A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.

Entropy measures of type-2 intuitionistic fuzzy sets and type-2 triangular intuitionistic trapezodial fuzzy sets

In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.

Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function

Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.

Success Factors of Biotechnology Industry Based on Triangular Fuzzy Number

Based on the theory of competitive advantage and value chain, this paper establishes the indicator system, and develop the strategic framework using the fuzzy Delphi method. Then the triangular fuzzy number model is established using Fuzzy Analytic Hierarchy Process, and the key factors influencing biotechnology industry are extracted. The results show that in terms of weight, the key factors influencing the success of biotechnology industry are sequenced as follows: "open innovation capacity", "quality and cost control ability", "advanced customer-oriented product manufacturing capacity", "technology R & D personnel's capacity", "brand image building capacity", "logistics and sales capacity", "grasping the market demand trends". The manufacturers and government decision-making body can use this as the basis, to promote the development of the biotechnology industry.

On Development of Fuzzy Controller: The Case of Gaussian and Triangular Membership Functions

In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice however, such domains are hardly triangular and in fact for most engineering applications the membership functions are usually Gaussian and sometimes cosine. In an earlier paper, we derived explicit Fourier series expressions for systematic and dynamic computation of grade of membership in the overlap and non-overlap regions of triangular Fuzzy sets. In another paper, we extended the methodology to cover cases of cosine, exponential and Gaussian Fuzzy sets by presenting explicit Fourier series representation for encoding fuzziness in the overlap and non-overlap domains of Fuzzy sets. This current paper presents the development of a “Fuzzy Controller” device, which incorporates the formal mathematical representation for computing grade of membership of Gaussian and triangular Fuzzy sets. It is shown that triangular approximation of Gaussian membership function in Fuzzy control can lead to wrong linguistic classification which may have adverse effects on operational and control decisions. The development of the Fuzzy controller demonstrates that the proposed technique can indeed be incorporated in engineering systems for dynamic and systematic computation of grade of membership in the overlap and non-overlap regions of Fuzzy sets;and thus provides a basis for the design of embedded Fuzzy controller for mission critical applications.

Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.

Analysis of Syetem Reliability in Manufacturing Cell Based on Triangular Fuzzy Number

Due to lacking of test-data and field-data in reliability research during the design stage of manufacturing cell sys- tem.The degree of manufacturing cell system reliability research is increased.In order to deal with the deficient data and the un- certainty occurred from analysis and judgment,the paper discussed a method for studying reliability of manufacturing cell system through the analysis of fuzzy fault tree,which was based on triangular fuzzy number.At last,calculation case indicated that it would have great significance for ascertaining reliability index,maintenance and establishing keeping strategy towards manufac- turing cell system.

Obtaining Crisp Priorities for Triangular and Trapezoidal Fuzzy Judgments

This paper proposes anoptimal fuzzy-based model for obtaining crisp priorities for Fuzzy-AHP comparison matrices.Crisp judgments cannot be given for real-life situations,as most of these include some level of fuzziness and com-plexity.In these situations,judgments are represented by the set of fuzzy numbers.Most of the fuzzy optimization models derive crisp priorities for judgments repre-sented with Triangular Fuzzy Numbers(TFNs)only.They do not work for other types of Triangular Shaped Fuzzy Numbers(TSFNs)and Trapezoidal Fuzzy Numbers(TrFNs).To overcome this problem,a sum of squared error(SSE)based optimization model is proposed.Unlike some other methods,the proposed model derives crisp weights from all of the above-mentioned fuzzy judgments.A fuzzy number is simulated using the Monte Carlo method.A threshold-based constraint is also applied to minimize the deviation from the initial judgments.Genetic Algorithm(GA)is used to solve the optimization model.We have also conducted casestudiesto show the proposed approach’s advantages over the existingmethods.Results show that the proposed model outperforms other models to minimize SSE and deviation from initial judgments.Thus,the proposed model can be applied in various real time scenarios as it can reduce the SSE value upto 29%compared to the existing studies.

FUZZY ALGEBRA IN TRIANGULAR NORM SYSTEM

Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).

An Evaluation Model of Graduation Thesis Results Based on Triangular Fuzzy Number

The evaluation of thesis by undergraduate has the characteristics of multi-factor, multi-layer and easy to be affected by subjective factors. To reduce the subjectivity, triangular fuzzy number is used as index set to give weight, and on this basis, fuzzy comprehensive evaluation is used to evaluate the quality of graduation thesis. The empirical analysis shows that the combination of triangular fuzzy number and fuzzy comprehensive evaluation has certain practical value in the quality evaluation of graduation thesis.

Application of Nonlinear Triangular Fuzzy Fault Tree Algorithm in Predicting Lithium Battery Air Transport Accidents

The traditional triangular fuzzy fault tree prediction model adopts the linear approximation method.Therefore,the accident prediction error is large.Based on the analysis of the error sources and the fuzzy set,the precise calculation method of the event at the top of the fault tree is given.By using the numerical calculation software,an accurate calculation method of nonlinear triangular fuzzy accident prediction was adopted to predict lithium battery air transport fire accidents,and the fuzzy importance of the cause event was calculated.

New Methods to Solve Fuzzy Shortest Path Problems

This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers (TFN). Because of the characteristic of TFNs, the length of any path p from s to t , which equals the extended sum of all arcs belonging to p , is also TFN. Therefore, the fuzzy shortest path problem (FSPP) becomes to select the smallest among all those TFNs corresponding to different paths from s to t (specifically, the smallest TFN represents the shortest path). Based on Adamo's method for ranking fuzzy number, the pessimistic method and its extensions - optimistic method and λ combination method, are presented, and the FSPP is finally converted into the crisp shortest path problems.

Method based on fuzzy linguistic scale and FIOWGA operator for decision-making problems

In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness.

Fuzzy决策中有限方案的群体一致性评价方法与算法

运用三角模糊数的概念提出两种有限方案的群体评价方法：１）根据个体加权向量提出衡量个体间一致性的相似度量函数，由此构造个体、群体的一致性指标，并给出群体一致性的定义，用个体指标提出由个体加权向量寻求群体加权向量的两种方法；２）利用三角模糊数构造语言评价集，并给出一种基于语言的方案评价方法与算法。

基于Fuzzy-IPA的景区游客满意度影响因素的实证研究

景区产品或服务感知不仅具有主观性和不确定性,且感知差异也不是呈离散态,而是具有连续性。传统的感知表现测量方法是采用离散的数值表示状态的转变,如"满意→非常满意",表示为"4→5",呈现跳跃式的转变,忽略了感知的缓冲区域。因此,本文首先依据三角模糊评价理论,采用三角模糊值表示游客的感知表现,用连续性的变化更为客观地描述游客感知表现,如"满意→非常满意"表示为"(50,75,100)→(75,100,100)";其次运用去模糊化法则,把产品或服务感知表现的三角模糊值转化为逻辑数值,结合传统的IPA,设计满意度影响因素的Fuzzy-IPA分析方法,探索景区游客满意度影响因素的关键性因素。

基于fuzzy TOPSIS的城市水资源适应能力评估方法研究

适应能力作为一种基于政策响应的独立的气候变化应对方式,已逐渐成为研究气候问题的焦点。参考国外文献中适应能力评估指标体系建立的原则和方法,本研究构建了包含自然资源、人口与社会、基础设施、管理与制度4个方面12项指标的城市水资源适应能力评估指标体系,并利用层次分析法(AHP)确定每项指标的权重。针对指标数据的不确定性,将结合了三角模糊数的逼近理想解排序法(fuzzy TOPSIS)引入适应能力评估中,构建了一套完整的水资源适应能力评估方法。通过对北京多区域水资源适应能力的评估,证明了该方法在实际应用中具有较强的可操作性。针对评估结果,为北京市水资源系统提出针对性适应性建议。

结合Fuzzy-ANP和灰色评价的管制系统运行质量评估模型

在保证管制系统安全运行的前提下,提高空中交通管制系统的运行质量可以提高航空运输效率、降低运行成本、减少空中交通拥堵,而评估管制系统运行质量的水平是提高运行质量的前提,因此有必要对管制系统的运行质量进行评估。分析了管制系统的动态运行过程以及各个过程的影响因素,建立了管制系统运行质量评估指标体系,利用网络层次分析法分析各指标的相关性,计算出指标体系中各层指标的权重,根据灰色综合评价方法建立了管制系统质量评估模型。算例表明,模型具有有效性和实用性。

基于混合fuzzy entropy-TOPSIS法的供应链范式选择

针对精益、敏捷、精敏供应链范式选择决策涉及到多种定性指标和定量指标这一特点,提出一种基于模糊集理论、熵和TOPSIS的混合型多属性决策模型。为了避免主观赋权法无法反映客观条件变化,或客观赋权法无法反映专家经验的双重弊端,在对定量指标赋权时,采用主观赋权的三角模糊数法和客观赋权的熵权法对定量指标进行组合赋权。对于定性指标仅依靠三角模糊数法确定其权重。然后,运用fuzzy TOPSIS法选择出最佳的供应链范式。最后通过实例对模型进行验证以及对评价指标权重进行敏感性分析,证实了该模型能为企业选择适用自身运作的供应链范式提供高效方法。

Fuzzy概率空间的Fuzzy格刻划

本文研究了Fuzzy概率空间中Fuzzy事件及概率的代数性质.利用Fuzzy概率空间中的概率为集函数这一特征和Fuzzy格的相关理论,得到了Fuzzy概率空间中的概率是从一个Fuzzy格到某个区间的Fuzzy格模同态,并将概率分解成Fuzzy格同态与Fuzzy格模同态的乘积.

整体偏联系数与随机模拟耦合的水资源承载力评价方法

为定量评价区域水资源承载力、挖掘区域水资源承载力评价过程中的不确定性信息、合理构造集对分析联系数分量的迁移率矩阵,提出采用基于同异反总关系程度“a+b+c”度量的整体偏联系数方法计算得到修正联系数分量,再结合三角模糊数随机模拟方法,构建了基于整体偏联系数与随机模拟耦合的水资源承载力评价方法。文中模型在宿州市2011—2019年的应用结果表明:宿州市水资源承载能力总体偏低,除2018年以外,其余年份水资源承载力评价等级均在2级以上,但是评价等级有逐年下降趋势,水资源承载力呈现正向改善的趋势;水资源承载力级别特征值全部落在本文方法计算出的评价区间内,认为该方法合理,与基于偏联系数原理构造的迁移率矩阵计算的评级等级基本一致且误差更小,说明该方法在联系数分量迁移转化时更合理,可为判别区域水资源承载力评价等级、合理调控区域水资源承载力提供有效途径。