Approaches based on computing with words find good applicability in decision making systems. Predominantly finding their basis in type-1 fuzzy sets, computing with words approaches employ type-1 fuzzy sets as semantics of the linguistic terms. However, type-2 fuzzy sets have been proven to be scientifically more appropriate to represent linguistic information in practical systems. They take into account both the intra-uncertainty as well as the inter-uncertainty in cases where the linguistic information comes from a group of experts. Hence in this paper, we propose to introduce linguistic terms whose semantics are denoted by interval type-2 fuzzy sets within the hesitant fuzzy linguistic term set framework, resulting in type-2 fuzzy sets based hesitant fuzzy linguistic term sets. We also introduce a novel method of computing type-2 fuzzy envelopes out of multiple interval type-2 fuzzy sets with trapezoidal membership functions. Furthermore, the proposed framework with interval type-2 fuzzy sets is applied on a supplier performance evaluation scenario. Since humans are predominantly involved in the entire process of supply chain, their feedback is crucial while deciding many factors. Towards the end of the paper, we compare our presented model with various existing models and demonstrate the advantages of the former.
Quchan University of Technology（库昌理工大学）；University of Melbourne（墨尔本大学）
This contribution reviews critically the existing entropy measures for probabilistic hesitant fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively distinguish a variety of different PHFSs in some cases. In the sequel, we develop a new axiomatic framework of entropy measures for probabilistic hesitant fuzzy elements (PHFEs) by considering two facets of uncertainty associated with PHFEs which are known as fuzziness and nonspecificity. Respect to each kind of uncertainty, a number of formulae are derived to permit flexible selection of PHFE entropy measures. Moreov…
Quchan University of Technology（古昌理工大学）；University of Melbourne（墨尔本大学）
Generally, the criteria involved in a decision making problem are interactive or inter-dependent, and therefore aggregating them by the use of traditional operators which are based on additive measures is not logical. This verifies that we have to implement fuzzy measures for modelling the interaction phenomena among the criteria.On the other hand, based on the recent extension of hesitant fuzzy set, called higher order hesitant fuzzy set (HOHFS) which allows the membership of a given element to be defined in forms of several possible generalized types of fuzzy set, we encourage to propose the…
Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets
School of Management, Jiangsu University（江苏大学管理学院）；Business School, Sichuan University（四川大学商学院）；School of Economics and Management, Jiangsu University of Science and Technology（江苏科技大学经济管理学院）；School of Economics and Management, Nanjing University of Science and Technology（南京理工大学经济管理学院）
South China University of Technology（华南理工大学）；National Institute of Agricultural Botany（英国国家农业植物研究所）；The University of Manchester（曼彻斯特大学）
Hesitant fuzzy linguistic preference relation (HFLPR) is of interest because it provides an efficient way for opinion expression under uncertainty. For enhancing the theory of decision making with HFLPR, the paper introduces an algorithm for group decision making with HFLPRs based on the acceptable consistency and consensus measurements, which involves (1) defining a hesitant fuzzy linguistic geometric consistency index (HFLGCI) and proposing a procedure for consistency checking and inconsistency improving for HFLPR; (2) measuring the group consensus based on the similarity between the origina…
Teranga Go!: Carpooling Collaborative Consumption Community with multi-criteria hesitant fuzzy linguistic term set opinions to build confidence and trust
University of Granada（格拉纳达大学）；Andalusian Research Institute in Data Science and Computational Intelligence, DaSCI（安达卢西亚数据科学与计算智能研究所（DaSCI））
Centro Singular de Investigación en Tecnoloxías da Información (CiTIUS), Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学信息技术 singular 研究中心（CiTIUS））
Fuzzy quantification is a subtopic of fuzzy logic which deals with the modelling of the quantified expressions we can find in natural language. Fuzzy quantifiers have been successfully applied in several fields like fuzzy, control, fuzzy databases, information retrieval, natural language generation, etc. Their ability to model and evaluate linguistic expressions in a mathematical way, makes fuzzy quantifiers very powerful for data analytics and data mining applications. In this paper we will give a general overview of the main applications of fuzzy quantifiers in this field as well as some ide…
CSIRO Mathematical and Information Sciences（澳大利亚联邦科学与工业研究组织数学与信息科学研究所）
Most fuzzy systems including fuzzy decision support and fuzzy control systems provide out-puts in the form of fuzzy sets that represent the inferred conclusions. Linguistic interpretation of such outputs often involves the use of linguistic approximation that assigns a linguistic label to a fuzzy set based on the predefined primary terms, linguistic modifiers and linguistic connectives. More generally, linguistic approximation can be formalized in the terms of the re-translation rules that correspond to the translation rules in ex-plicitation (e.g. simple, modifier, composite, quantification a…
Neutrosophic theory and applications have been expanding in all directions at an astonishing rate especially after the introduction the journal entitled Neutrosophic Sets and Systems. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structure such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hes…
In this paper we deal with the problem of extending Zadeh's operators on fuzzy sets (FSs) to interval-valued (IVFSs), set-valued (SVFSs) and type-2 (T2FSs) fuzzy sets. Namely, it is known that seeing FSs as SVFSs, or T2FSs, whose membership degrees are singletons is not order-preserving. We then describe a family of lattice embeddings from FSs to SVFSs. Alternatively, if the former singleton viewpoint is required, we reformulate the intersection on hesitant fuzzy sets and introduce what we have called closed-valued fuzzy sets. This new type of fuzzy sets extends standard union and intersection…
Linguistic Fuzzy Information Evolution with Random Leader Election Mechanism for Decision-Making Systems
School of Mechanical and Aerospace Engineering, Nanyang Technological University（南洋理工大学机械与航天工程学院）；Department of Electrical and Computer Engineering, University of Alberta（阿尔伯塔大学电气与计算机工程系）；School of Electro-Mechanical Engineering（机电工程学院）；Faculty of Engineering, King Abdulaziz University（阿卜杜勒阿齐兹大学工程学院）
In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera & Martinez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the computations are accomplished without loss of information while the results of the decision-making p…
Preparatory institute of engineering studies of Monastir（莫纳斯提尔工程研究预备学院）
The main objective of this paper is to develop a new semantic Network structure, based on the fuzzy sets theory, used in Artificial Intelligent system in order to provide effective on-line assistance to users of new technological systems. This Semantic Networks is used to describe the knowledge of an "ideal" expert while fuzzy sets are used both to describe the approximate and uncertain knowledge of novice users who intervene to match fuzzy labels of a query with categories from an "ideal" expert. The technical system we consider is a word processor software, with Objects such as "Word" and Go…
Centro de Investigación en Tecnoloxías da Información (CITIUS)（信息技术研究中心（CITIUS））；University of Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）
Syllogism is a type of deductive reasoning involving quantified statements. The syllogistic reasoning scheme in the classical Aristotelian framework involves three crisp term sets and four linguistic quantifiers, for which the main support is the linguistic properties of the quantifiers. A number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main support is cardinality calculus. In this paper we analyze fuzzy syllogistic models previously described by Zadeh and Dubois et al. and compare their behavior with that of the classical Aristotelian framewor…
Trapeznikov Institute of Control Science Russian Academy of Sciences（俄罗斯科学院特拉佩兹尼科夫控制科学研究所）
A concept of multi-valued cognitive maps is introduced in this paper. The concept expands the fuzzy one. However, all variables and weights are not linearly ordered in the concept, but are only partially-ordered. Such an ap- proach allows us to operate in cognitive maps with partially-ordered linguis- tic variables directly, without vague fuzzification/defuzzification methods. Hence, we may consider more subtle differences in degrees of experts' uncer- tainty, than in the fuzzy case. We prove the convergence of such cognitive maps and give a simple computational example which demonstrates usin…
Centro Singular en Investigación en Tecnoloxías da Información (CiTIUS), Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学信息技术研究中心）；University of Aberdeen（阿伯丁大学）；Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；University of Dundee（邓迪大学）
Vagueness and uncertainty management is counted among one of the challenges that remain unresolved in systems that generate texts from non-linguistic data, known as data-to-text systems. In the last decade, work in fuzzy linguistic summarization and description of data has raised the interest of using fuzzy sets to model and manage the imprecision of human language in data-to-text systems. However, despite some research in this direction, there has not been an actual clear discussion and justification on how fuzzy sets can contribute to data-to-text for modeling vagueness and uncertainty in wo…
Double Fuzzy Probabilistic Interval Linguistic Term Set and a Dynamic Fuzzy Decision Making Model based on Markov Process with tts Application in Multiple Criteria Group Decision Making
Centro Singular de Investigación en Tecnoloxías da Información (CiTIUS)（信息科技卓越研究中心（CiTIUS））；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）
We explore the implications of using fuzzy techniques (mainly those commonly used in the linguistic description/summarization of data discipline) from a natural language generation perspective. For this, we provide an extensive discussion of some general convergence points and an exploration of the relationship between the different tasks involved in the standard NLG system pipeline architecture and the most common fuzzy approaches used in linguistic summarization/description of data, such as fuzzy quantified statements, evaluation criteria or aggregation operators. Each individual discussion …
Dokuz Eylul University（多库兹·埃吕尔大学）；Sumgait State University（苏姆盖特国立大学）
In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers are commonly performed. Aggregation and defuzzification operations are some of these often used operations. Many aggregation and defuzzification operators produce results independent to the decision makers strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take into account the level weights and the decision makers optimism strategy. This gives flexibility to the WABL operator and, through machine learning, can be trained in the direction of the decision m…
National University of Sciences and Technology (NUST)（国立科技大学（NUST））
This paper models a decision support system to predict the occurance of suicide attack in a given collection of cities. The system comprises two parts. First part analyzes and identifies the factors which affect the prediction. Admitting incomplete information and use of linguistic terms by experts, as two characteristic features of this peculiar prediction problem we exploit the Theory of Fuzzy Soft Sets. Hence the Part 2 of the model is an algorithm vz. FSP which takes the assessment of factors given in Part 1 as its input and produces a possibility profile of cities likely to receive the ac…
Fuzzy Information Evolution with Three-Way Decision in Social Network Group Decision-Making
Department of Electrical Engineering, Chalmers University of Technology（皇家理工学院电子工程系）；School of Automation, Northwestern Polytechnical University（西北工业大学自动化学院）；Faculty of Informatics and Management, University of Hradec Kralove（哈拉德·克拉洛夫大学信息与管理学院）；Andalusian Research Institute in Data Science and Computational Intelligence（安达卢西亚数据科学与计算智能研究所）；Department of Computer Science and Artificial Intelligence, University of Granada（格拉纳达大学计算机科学与人工智能系）
In the era of Industry 4.0, the focus is on the minimization of human element and maximizing the automation in almost all the industrial and manufacturing establishments. These establishments contain numerous processing systems, which can execute a number of tasks, in parallel with minimum number of human beings. This parallel execution of tasks is done in accordance to a scheduling policy. However, the minimization of human element beyond a certain point is difficult. In fact, the expertise and experience of a group of humans, called the experts, becomes imminent to design a fruitful scheduli…
Northeastern University（东北大学）；Kitami Institute of Technology（北见工业大学）
Supplier selection problem has gained extensive attention in the prior studies. However, research based on Fuzzy Multi-Attribute Decision Making (F-MADM) approach in ranking resilient suppliers in logistic 4 is still in its infancy. Traditional MADM approach fails to address the resilient supplier selection problem in logistic 4 primarily because of the large amount of data concerning some attributes that are quantitative, yet difficult to process while making decisions. Besides, some qualitative attributes prevalent in logistic 4 entail imprecise perceptual or judgmental decision relevant inf…
Modeling Wise Decision Making: A Z-Number Fuzzy Framework Inspired by Phronesis
School of AI and Data Science, Indian Institute of Technology Jodhpur（人工智能与数据科学学院，印度理工学院贾姆纳格尔）；School of Liberal Arts, Indian Institute of Technology Jodhpur（人文学院，印度理工学院贾姆纳格尔）；Department of Computer Science and Engineering, Indian Institute of Technology Jodhpur（计算机科学与工程系，印度理工学院贾姆纳格尔）
本文提出基于 Z 数的模糊推理框架，将智慧决策建模为智慧分数与置信度，并通过 100 人道德困境实验验证其聚合与区分效度。
Khulna University of Engineering & Technology（库尔纳工程技术大学）
The Decision Support System (DSS) contains more than one antecedent and the degrees of strength of the antecedents need to be combined to determine the overall strength of the rule consequent. The membership values of the linguistic variables in Fuzzy have to be combined using an aggregation operator. But it is not feasible to predefine the form of aggregation operators in decision making. Instead, each rule should be found based on the feeling of the experts and on their actual decision pattern over the set of typical examples. Thus this work illustrates how the choice of aggregation operator…
Supplier selection is a typical multi-criteria decision making (MCDM) problem and lots of uncertain information exist inevitably. To address this issue, a new method was proposed based on interval data fusion. Our method follows the original way to generate classical basic probability assignment(BPA) determined by the distance among the evidences. However, the weights of criteria are kept as interval numbers to generate interval BPAs and do the fusion of interval BPAs. Finally, the order is ranked and the decision is made according to the obtained interval BPAs. In this paper, a numerical exam…
In the framework of Granular Computing (GC), Interval type 2 Fuzzy Sets (IT2 FSs) play a prominent role by facilitating a better representation of uncertain linguistic information. Perceptual Computing (Per C), a well known computing with words (CWW) approach, and its various applications have nicely exploited this advantage. This paper reports a novel Per C based approach for student strategy evaluation. Examinations are generally oriented to test the subject knowledge of students. The number of questions that they are able to solve accurately judges success rates of students in the examinati…
Thus far, limited research has been performed on resilient supplier selection - a problem that requires simultaneous consideration of a set of numerical and linguistic evaluation criteria, which are substantially different from traditional supplier selection problem. Essentially, resilient supplier selection entails key sourcing decision for an organization to gain competitive advantage. In the presence of multiple conflicting evaluation criteria, contradicting decision makers, and imprecise decision relevant information (DRI), this problem becomes even more difficult to solve with the classic…
Measuring Perceived Trust in XAI-Assisted Decision-Making by Eliciting a Mental Model
Eindhoven University of Technology（埃因霍温理工大学）；Eindhoven Artificial Intelligence Systems Institute（埃因霍温人工智能系统研究所）；Ca’ Foscari University of Venice（威尼斯大学）
