investigate the fuzzy multi-attribute group decision making (FMAGDM) problems in which all the information provided by the decision makers (DMs) is expressed as the trapezoidal interval type-2 fuzzy sets (IT2 FS). We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two trapezoidal IT2 FS. Then, we develop two aggregation techniques called the trapezoidal interval type-2 fuzzy geometric Bonferroni mean (TIT2FGBM) operator and the trapezoidal interval type-2 fuzzy weighted geometric Bonferroni mean (TIT2FWGBM) operator. We study its properties and discuss its special cases. Based on the TIT2FWGBM operator and the possibility degree, the method of FMAGDM with trapezoidal interval type-2 fuzzy information is proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.     

Conceptual design evaluation using interval type-2 fuzzy information axiom

Concept selection is the most critical part of the design process as it determines the direction of subsequent design stages. In addition, it is a difficult task because available information for decision-making at this stage is imprecise and subjective. This necessitates the need for fuzzy decision models for selecting the best conceptual design among a set of alternatives. Although ordinary fuzzy sets cover uncertainties of linguistic words to some extent, it is recommended to use interval type-2 fuzzy sets (IT2FS) to capture potential uncertainties of words. This paper presents a new concept selection methodology that extends the fuzzy information axiom (FIA) approach to incorporate IT2FSs. The proposed methodology is called interval-type-2 fuzzy information axiom (IT2-FIA). IT2-FIA method is also enriched by using ordered weighted geometric aggregation operator to include the decision maker's attitude during the aggregation process. A case study is given to demonstrate the potential of the methodology.     

An interval type-2 fuzzy PROMETHEE method using a likelihood-based outranking comparison approach

Based on the preference ranking organization method for enrichment evaluations (PROMETHEE), the purpose of this paper is to develop a new multiple criteria decision-making method that uses the approach of likelihood-based outranking comparisons within the environment of interval type-2 fuzzy sets. Uncertain and imprecise assessment of information often occurs in multiple criteria decision analysis (MCDA). The theory of interval type-2 fuzzy sets is useful and convenient for modeling impressions and quantifying the ambiguous nature of subjective judgments. Using the approach of likelihood-based outranking comparisons, this paper presents an interval type-2 fuzzy PROMETHEE method designed to address MCDA problems based on interval type-2 trapezoidal fuzzy (IT2TrF) numbers. This paper introduces the concepts of lower and upper likelihoods for acquiring the likelihood of an IT2TrF binary relationship and defines a likelihood-based outranking index to develop certain likelihood-based preference functions that correspond to several generalized criteria. The concept of comprehensive preference measures is proposed to determine IT2TrF exiting, entering, and net flows in the valued outranking relationships. In addition, this work establishes the concepts of a comprehensive outranking index, a comprehensive outranked index, and a comprehensive dominance index to induce partial and total preorders for the purpose of acquiring partial ranking and complete ranking, respectively, of the alternative actions. The feasibility and applicability of the proposed method are illustrated with two practical applications to the problem of landfill site selection and a car evaluation problem. Finally, a comparison with other relevant methods is conducted to validate the effectiveness of the proposed method.     

Local consistency adjustment strategy and DEA – driven interval type-2 trapezoidal fuzzy decision-making model and its application for fog-haze factor assessment problem

This paper aims to develop a novel decision-making method with interval type-2 trapezoidal fuzzy preference (IT2TrFPR), which can deal with the complex decision information presented in the form of interval type-2 trapezoidal fuzzy numbers. In this paper, we mainly propose a novel interval type-2 trapezoidal fuzzy decision-making method with local consistency adjustment strategy and data envelopment analysis (DEA). Considering the harm of fog-haze pollution to the environment and human life, we apply the decision-making method to the problem about influence factors of for-haze weather. Firstly, we introduce the definition of IT2TrFPR that sufficiently expresses the uncertainty of original decision-making information. After that, we show the definition of the order consistency and additive consistency for IT2TrFPR. Considering that the original IT2TrFPR given by decision-makers usually does not satisfy the characteristic of consistency, to transform the unacceptable additive consistent IT2TrFPRs into acceptable ones, we design a consistency-improving algorithm that uses the local adjustment approach to preserve the original decision-making information as much as possible and avoids the original information loss. Then, an output-oriented interval type-2 trapezoidal fuzzy DEA model and the concept for quasi interval type-2 trapezoidal fuzzy priority weight are developed to derive the interval type-2 trapezoidal fuzzy priority weight vector (IT2TrFPW) and obtain the final ranking result of alternatives. Finally, the effectiveness of the proposed decision-making method is demonstrated by a numerical example of selecting the most crucial fog-haze influence factor. Meanwhile, we also conduct a comparative analysis by comparing our method with the existing methods to show some merits of the proposed method.

     

Bearing condition prediction considering uncertainty: An interval type-2 fuzzy neural network approach

Rolling-element bearings are critical components of rotating machinery. It is important to accurately predict in real-time the health condition of bearings so that maintenance practices can be scheduled to avoid malfunctions or even catastrophic failures. In this paper, an Interval Type-2 Fuzzy Neural Network (IT2FNN) is proposed to perform multi-step-ahead condition prediction of faulty bearings. Since the IT2FNN defines an interval type-2 fuzzy logic system in the form of a multi-layer neural network, it can integrate the merits of each, such as fuzzy reasoning to handle uncertainties and neural networks to learn from data. The interval type-2 fuzzy linguistic process in the IT2FNN enables the system to handle prediction uncertainties, since the type-2 fuzzy sets are such sets whose membership grades are type-1 fuzzy sets that can be used in failure prediction due to the difficult determination of an exact membership function for a fuzzy set. Noisy data of faulty bearings are used to validate the proposed predictor, whose performance is compared with that of a prevalent type-1 condition predictor called Adaptive Neuro-Fuzzy Inference System (ANFIS). The results show that better prediction accuracy can be achieved via the IT2FNN.     

Data-driven modeling and optimization of thermal comfort and energy consumption using type-2 fuzzy method

In the research domain of intelligent buildings and smart home, modeling and optimization of the thermal comfort and energy consumption are important issues. This paper presents a type-2 fuzzy method based data-driven strategy for the modeling and optimization of thermal comfort words and energy consumption. First, we propose a methodology to convert the interval survey data on thermal comfort words to the interval type-2 fuzzy sets (IT2 FSs) which can reflect the inter-personal and intra-personal uncertainties contained in the intervals. This data-driven strategy includes three steps: survey data collection and pre-processing, ambiguity-preserved conversion of the survey intervals to their representative type-1 fuzzy sets (T1 FSs), IT2 FS modeling. Then, using the IT2 FS models of thermal comfort words as antecedent parts, an evolving type-2 fuzzy model is constructed to reflect the online observed energy consumption data. Finally, a multiobjective optimization model is presented to recommend a reasonable temperature range that can give comfortable feeling while reducing energy consumption. The proposed method can be used to realize comfortable but energy-saving environment in smart home or intelligent buildings.     

Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets

In this paper, we present a new method to deal with fuzzy multiple attributes group decision-making problems based on ranking interval type-2 fuzzy sets. First, we propose a new method for ranking interval type-2 fuzzy sets. Then, we propose a new method for fuzzy multiple attributes group decision-making based on the proposed ranking method of interval type-2 fuzzy sets. We also use some examples to illustrate the fuzzy multiple attributes group decision-making process of the proposed method. The proposed method is simpler than the methods presented in [Chen and Lee, 2010a] and [Lee and Chen, 2010b] for fuzzy multiple attributes group decision-making based on interval type-2 fuzzy sets. It provides us with a useful way for dealing with fuzzy multiple attributes group decision-making problems based on interval type-2 fuzzy sets.     

Aggregation Using the Linguistic Weighted Average and Interval Type-2 Fuzzy Sets

The focus of this paper is the linguistic weighted average (LWA), where the weights are always words modeled as interval type-2 fuzzy sets (IT2 FSs), and the attributes may also (but do not have to) be words modeled as IT2 FSs; consequently, the output of the LWA is an IT2 FS. The LWA can be viewed as a generalization of the fuzzy weighted average (FWA) where the type-1 fuzzy inputs are replaced by IT2 FSs. This paper presents the theory, algorithms, and an application of the LWA. It is shown that finding the LWA can be decomposed into finding two FWAs. Since the LWA can model more uncertainties, it should have wide applications in distributed and hierarchical decision-making.     

Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS

The aim of this paper is to propose a method to aggregate the opinion of several decision makers on different criteria, regarding a set of alternatives, where the judgment of the decision makers are represented by generalized interval-valued trapezoidal fuzzy numbers. A generalized interval valued trapezoidal fuzzy number based technique for order preference by similarity to ideal solution is proposed that can reflect subjective judgment and objective information in real life. The weights of criteria and performance rating values of criteria are linguistic variables expressed as generalized interval-valued trapezoidal fuzzy numbers. Finally, an illustrative example is provided to elaborate the proposed method for the selection of a suitable robot according to our requirements.     

A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets

Ranking methods, similarity measures and uncertainty measures are very important concepts for interval type-2 fuzzy sets (IT2 FSs). So far, there is only one ranking method for such sets, whereas there are many similarity and uncertainty measures. A new ranking method and a new similarity measure for IT2 FSs are proposed in this paper. All these ranking methods, similarity measures and uncertainty measures are compared based on real survey data and then the most suitable ranking method, similarity measure and uncertainty measure that can be used in the computing with words paradigm are suggested. The results are useful in understanding the uncertainties associated with linguistic terms and hence how to use them effectively in survey design and linguistic information processing.     

Uncertainty measures for interval type-2 fuzzy sets

Fuzziness (entropy) is a commonly used measure of uncertainty for type-1 fuzzy sets. For interval type-2 fuzzy sets (IT2 FSs), centroid, cardinality, fuzziness, variance and skewness are all measures of uncertainties. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use a Representation Theorem for IT2 FSs. Formulas for computing the cardinality, fuzziness, variance and skewness of an IT2 FS are derived. These definitions should be useful in IT2 fuzzy logic systems design using the principles of uncertainty, and in measuring the similarity between two IT2 FSs.     

A new trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted averaging operator and its application for enterprise location

Recently some new models based on Pythagorean fuzzy sets (PFSs) have been proposed to deal with the uncertainty in multiple attribute group decision making (MAGDM) problems. In this paper, considering linguistic variables and entropic, we propose a new trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted averaging operator to solve MAGDM problems. Next, we study some main properties by utilizing some operational laws of the trapezoidal Pythagorean fuzzy linguistic variables. Finally, a numerical example concerning the enterprise location is given to illustrate the practicality and effectiveness of the proposed operator.     

Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets

In this paper, we present a new method to handle fuzzy multiple attributes group decision-making problems based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. First, we present the arithmetic operations between interval type-2 fuzzy sets. Then, we present a fuzzy ranking method to calculate the ranking values of interval type-2 fuzzy sets. We also make a comparison of the ranking values of the proposed method with the existing methods. Based on the proposed fuzzy ranking method and the proposed arithmetic operations between interval type-2 fuzzy sets, we present a new method to handle fuzzy multiple attributes group decision-making problems. The proposed method provides us with a useful way to handle fuzzy multiple attributes group decision-making problems in a more flexible and more intelligent manner due to the fact that it uses interval type-2 fuzzy sets rather than traditional type-1 fuzzy sets to represent the evaluating values and the weights of attributes.     

A consensus model for group decision making under interval type-2 fuzzy environment

We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.     

绿色供应商选择的梯形模糊软集群决策模型

针对考虑评价专家评价信息的绿色供应商选择问题,提出了一种基于梯形模糊软集的绿色供应商选择多属性群决策模型。各专家选定不同的评价指标集及使用语言变量进行评价,利用“与”运算对各专家的评价信息进行集结,并得到信息集结后的梯形模糊软集;然后以此作为多属性决策的初始决策矩阵,在梯形模糊软集加权规范化的基础上通过计算正负理想解距离以及相对贴近度,得到最优决策。最后通过算例说明了该方法的可行性和有效性。     

基于区间二型模糊熵的多属性决策方法

针对属性权重信息完全未知的区间二型模糊多属性决策问题,提出了一种基于区间二型模糊熵的多属性决策方法。为了量化区间二型模糊集的不确定信息,通过引入模糊因子、犹豫因子和区间因子建立了区间二型模糊熵的公理化准则,并分别基于欧氏距离、海明距离和广义距离给出了三种熵计算公式。同时,根据决策问题中总体不确定性最小化的原则,结合熵公式构建数学规划模型来确定属性权重,利用得分函数给出了具体的决策步骤,并通过实例分析验证了该决策方法的有效性和灵活性。     

基于熵和风险态度的二型模糊多属性决策方法

针对属性权重信息完全未知的二型模糊多属性决策问题,提出了一种基于二型模糊熵和决策者风险态度的决策方法。首先,为了准确测度二型模糊集（T2FS）的不确定性,通过引入模糊因子和犹豫因子建立了二型模糊熵的公理化准则,并基于距离测度给出了对应的计算公式。其次,为了减少整体不确定信息对决策结果的影响,结合二型模糊熵构建非线性规划模型来确定属性权重。同时,将决策者的风险态度引入二型模糊信息的得分函数中并给出具体的决策步骤。最后,通过实例分析验证了该决策方法的可行性,并与现有文献对比发现该决策方法更具有灵活性。     

基于区间梯形二型犹豫模糊数的多准则决策方法

针对准则权重不完全的犹豫模糊多准则决策问题,提出基于区间梯形二型犹豫模糊数的决策方法.首先,给出区间梯形二型犹豫模糊数,根据几何面积法定义区间梯形二型犹豫模糊数的可能度和差异度;然后,利用差异度和离差最大化模型得到各准则权重,基于TOPSIS思想得到各方案的综合贴近度,并对方案进行排序;最后,通过算例分析和对比分析验证了所提出方法的可行性和有效性.     

On the difference in control performance of interval type-2 fuzzy PI control system with different FOU shapes

Interval type-2 fuzzy logic controllers (IT2-FLCs) have been attracting a lot of attention. However, challenges in designing IT2-FLCs still remain. One of the main challenges is to choose the appropriate FOU shape for interval type-2 fuzzy sets (IT2-FSs). This paper aims to analyse the differences in control performance between three IT2 fuzzy PI controllers (IT2-F-PICs) with different FOU shapes as antecedent sets, namely the triangular top wide IT2 fuzzy set, the triangular bottom wide IT2 fuzzy set and the trapezoidal (also called parallel) IT2 fuzzy set. First, the analytical structures of these IT2-FLCs are derived and the mathematical input–output equations are obtained. Three interesting differences between the analytical structures and input–output relationship of the IT2-F-PICs are then presented. From the differences in the analytical structures of the three IT2-F-PICs and numerical simulation results, it is demonstrated that IT2-F-PICs with trapezoidal (IT2-F-PI-P) and triangular bottom wide (IT2-F-PI-BW) antecedent sets with the potential to provide faster transient response and faster settling time than the IT2-F-PICs with triangular top wide (IT2-F-PI-TW). In addition, IT2-F-PI-P is better able to handle plant uncertainties and disturbances than IT2-F-PI-BW and IT2-F-PI-TW. The contribution of this paper is to provide insights into the performance differences between different FOU shaped controllers, which in turns allowing control designers to select the appropriate FOU shape in order to meet design requirements.     

Investment project evaluation by a decision making methodology based on type-2 fuzzy sets

Although investment projects supported by the state are extremely important in terms of national policy the projects to be transferred from the common public funds brings with it many problems. Highly transparent and comprehensive evaluation model are required to transfer the public resources to the right investment projects. It is necessary to consider many criteria for the evaluation of an investment project. These criteria are generally subjective and extremely difficult to express in numbers. However, using the fuzzy sets provide huge facilities to decision makers in project evaluation process with linguistic variables and measurement challenges. In this study, a new evaluation model for investment projects have been proposed for development agencies operating in Turkey. To address ambiguities and relativities in real world scenarios more conveniently, type-2 fuzzy sets and crisp sets have been simultaneously used. The proposed model for the investment project evaluation problem composed of type-2 fuzzy AHP and type-2 fuzzy TOPSIS methods. The proposed fuzzy MCDM method consists of three phases: (1) identify the criteria to be used in the model, (2) type-2 fuzzy AHP computations, (3) evaluation of investment projects with type-2 fuzzy TOPSIS and determination of the final rank. To perceive proposed model better, an application with real case data have been performed in Middle Black Sea Development Agency in Turkey. As a consequence of this application, it has been observed that the proposed model have proved effective in evaluation of alternatives in multi-criteria group decision making problems in a broader perspective and flexible fashion.