Multi-Granularity Neighborhood Fuzzy Rough Set Model on Two Universes

The two universes multi-granularity fuzzy rough set model is an effective tool for handling uncertainty problems between two domains with the help of binary fuzzy relations. This article applies the idea of neighborhood rough sets to two universes multi-granularity fuzzy rough sets, and discusses the two-universes multi-granularity neighborhood fuzzy rough set model. Firstly, the upper and lower approximation operators are defined in the two universes multi-granularity neighborhood fuzzy rough set model. Secondly, the properties of the upper and lower approximation operators are discussed. Finally, the properties of the two universes multi-granularity neighborhood fuzzy rough set model are verified through case studies.

Linguistic Dynamic Modeling and Analysis of Psychological Health State Using Interval Type-2 Fuzzy Sets

The study of psychological health state is helpful to build appropriate models and take effective intervention strategies, and the results benefit the intervened released from psychological distress within the shortest possible time. In this paper, interval type-2 fuzzy sets and fuzzy comprehension evaluation are applied in the analysis of mental health status and crisis intervention. A closed-loop linguistic dynamic intervention model for psychological health state is built. Linguistic dynamic systems based on interval type-2 fuzzy sets are used to describe and analyze the evolutionary process of psychological health status. © 2014 Chinese Association of Automation.

Fuzzy interval linguistic sets with applications in multi-attribute group decision making

Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.

Cubic q-Rung Orthopair Fuzzy Linguistic Set and Their Application to Multiattribute Decision-making with Muirhead Mean Operator

The objective of this paper is to present a new concept,named cubic q-rung orthopair fuzzy linguistic set(Cq-ROFLS),to quantify the uncertainty in the information.The proposed Cq-ROFLS is a qualitative form of cubic q-rung orthopair fuzzy set,where membership degrees and nonmembership degrees are represented in terms of linguistic variables.The basic notions of Cq-ROFLS have been introduced and study their basic operations and properties.Furthermore,to aggregate the different pairs of preferences,we introduce the Cq-ROFL Muirhead mean-(MM),weighted MM-,dual MM-based operators.The major advantage of considering the MM is that it considers the interrelationship between more than two arguments at a time.On the other hand,the Cq-ROFLS has the ability to describe the qualitative information in terms of linguistic variables.Several properties and relation of the derived operators are argued.In addition,we also investigate multiattribute decision-making problems under the Cq-ROFLS environment and illustrate with a numerical example.Finally,the effectiveness and advantages of the work are established by comparing with other methods.

Linguistic approaches to multiple attribute decision making in uncertain linguistic setting

We studied multiple attribute decision-making problems with uncertain linguistic information, in which the preference values took the form of uncertain linguistic variables. We introduced some operational laws of uncertain linguistic variables and a formula for the comparison between two uncertain linguistic variables. We proposed two new aggregation operators called extended uncertain linguistic aggregation (EULA) operator and interval linguistic aggregation (ILA) operator, and then develop an EULA operator-based linguistic approach and an ILA operator-based linguistic approach, respectively, to multiple attribute decision making in uncertain linguistic setting. The approaches were straightforward and do not produce any loss of information. Finally, an illustrative example was given to verify the developed approaches and to demonstrate their practicality and effectiveness.

An Evidence-Based CoCoSo Framework with Double Hierarchy Linguistic Data for Viable Selection of Hydrogen Storage Methods

Hydrogen is the new age alternative energy source to combat energy demand and climate change.Storage of hydrogen is vital for a nation’s growth.Works of literature provide different methods for storing the produced hydrogen,and the rational selection of a viable method is crucial for promoting sustainability and green practices.Typically,hydrogen storage is associated with diverse sustainable and circular economy(SCE)criteria.As a result,the authors consider the situation a multi-criteria decision-making(MCDM)problem.Studies infer that previous models for hydrogen storage method(HSM)selection(i)do not consider preferences in the natural language form;(ii)weights of experts are not methodically determined;(iii)hesitation of experts during criteria weight assessment is not effectively explored;and(iv)three-stage solution of a suitable selection of HSM is unexplored.Driven by these gaps,in this paper,authors put forward a new integrated framework,which considers double hierarchy linguistic information for rating,criteria importance through inter-criteria correlation(CRITIC)for expert weight calculation,evidence-based Bayesian method for criteria weight estimation,and combined compromise solution(CoCoSo)for ranking HSMs.The applicability of the developed framework is testified by using a case example of HSM selection in India.Sensitivity and comparative analysis reveal the merits and limitations of the developed framework.

Dynamic hesitant fuzzy linguistic group decision-making from a reliability perspective

A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.

Medical Waste Treatment Station Selection Based on Linguistic q-Rung Orthopair Fuzzy Numbers

During the COVID-19 outbreak,the use of single-use medical supplies increased significantly.It is essential to select suitable sites for establishing medical waste treatment stations.It is a big challenge to solve the medical waste treatment station selection problem due to some conflicting factors.This paper proposes a multi-attribute decision-making(MADM)method based on the partitioned Maclaurin symmetric mean(PMSM)operator.For the medical waste treatment station selection problem,the factors or attributes(these two terms can be interchanged.)in the same clusters are closely related,and the attributes in different clusters have no relationships.The partitioned Maclaurin symmetric mean function(PMSMF)can handle these complex attribute relationships.Hence,we extend the PMSM operator to process the linguistic q-rung orthopair fuzzy numbers(Lq-ROFNs)and propose the linguistic q-rung orthopair fuzzy partitioned Maclaurin symmetric mean(Lq-ROFPMSM)operator and its weighted form(Lq-ROFWPMSM).To reduce the negative impact of unreasonable data on the final output results,we propose the linguistic q-rung orthopair fuzzy partitioned dual Maclaurin symmetric mean(Lq-ROFPDMSM)operator and its weighted form(Lq-ROFWPDMSM).We also discuss the characteristics and typical examples of the above operators.A novel MADM method uses the Lq-ROFWPMSM operator and the Lq-ROFWPDMSM operator to solve the medical waste treatment station selection problem.Finally,the usability and superiority of the proposed method are verified by comparing it with previous methods.

Three-way group decision making with linguistic evaluations

Based on linguistic evaluations, a linguistic threeway decision method is proposed. First, the alternatives are rated in linguistic forms and divided into acceptance, rejection and uncertainty regions. Secondly, the linguistic three-way group decision steps are provided. Specifically, the experts determine the lower bound and upper bound of the uncertainty region, respectively. When the evaluation is superior to the upper bound, the corresponding alternative is put into the acceptance region directly. Similarly, when the evaluation is inferior to the lower bound, the corresponding alternative is put into the rejection region directly, and the remaining alternatives are put into the uncertain region. Moreover, the objects in the uncertainty region are especially discussed. The linguistic terms are transformed into fuzzy numbers and then aggregated. Finally, a recommendation example is provided to illustrate the practicality and validity of the proposed method.

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.

A BENCHMARK EXERCISE ON FUZZY SET THEORY BASED EXPERT JUDGEMENT TECHNIQUE

It is sometimes impossible to make a correct decision in a certain engineering task without the help from professional expert judgments. Even though there are different expert opinions available, however, they should be appropriately aggregated to a useful form for making an acceptable engineering decision. This paper proposed a technique which utilizes the fuzzy set theory in the aggregation of expert judgments. In the technique, two main key concepts are employed: linguistic variables and fuzzy numbers. Linguistic variables first represent the relative importance of evaluation criteria under consideration and the degree of confidence on each expert perceived by the decision maker, and then are replaced by suitable triangular fuzzy numbers for arithmetic manipulation. As a benchmark problem, the pressure increment in the containment of Sequoyah nuclear power plant due to reactor vessel breach was estimated to verify and validate the proposed technique.

A Hybrid Learning Method for the Data-Driven Design of Linguistic Dynamic Systems

In lots of data based prediction or modeling applications,uncertainties and/or noises in the observed data cannot be avoided.In such cases,it is more preferable and reasonable to provide linguistic(fuzzy)predicted results described by fuzzy memberships or fuzzy sets instead of the crisp estimates depicted by numbers.Linguistic dynamic system(LDS)provides a powerful tool for yielding linguistic(fuzzy)results.However,it is still difficult to construct LDS models from observed data.To solve this issue,this paper first presents a simplified LDS whose inputoutput mapping can be determined by closed-form formulas.Then,a hybrid learning method is proposed to construct the data-driven LDS model.The proposed hybrid learning method firstly generates fuzzy rules by the subtractive clustering method,then carries out further optimization of centers of the consequent triangular fuzzy sets in the fuzzy rules,and finally adopts multiobjective optimization algorithm to determine the left and right end-points of the consequent triangular fuzzy sets.The proposed approach is successfully applied to three real-world prediction applications which are:prediction of energy consumption of a building,forecasting of the traffic flow,and prediction of the wind speed.Simulation results show that the uncertainties in the data can be effectively captured by the linguistic(fuzzy)estimates.It can also be extended to some other prediction or modeling problems,in which observed data have high levels of uncertainties.

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。

Warhead power assessment based on double hierarchy hesitant fuzzy linguistic term sets theory and gained and lost dominance score method

Warhead power assessment of the anti-ship missile plays a vital role in determining the optimal design of missile, thus having important strategic research significance. However, in the assessment process, expert’s judgement will directly affect the assessment accuracy. In addition,there are many criteria involved in the missile design alternatives. Some criteria with poor performance may be compensated by other criteria with excellent performance, and then it is impossible to find the truly optimal alternative. Aimed at solving these problems, this paper proposes a synthetical assessment process based on fuzzy hesitant linguistic term set and the Gained and Lost Dominance Score(GLDS) method. In order to improve the assessment accuracy of experts and solve the problem that experts generate different opinions, combined with the advantages of fuzzy hesitant sets and linguistic term sets, the double hierarchy hesitant fuzzy linguistic term sets are used in this paper to improve the accuracy of expert’s judgement. In order to effectively combine expert’s experience with the data of criteria, the evidence theory and entropy weight method are used to transfer the expert’s judgement to the weight. In order to avoid selecting defective alternative of missile design, the GLDS is used to fuse expert information and criteria information. Sensitivity analysis shows that the assessment process has sensitivity to some extent. However, when the fluctuation of expert’s assessment makes the fluctuation of θ in the range of-5% to 5%, the impact on the results is not quite conspicuous. The analysis of calculation result and comparative analysis show that the assessment process proposed in this paper is accurate enough, has great advantage in selecting the current and potential optimal alternative of missile design, and avoids the alternatives with low criteria performance that cannot be compensated by other criteria being selected.

Fuzzy Logic in the Quantum Mechanical Worldview;Related to Zadeh, Wittgenstein, Moore, Saussure, Quine, Lewis Carroll, etc.

Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus we think that quantum language is one of the most powerful scientific theories, like statistics. In this paper we justify Zadeh’s fuzzy sets theory in quantum language, that is, fuzzy propositions are identified with binary measurements. This implies that the definition of “proposition” is, for the first time, acquired in the field of non-mathematics. Further, we assert that fuzzy logic is more natural than crisp logic in science. And furthermore, we discuss and solve Saussure’s linguistics, Moore’s paradox, Quine’s analytic-synthetic distinction and Lewis Carroll’s logical paradox. Therefore, from the philosophical point of view, our result gives a complete answer to Wittgenstein’s problem: “Why does logic work in our world?” and “What is a scientific proposition?” in his picture theory. That is, we simultaneously justify both Zadeh’s fuzzy sets and Wittgenstein’s picture theory in the quantum mechanical worldview.

基于FDHHFLTS-BN的海底管道泄漏失效风险定量分析

为预防海底油气管道泄漏失效事故,提出基于自由双层次犹豫模糊语言术语集(FDHHFLTS)和贝叶斯网络(BN)的FDHHFLTS-BN风险分析方法,用于分析海底油气管道泄漏失效事故概率及事故的关键风险因素。将故障树模型转换为BN结构,由专家根据FDHHFLTS评估基本事件发生可能性;采用最佳最差法(BWM)确定专家权重,结合相似性聚合方法(SAM)聚合专家意见;依据构建的BN模型,正向推理得到事故发生概率,反向推理得到后验概率,并进行敏感性分析。将该方法应用于实例分析,结果表明:分析段海底管道泄漏事故的概率值为P=6.20×10^(-3);焊缝施工缺陷、材料施工缺陷和渔具作用等为事故发生的关键因素;与传统方法对比分析结果证明,所提方法在确定海底管道风险方面具有一定的优势。

基于多粒度犹豫模糊语言术语集的TOPSIS决策方法研究

为了解决在实际决策时,由于知识背景不同决策者采用不同粒度语言术语集来表达而导致决策结果不准确的问题,本文提出了一种基于多粒度犹豫模糊语言术语集的逼近理想解排序(technique for order preference by similarity to ideal solution,TOPSIS)决策方法。首先选用各术语集中的最大粒度作为标准粒度,通过转换算法将每个决策者的语言术语集转换到同一标准粒度下进行集结,得出相应的隶属度语言术语集;然后结合TOPSIS方法,计算每个备选方案与正、负理想点距离,以相对贴近度的大小排序实现最优方案的选择;最后,通过一个实例,验证该方法的可行性和优越性。本文所提方法可应用于最优方案的选择问题中,提升决策结果准确度。

基于后悔理论的多属性决策方法及其在就业选择中的应用

针对决策者在决策过程所产生的心理行为和决策属性权重未知的决策问题,提出基于后悔理论的语言直觉模糊多属性决策方法并用于就业选择。基于Jensen-Shannon散度提出语言直觉模糊JS距离,并通过对比分析验证其合理性。将给出的JS距离和后悔理论相结合,利用后悔值最小化和欣喜值最大化构建赋权模型,并与决策效用值聚合给出备选方案排序。将提出的方法应用于某计算机系学生对就业的选择实例中,通过与其他决策方法进行比较分析,证明了所提方法在就业选择中的有用性和有效性。

区间二元语言毕达哥拉斯模糊信息下MULTIMOORA和ELECTRE方法

为了解决复杂模糊环境下的多属性决策问题,提出一种基于区间二元语言毕达哥拉斯模糊信息的MULTIMOORA和ELECTRE方法。首先结合毕达哥拉斯语言集和区间二元语言变量,提出了关于隶属度,非隶属度和语言变量均为区间值的区间二元语言毕达哥拉斯模糊集。其次对于传统MULTIMOORA方法中未考虑各模型权重的情况,构建单目标优化模型来确定模型权重。最后提出区间二元语言毕达哥拉斯模糊信息的MULTIMOORA和ELECTRE方法并且通过实例说明了该方法的可行性和有效性。

Multi-attribute group decision-making method with linguistic q-rung orthopair fuzzy information based on bi-direction Choquet integral

Purpose-The purpose of this paper is to develop the linguistic q-rung orthopair fuzzy set(LqROFS)information VIKOR method based on the bi-direction Choquet integral(BDCI),taking into account the correlation between information.The method can enrich the existing studies related to LqROFS information and better solve the problem of MAGDM problem.Design/methodology/approach-Since applying Choquet integral(CI)depict information interaction is a common operation in MAGDM.However,the traditional CI has some limitations.The unidirectional alignment may affect the MAGDM results.Therefore,a LqROFS-VIKOR method based on BDCI is proposed,where BDCI is used to aggregate the decision matrix.Furthermore,it is not reasonable to apply exact numbers to express the similarity between two qualitative data.Then a new method of defining similarity using linguistics is proposed.The similarity is used to calculate attribute weights.Findings-The validity and potential application of MAGMD method with linguistic q-rung orthopair fuzzy information based on BDCI are demonstrated in a numerical examples study.Originality/value-According to the study of available literature,the current research on LqROFS is incomplete.The existing studies of both similarity and aggregate operators have certain shortcomings.The definition of similarity proposed in this paper is more in line with reality.And compared with the existing methods,the BDCI-based aggregate operator can describe the interaction between information more reasonably.Based on this VIKOR method based on BDCI under the LqROFS environment can better select the alternative.