On Two‐Player Interval‐Valued Fuzzy Bayesian Games

Game theory is an important basis to simulate several situations where multiple agents interact strategically for decision making and support. In many applications, such as auctions, frequently used for resource management involving two or more agents competing for the resources, the interacting agents only know their own characteristics and must make decisions while having to estimate the characteristics of the others. When probabilities are assigned for the different types of the interacting agents, this kind of strategic interaction constitutes a Bayesian game. In cases in which it is very difficult to characterize the private information of each agent, the payoffs can be given by approximate (not probabilistic) values, but the concept of Bayesian Nash equilibrium cannot be applied in this context. Fuzzy set theory is an excellent basis for studying this type of game, where the payoffs are represented by fuzzy numbers. When it is the case that there is also uncertainty about such fuzzy numbers, the use of interval fuzzy numbers appears as a good modeling alternative. This paper introduces an approach for interval‐based fuzzy Bayesian games, based on interval‐valued fuzzy probabilities for modeling the types of agents involved in the interaction. We present two different case studies, namely the (Interval) Fuzzy Bayesian Hiring Game and (Interval) Fuzzy Bayesian Prisoner's Dilemma with Moral Standards, comparing the results obtained with the crisp, fuzzy and interval fuzzy approaches, highlighting a particular case in which the interval fuzzy approach presents a solution although the two other do not.     

Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation Operators

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with interval‐valued Pythagorean fuzzy sets (IVPFSs). First, the concept, operational laws, score function, and accuracy function of IVPFSs are defined. Then, based on the operational laws, two interval‐valued Pythagorean fuzzy aggregation operators are developed for aggregating the interval‐valued Pythagorean fuzzy information, such as interval‐valued Pythagorean fuzzy weighted average (IVPFWA) operator and interval‐valued Pythagorean fuzzy weighted geometric (IVPFWG) operator. A series of inequalities of aggregation operators are studied. Later, we develop some interval‐valued Pythagorean fuzzy point operators. Moreover, combining the interval‐valued Pythagorean fuzzy point operators with IVPFWA operator, we present some interval‐valued Pythagorean fuzzy point weighted averaging (IVPFPWA) operators, which can adjust the degree of the aggregated arguments with some parameters. Then, we propose an interval‐valued Pythagorean fuzzy ELECTRE method to solve uncertainty MAGDM problem. Finally, an illustrative example for evaluating the software developments is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Cluster Analysis Based on T‐transitive Interval‐Valued Fuzzy Relations

In this paper, we consider cluster analysis based on T‐transitive interval‐valued fuzzy relations. A fuzzy relation with its partitional tree for obtaining an agglomerative hierarchical clustering has been studied and applied. In general, these fuzzy‐relation‐based clustering approaches are based on real‐valued memberships of fuzzy relations. Since interval‐valued memberships may be better than real‐valued memberships to represent higher order imprecision and vagueness for human perception, in this paper we first extend fuzzy relations to interval‐valued fuzzy relations and then construct a clustering algorithm based on the proposed T‐transitive interval‐valued fuzzy relations. We use two examples to demonstrate the efficiency and usefulness of the proposed method. In practical application, we apply the proposed clustering method to performance evaluations for academic departments of higher education by using actual engineering school data in Taiwan.     

A Novel Method for Multiattribute Decision Making with Interval‐Valued Pythagorean Fuzzy Linguistic Information

Pythagorean fuzzy set (PFS), proposed by Yager (2013), is a generalization of the notion of Atanassov's intuitionistic fuzzy set, which has received more and more attention. In this paper, first, we define the weighted Minkowski distance with interval‐valued PFSs. Second, inspired by the idea of the Pythagorean fuzzy linguistic variables, we define a new fuzzy variable called interval‐valued Pythagorean fuzzy linguistic variable set (IVPFLVS), and the operational laws, score function, accuracy function, comparison rules, and distance measures of the IVPFLVS are defined. Third, some aggregation operators are presented for aggregating the interval‐valued Pythagorean fuzzy linguistic information such as the interval‐valued Pythagorean fuzzy linguistic weighted averaging (IVPFLWA), interval‐valued Pythagorean fuzzy linguistic ordered weighted averaging (IVPFLOWA) , interval‐valued Pythagorean fuzzy linguistic hybrid averaging, and generalized interval‐valued Pythagorean fuzzy linguistic ordered weighted average operators. Fourth, some desirable properties of the IVPFLWA and IVPFLOWA operators, such as monotonicity, commutativity, and idempotency, are discussed. Finally, based on the IVPFLWA or interval‐valued Pythagorean fuzzy linguistic geometric weighted operator, a practical example is provided to illustrate the application of the proposed approach and demonstrate its practicality and effectiveness.     

Correlation for Dual Hesitant Fuzzy Sets and Dual Interval‐Valued Hesitant Fuzzy Sets

Ever since fuzzy set has been introduced, several extensions have been established, such as interval‐valued fuzzy sets, Atanassov's intuitionistic fuzzy sets, interval‐valued Atanassov's intuitionistic fuzzy sets, fuzzy multisets, hesitant fuzzy sets, interval‐valued hesitant fuzzy sets, and dual hesitant fuzzy sets. In this contribution, we propose dual interval‐valued hesitant fuzzy sets, which encompass fuzzy sets and its aforementioned extensions as special cases. Because of the importance of correlation measure in data analysis, we propose an approach for deriving the correlation coefficient of dual hesitant fuzzy sets, and then extend the approach to the dual interval‐valued hesitant fuzzy set theory. We also put forward some formulas to create new correlation coefficients for fuzzy sets and its extensions in a general way. In addition, we give a practical example to illustrate the application of correlation coefficient for dual hesitant fuzzy sets in medical diagnosis.     

Context‐Centric Speech‐Based Human–Computer Interaction

This paper describes research that addresses the problem of dialog management from a strong, context‐centric approach. We further present a quantitative method of measuring the importance of contextual cues when dealing with speech‐based human–computer interactions. It is generally accepted that using context in conjunction with a human input, such as spoken speech, enhances a machine's understanding of the user's intent as a means to pinpoint an adequate reaction. For this work, however, we present a context‐centric approach in which the use of context is the primary basis for understanding and not merely an auxiliary process. We employ an embodied conversation agent that facilitates the seamless engagement of a speech‐based information‐deployment entity by its human end user. This dialog manager emphasizes the use of context to drive its mixed‐initiative discourse model. A typical, modern automatic speech recognizer (ASR) was incorporated to handle the speech‐to‐text translations. As is the nature of these ASR systems, the recognition rate is consistently less than perfect, thus emphasizing the need for contextual assistance. The dialog system was encapsulated into a speech‐based embodied conversation agent platform for prototyping and testing purposes. Experiments were performed to evaluate the robustness of its performance, namely through measures of naturalness and usefulness, with respect to the emphasized use of context. The contribution of this work is to provide empirical evidence of the importance of conversational context in speech‐based human–computer interaction using a field‐tested context‐centric dialog manager.     

An Interval‐Valued Pythagorean Fuzzy Outranking Method with a Closeness‐Based Assignment Model for Multiple Criteria Decision Making

The concept of interval‐valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real‐world applications. This paper focuses on multiple criteria decision analysis involving IVPF information and proposes a new outranking decision‐making method that uses a closeness‐based assignment model. In contrast to the existing assignment‐based methodology, the uniqueness of this paper is the consideration of uncertain information represented by IVPF values, the determination of criterion‐wise precedence rankings based on a closeness‐based approach, and the development of a new measure for scalar representation. First, to underlie anchored judgments in subjective decision‐making processes, this paper presents a compromising concept of the closeness index with the positive‐ideal and negative‐ideal IVPF values to identify criterion‐wise precedence ranks among alternatives. Next, this paper defines the concept of matrices of precedence frequency and contribution to provide a basis for the proposed assignment model. To overcome the difficulty of lacking nontrivial scalar representations, a useful measure is also developed to appropriately describe IVPF values. Based on a closeness‐based assignment approach, a novel outranking decision‐making method is proposed to transform the extended criterion‐wise ranks into the ultimate priority orders of the alternatives. The proposed method is first implemented in a practical problem of selecting a bridge construction method to demonstrate its feasibility and applicability. Moreover, its practicality and effectiveness are verified through a comparative analysis with relevant assignment‐based approaches. Further comparative analyses with newly developed IVPF decision‐making methods are conducted for both a risk evaluation problem and an investment problem to examine the advantages of the proposed method and extend the current technique by considering distinct preference information for adapting to the particularities in practice.     

Intuitionistic Fuzzy Interval‐Valued Linguistic Entropic Combined Weighted Averaging Operator for Linguistic Group Decision Making

Entropy, a basic concept of measuring the amount of information and the degree of confusion, has been applied in many weighted averaging operators in the linguistic group decision making. In the paper, we construct an intuitionistic fuzzy linguistic entropy based on the intuitionistic fuzzy entropy and the intuitionistic fuzzy linguistic variable. Then, inspired by operations of concentration and dilation (De SK, Biswas R, and Roy AR, Fuzzy Sets Syst. 2000;114(3):477?484), we extend the intuitionistic fuzzy linguistic entropy to the intuitionistic fuzzy interval‐valued linguistic entropy. After that, the intuitionistic fuzzy interval‐valued linguistic entropic combined weighted averaging (IFIVLECWA) operator is proposed for multiple attribute linguistic group decision making. Finally, a numerical example about the selection of optimal alternative(s) is presented to illustrate the applicability and effectiveness of the proposed method.     

Aggregation Operators of Interval‐Valued 2‐Tuple Linguistic Information

The group decision‐making problem with linguistic information evaluation values of decision makers are used based on 2‐tuple interval‐valued. Operational laws on interval value 2‐tuple are introduced. On the basis of these laws, new aggregation operators are introduced by using the Choquet integral. A multiple attribute decision‐making method based on these aggregation operators is proposed. An example is given to illustrate the efficiency, practicality, and feasibility of our method.     

An Alternative Type Reduction Approach Based on Information Combination with Interval Operations for Interval‐Valued Fuzzy Sliding Controllers

In this paper, an alternative type reduction approach based on information combination with crisp interval operations (crisp interval operation type reduction [CIOTR]) is presented to avoid the time‐consuming difficulty in the type reduction procedure for the mainly used interval‐valued membership functions (MFs). Multiinformation is considered to be included in the primary MF of an interval‐valued fuzzy set (FS). Interval operations are utilized to combine the multiinformation. With the integrated information, an interval‐valued FS is reduced to be a simple FS. The proposed type reduction approach (CIOTR) is also applied to the design of a hybrid interval‐valued fuzzy sliding controller (HFSC^IV) for a double‐pendulum‐and‐cart system. The simulation results are included to show the effectiveness of the designed HFSCs^IV using the CIOTR.     

Interval‐Valued Intuitionistic Fuzzy Multiattribute Group Decision Making Based on Cross Entropy Measure and Choquet Integral

In this paper, a new operator called the arithmetic interval‐valued intuitionistic fuzzy Choquet aggregation (AIVIFCA) operator is defined. Since interactions between elements might exist in all their combinations, the generalized Shapley AIVIFCA (GSAIVIFCA) operator is introduced. Further, to simplify the complexity of solving a fuzzy measure, the 2‐additive generalized Shapley AIVIFCA (2AGSAIVIFCA) operator is presented. Moreover, a decision procedure to interval‐valued intuitionistic fuzzy multiattribute group decision making is developed. When the weight vectors on attribute set and expert set are not exactly known, the models for obtaining the optimal fuzzy measures are established by using the defined cross entropy measure and the Shapley function. Finally, a numerical example is provided to illustrate the developed procedure.     

Correlation Coefficients of Interval‐Valued Hesitant Fuzzy Sets and Their Application Based on the Shapley Function

Interval‐valued hesitant fuzzy sets permit the membership degree of an element to have several possible interval values in [0, 1] rather than real numbers, which can well deal with inherent hesitancy and uncertainty in the human decision‐making process. In this paper, we first point out the issue of the existing correlation coefficients of interval‐valued hesitant fuzzy sets and then define several new ones, which do not have to consider the lengths of interval‐valued hesitant fuzzy elements and the arrangement of their possible interval values. Since the assumption that the elements in a set are independent is usually violated, we further define several Shapley weighted correlation coefficients, which consider their interactions. To deal with the situations where the elements are correlative and the weight formation is incompletely known, models for the optimal fuzzy measures on a feature set and on an attribute set are established, respectively. Finally, a procedure to pattern recognition and multiattribute decision making with incomplete weight information and interactive conditions is developed. Meanwhile, the corresponding examples are provided to show the practicality and feasibility of the proposed procedures.     

Group Decision Making Under Interval‐Valued Multiplicative Intuitionistic Fuzzy Environment Based on Archimedean t‐Conorm and t‐Norm

The main focus of this paper is to investigate group decision‐making (GDM) method under interval‐valued multiplicative intuitionistic fuzzy environment based on Archimedean t‐conorm and t‐norm. First of all, some operations laws are proposed for interval‐valued multiplicative intuitionistic fuzzy elements, which is an extension of multiplicative intuitionistic fuzzy operations developed earlier by other scholars. The effectiveness of these proposed operations is illustrated with some numerical examples. Then, a series of aggregation operators are proposed and the desirable properties are also studied. This paper reveals that some existing multiplicative intuitionistic fuzzy and interval‐valued multiplicative intuitionistic fuzzy aggregation operators are the special cases of the operators proposed in this paper. Finally, a GDM method based on proposed operators under interval‐valued multiplicative intuitionistic fuzzy environment is proposed, and a real case about annual evaluation for personnel of Zhejiang University of Finance and Economics is presented to illustrate the effectiveness of the proposed method.     

A Novel Approach for Linguistic Group Decision Making Based on Generalized Interval‐Valued Intuitionistic Fuzzy Linguistic Induced Hybrid Operator and TOPSIS

In the multiple attribute linguistic group decision making analysis with interval‐valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval‐valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order‐inducing variable and interval‐valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval‐valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision‐making approach based on GIVIFLIHA operator and interval‐valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility.     

A Review of Web‐Based Dietary Interventions: From the Human–Computer Interaction Practitioners' Perspective

Despite the popularity of web‐based dietary interventions, there are few evidence‐based, practical guidelines that help human–computer interaction (HCI) practitioners design new dietary intervention systems. We suspect that a lack of such guidelines is partly due to a chasm between two major research domains, healthcare and HCI. We believe that technologies developed in HCI are not used and evaluated by healthcare researchers, so we fail to accumulate experiences to develop guidelines. To assess the gap, we carefully selected 86 papers that employed and evaluated various web‐based dietary interventions in both fields and analyzed general characteristics, behavior change strategies, intervention media, and research outcomes used in each paper. Through this review, we reaffirmed our belief about the discrepancies between healthcare and HCI, and additional findings helped us offer some suggestions to close the gap. We also identified several interesting patterns among behavior change strategies, intervention media, and outcomes that provide potential topics for future research. © 2012 Wiley Periodicals, Inc.     

A Human–Computer Interface Using Symmetry Between Eyes to Detect Gaze Direction

In the cases of paralysis so severe that a person's ability to control movement is limited to the muscles around the eyes, eye movements or blinks are the only way for the person to communicate. Interfaces that assist in such communication are often intrusive, require special hardware, or rely on active infrared illumination. A nonintrusive communication interface system called EyeKeys was therefore developed, which runs on a consumer-grade computer with video input from an inexpensive Universal Serial Bus camera and works without special lighting. The system detects and tracks the person's face using multiscale template correlation. The symmetry between left and right eyes is exploited to detect if the person is looking at the camera or to the left or right side. The detected eye direction can then be used to control applications such as spelling programs or games. The game “BlockEscape” was developed to evaluate the performance of EyeKeys and compare it to a mouse substitution interface. Experiments with EyeKeys have shown that it is an easily used computer input and control device for able-bodied people and has the potential to become a practical tool for people with severe paralysis.      

Brian Shackel’s contribution to the written history of Human–Computer Interaction

In 1997, Brian Shackel published the article “Human–Computer Interaction – Whence and Whither?” In this early foray into historical reflection on the field, past work is covered with a focus on identifying European contributions, issues of particular contemporary interest are explored, and a set of 10-year predictions are offered. In this essay, from a vantage-point of an additional decade of history, insights of lasting value that Professor Shackel was uniquely positioned to glean are identified. His work is placed in the broader context now available, and an always-useful reminder of the difficulty of anticipating future events is provided.     

Pythagorean Fuzzy Clustering Analysis: A Hierarchical Clustering Algorithm with the Ratio Index‐Based Ranking Methods

The Pythagorean fuzzy set introduced by R. R. Yager in 2014 is a useful tool to model imprecise and ambiguous information appearing in decision and clustering problems. In this study, we present a general type of distance measure for Pythagorean fuzzy numbers (PFNs) and propose a novel ratio index‐based ranking method of PFNs. The novel ranking method of PFNs has more powerful ability to discriminate the magnitude of PFNs than the existing ranking methods for PFNs, which is further extended to compare the magnitude of interval‐valued Pythagorean fuzzy numbers (IVPFNs). The IVPFN is a new extension of PFN, which is parallel to interval‐valued intuitionistic fuzzy number. We introduce a general type of distance measure for IVPFNs. Afterwards, we study a kind of clustering problems in Pythagorean fuzzy environments in which the evaluation values are expressed by PFNs and/or IVPFNs and develop a novel Pythagorean fuzzy agglomerative hierarchical clustering approach. In the proposed clustering method, we define the concept of the dissimilarity degree between two clusters for each criterion and introduce the clustering procedure in the criteria level. To take all the criteria into account, we also introduce the overall clustering procedure, which is based on the overall dissimilarity degrees for a fixed aggregation operator such as the commonly used weighted arithmetic average operator or the ordered weighted averaging operator. In the overall clustering process, (1) we present a deviation degree‐based method to derive the weights of criteria and further obtain the overall clustering results if the weights of criteria are completely unknown; (2) we employ the ratio index‐based ranking method of IVPFNs to obtain the overall clustering results if the weights of criteria are given in advance and are expressed by IVPFNs. The salient feature of the proposed clustering method is that it not only can address the clustering problems in which the weights of criteria are not given precisely in advance but also can manage simultaneously the PFNs and IVPFNs data.     

基于属性权重区间监督的模糊C均值聚类算法

在加权模糊聚类算法中,属性权重确定的合理性是一个重要问题.鉴于用区间数描述决策者推理模糊性的优越性,提出属性权重用区间数表示,由区间层次分析法获得属性对聚类的贡献度,并以该区间为约束条件,提出了可同时获得属性权重和聚类结果的模糊C均值聚类新算法.实验结果表明,该算法以决策者的经验和偏好为监督,可避免迭代计算陷入不必要的局部极小解,能够提高权重分配的合理性,进而得到了更为准确的聚类结果.