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. Moreover, based on the proposed PHFE entropy measures, we introduce some entropy-based distance measures which are used in the portion of comparative analysis.
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 term…
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））
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 constructed a model to determine weights of criterias and presented a solution for determining the optimal alternative by using the constructed model and relationship analysis between criterias in fuzzy group decision-making problem with different forms of preference information of decision makers on criterias.
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…
Xi’an Jiaotong University（西安交通大学）；University of Electronic Science and Technology of China（电子科技大学）
We apply the Ordered Weighted Averaging (OWA) operator in multi-criteria decision-making. To satisfy different kinds of uncertainty, measure based dominance has been presented to gain the order of different criterion. However, this idea has not been applied in fuzzy system until now. In this paper, we focus on the situation where the linguistic satisfactions are fuzzy measures instead of the exact values. We review the concept of OWA operator and discuss the order mechanism of fuzzy number. Then we combine with measure-based dominance to give an overall score of each alternatives. An example i…
The purpose of this paper is to point to the usefulness of applying a linear mathematical formulation of fuzzy multiple criteria objective decision methods in organising business activities. In this respect fuzzy parameters of linear programming are modelled by preference-based membership functions. This paper begins with an introduction and some related research followed by some fundamentals of fuzzy set theory and technical concepts of fuzzy multiple objective decision models. Further a real case study of a manufacturing plant and the implementation of the proposed technique is presented. Em…
Suuplier selection is one of the most important functions of a purchasing department. Since by deciding the best supplier, companies can save material costs and increase competitive advantage.However this decision becomes compilcated in case of multiple suppliers, multiple conflicting criteria, and imprecise parameters. In addition the uncertainty and vagueness of the experts' opinion is the prominent characteristic of the problem. therefore an extensively used multi criteria decision making tool Fuzzy AHP can be utilized as an approach for supplier selection problem. This paper reveals the ap…
Silesian University in Opava, School of Business Administration in Karviná（奥帕瓦西里西亚大学，卡尔维纳商业管理学院）
In practice, a ranking of objects with respect to given set of criteria is of considerable importance. However, due to lack of knowledge, information of time pressure, decision makers might not be able to provide a (crisp) ranking of objects from the top to the bottom. Instead, some objects might be ranked equally, or better than other objects only to some degree. In such cases, a generalization of crisp rankings to fuzzy rankings can be more useful. The aim of the article is to introduce the notion of a fuzzy ranking and to discuss its several properties, namely orderings, similarity and inde…
Southwest Petroleum University（西南石油大学）；Zhuhai College of Jilin University（吉林大学珠海学院）；Karadeniz Technical University（黑海技术大学）；Shandong University of Finance and Economics（山东财经大学）；Shandong University（山东大学）；Beijing University of Technology（北京工业大学）
The picture fuzzy set, characterized by three membership degrees, is a helpful tool for multi-criteria decision making (MCDM). This paper investigates the structure of the closed operational laws in the picture fuzzy numbers (PFNs) and proposes efficient picture fuzzy MCDM methods. We first introduce an admissible order for PFNs and prove that all PFNs form a complete lattice under this order. Then, we give some specific examples to show the non-closeness of some existing picture fuzzy aggregation operators. To ensure the closeness of the operational laws in PFNs, we construct a new class of p…
Decision-making is a process of choosing among alternative courses of action for solving complicated problems where multi-criteria objectives are involved. The past few years have witnessed a growing recognition of Soft Computing technologies that underlie the conception, design and utilization of intelligent systems. Several works have been done where engineers and scientists have applied intelligent techniques and heuristics to obtain optimal decisions from imprecise information. In this paper, we present a concurrent fuzzy-neural network approach combining unsupervised and supervised learni…
Normally a decision support system is build to solve problem where multi-criteria decisions are involved. The knowledge base is the vital part of the decision support containing the information or data that is used in decision-making process. This is the field where engineers and scientists have applied several intelligent techniques and heuristics to obtain optimal decisions from imprecise information. In this paper, we present a hybrid neuro-genetic learning approach for the adaptation a Mamdani fuzzy inference system for the Tactical Air Combat Decision Support System (TACDSS). Some simulat…
University of Development Alternative (UODA)（发展替代大学）；University of Dhaka（达卡大学）
In various cases of decision analysis we use two popular methods: Analytical Hierarchical Process (AHP) and Fuzzy based AHP or Fuzzy AHP. Both the methods deal with stochastic data and can determine decision result through Multi Criteria Decision Making (MCDM) process. Obviously resulting values of the two methods are not same though same set of data is fed into them. In this research work, we have tried to observe similarities and dissimilarities between two methods outputs. Almost same trend or fluctuations in outputs have been seen for both methods for same set of input data which are not c…
State Islamic University of Sunan Kalijaga（苏南卡利加达国立伊斯兰大学）；University of Ahmad Dahlan（艾哈迈德·达兰大学）
As the education fees are becoming more expensive, more students apply for scholarships. Consequently, hundreds and even thousands of applications need to be handled by the sponsor. To solve the problems, some alternatives based on several attributes (criteria) need to be selected. In order to make a decision on such fuzzy problems, Fuzzy Multiple Attribute Decision Making (FMDAM) can be applied. In this study, Unified Modeling Language (UML) in FMADM with TOPSIS and Weighted Product (WP) methods is applied to select the candidates for academic and non-academic scholarships at Universitas Isla…
Southwest University（西南大学）；The Hong Kong Polytechnic University（香港理工大学）；University of British Columbia（不列颠哥伦比亚大学）；Vanderbilt University（范德堡大学）
How to express an expert's or a decision maker's preference for alternatives is an open issue. Consistent fuzzy preference relation (CFPR) is with big advantages to handle this problem due to it can be construed via a smaller number of pairwise comparisons and satisfies additive transitivity property. However, the CFPR is incapable of dealing with the cases involving uncertain and incomplete information. In this paper, a D numbers extended consistent fuzzy preference relation (D-CFPR) is proposed to overcome the weakness. The D-CFPR extends the classical CFPR by using a new model of expressing…
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
The goal of this paper is twofold. Once to highlight some basic problematic properties of the KH Fuzzy Rule Interpolation through examples, secondly to set up a brief Benchmark set of Examples, which is suitable for testing other Fuzzy Rule Interpolation (FRI) methods against these ill conditions. Fuzzy Rule Interpolation methods were originally proposed to handle the situation of missing fuzzy rules (sparse rule-bases) and to reduce the decision complexity. Fuzzy Rule Interpolation is an important technique for implementing inference with sparse fuzzy rule-bases. Even if a given observation h…
Goalkeeper (GK) is an expert in soccer and goalkeeping is a complete professional job. In fact, achieving success seems impossible without a reliable GK. His effect in successes and failures is more dominant than other players. The most visible mistakes in a game are those of goalkeeper's. In this paper the expert fuzzy system is used as a suitable tool to study the quality of a goalkeeper and compare it with others. Previously done researches are used to find the goalkeepers' indexes in soccer. Soccer experts have found that a successful GK should have some qualifications. A new pattern is of…
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）
Important advances have been made in the fuzzy quantification field. Nevertheless, some problems remain when we face the decision of selecting the most convenient model for a specific application. In the literature, several desirable adequacy properties have been proposed, but theoretical limits impede quantification models from simultaneously fulfilling every adequacy property that has been defined. Besides, the complexity of model definitions and adequacy properties makes very difficult for real users to understand the particularities of the different models that have been presented. In this…
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…
Mountain river torrents and snow avalanches generate human and material damages with dramatic consequences. Knowledge about natural phenomenona is often lacking and expertise is required for decision and risk management purposes using multi-disciplinary quantitative or qualitative approaches. Expertise is considered as a decision process based on imperfect information coming from more or less reliable and conflicting sources. A methodology mixing the Analytic Hierarchy Process (AHP), a multi-criteria aid-decision method, and information fusion using Belief Function Theory is described. Fuzzy S…
CSIR-Structural Engineering Research Centre（印度科学与工业研究委员会-结构工程研究中心）；Academy of Scientific and Innovative Research（科学与创新研究院）
In multi-criteria decision making (MCDM) problems, ratings are assigned to the alternatives on different criteria by the expert group. In this paper, we propose a thermodynamically consistent model for MCDM using the analogies for thermodynamical indicators - energy, exergy and entropy. The most commonly used method for analysing MCDM problem is Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The conventional TOPSIS method uses a measure similar to that of energy for the ranking of alternatives. We demonstrate that the ranking of the alternatives is more meaningful …
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 …
In an automated search system, similarity is a key concept in solving a human task. Indeed, human process is usually a natural categorization that underlies many natural abilities such as image recovery, language comprehension, decision making, or pattern recognition. In the image search axis, there are several ways to measure the similarity between images in an image database, to a query image. Image search by content is based on the similarity of the visual characteristics of the images. The distance function used to evaluate the similarity between images depends on the criteria of the searc…
S$^2$FS: Spatially-Aware Separability-Driven Feature Selection in Fuzzy Decision Systems
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 Computer Science, Nanjing University（南京大学计算机科学学院）；School of Computer, Jiangsu University of Science and Technology（江苏科技大学计算机学院）
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…
University of Ottawa（渥太华大学）；Methodist University of Piracicaba（皮拉西卡巴卫理公会大学）；University of Campinas（坎皮纳斯大学）；Embrapii-Brazilian Association for Industrial Research and Innovation（Embrapii-巴西工业研究与创新协会）；Mackenzie Presbyterian University（麦肯齐长老会大学）；KMI Software Consulting（KMI软件咨询公司）
Despite the availability of qualified research personnel, up-to-date research facilities and experience in developing applied research and innovation, many worldwide research institutions face difficulties when managing contracted Research and Development (R&D) projects due to expectations from Industry (private sector). Such difficulties have motivated funding agents to create evaluation processes to check whether the operational procedures of funded research institutions are sufficient to provide timely answers to demand for innovation from industry and also to identify aspects that require …
The Tournament Tree Method for preference elicitation in Multi-criteria decision-making
Department of Mathematics, Universidad de Ja \'e n, 23071 Ja \'e n, Spain；Department of Computer Science, Universidad de Ja \'e n, 23071 Ja \'e n, Spain
