Intuitionistic fuzzy C-means clustering algorithms

Intuitionistic fuzzy sets(IFSs) are useful means to describe and deal with vague and uncertain data.An intuitionistic fuzzy C-means algorithm to cluster IFSs is developed.In each stage of the intuitionistic fuzzy C-means method the seeds are modified,and for each IFS a membership degree to each of the clusters is estimated.In the end of the algorithm,all the given IFSs are clustered according to the estimated membership degrees.Furthermore,the algorithm is extended for clustering interval-valued intuitionistic fuzzy sets(IVIFSs).Finally,the developed algorithms are illustrated through conducting experiments on both the real-world and simulated data sets.

Modeling and applying credible interval intuitionistic fuzzy reciprocal preference relations in group decision making

Intuitionistic fuzzy preference relations are powerful techniques used to express uncertain preference information. However, simultaneously providing the exact priority and non-priority intensities could be difficult in real applications. A credible interval intuitionistic fuzzy number (CIIFN) is introduced and a credible interval intuitionistic fuzzy reciprocal preference relation (CIIFRPR) is developed to solve this issue. Unlike intuitionistic fuzzy preference relations, the new preference relations use the CIIFNs to express the preference information such that the decision makers simply provide the priority intensity with interval-valued numbers and calculate the non-preference intensity with the transformed method, which avoids a complex evaluation of non-priority information. Furthermore, some basic operations and comparison laws are investigated, based on which three credible interval intuitionistic fuzzy aggregation operators are proposed. Two models are presented to manage the group decision-making. Finally, a practical case is used to demonstrate the feasibility and reasonability of the proposed preference relations and aggregation operators. ? 2017 Beijing Institute of Aerospace Information.

Insights into financial technology (FinTech):a bibliometric and visual study

This paper conducted a comprehensive analysis based on bibliometrics and science mapping analysis.First,848 publications were obtained from Web of Science.Their fundamental characteristics were analyzed,including the types,annual publications,hot research directions,and foci(by theme analysis,co-occurrence analysis,and timeline analysis of author keywords).Next,the prolific objects(at the level of countries/regions,institutions,journals,and authors)and corresponding pivotal cooperative relationship networks were used to highlight who pays attention to FinTech.Furthermore,the citation structures of authors and journals were investigated,including citation and co-citation.Additionally,this paper presents the burst detection analysis of cited authors,journals,and references.Finally,combining the analysis results with the current financial environment,the challenges and future development opportunities are discussed further.Accordingly,a comprehensive study of the FinTech documents not only reviews the current research characteristics and trajectories but also helps scholars find the appropriate research entry point and conduct in-depth research.

An Emergency Shelter Location Model Based on the Sense of Security and the Reliability Level

Based on the value function of the prospect theory,this paper constructs a security function,which is used to describe the victims’feelings about the distance in emergency evacuation.Since different paths between the demand points and the emergency shelters are generally of different importance degrees,they are divided into main paths and auxiliary paths.The security function values and the reliability levels of main paths and auxiliary paths are given different weights.The weighted sum of the security function values and the weighted sum of the reliability level function values of all demand points are maximized to determine the location and the number of the emergency shelters,the transfer paths,the reinforced edges and the incremental reliability level of the selected edge.In order to solve the model,a two-stage simulated annealing-particle swarm optimization algorithm is proposed.In this algorithm,the particle swarm optimization(PSO)algorithm is embedded into the simulated annealing(SA)algorithm.The cumulative probability operator and the cost probability operator are formed to determine the evolution of the particles.Considering the budget constraint,the algorithm eliminates the shelter combinations that do not meet the constraint,which greatly saves the calculation time and improves the efficiency.The proposed algorithm is applied to a case,which verifies its feasibility and stability.The model and the algorithm of this paper provide a basis for emergency management departments to make the earthquake emergency planning.

A Confidence-based Consensus Model for Multi-Attribute Group Decision Making:Exploring the Bounded Trust Propagation and Personalized Adjustment Willingness

Social trust network(STN)and minimum cost consensus(MCC)models have been widely used to address consensus issues in multi-attribute group decision-making(MAGDM)problems with limited resources.However,most researchers have overlooked the decision maker‘(DMs)’confidence levels(CLs)and adjustment willingness implicit in their evaluations.To address these problems,this paper explores a confidence-based MCC model that considers DMs’adjustment willingness in the STN.The proposed model includes several modifications to the traditional trust propagation and consensus optimization models.Firstly,the improved method for measuring CLs of DMs and the confidence-based normalization approach are defined,respectively.Secondly,the bounded trust propagation operator is proposed,which considers the credibility of mediators to complete the STN.Thirdly,the identification rules based on the consensus index and CL are defined,and the MCC model with personalized cost functions and acceptable adjustment thresholds is built to automatically generate adjustment values for non-consensus DMs.Finally,a model to identify the non-cooperative behavior at the element level is established and the hybrid MCC model with persuasion strategies is provided.Finally,a case study is processed to verify the applicability of the proposed model,and comparison and sensitivity analysis are conducted to highlight its benefits.

ORDERED WEIGHTED DISTANCE MEASURE

The aim of this paper is to develop an ordered weighted distance （OWD） measure, which is the generalization of some widely used distance measures, including the normalized Hamming distance, the normalized Euclidean distance, the normalized geometric distance, the max distance, the median distance and the rain distance, etc. Moreover, the ordered weighted averaging operator, the generalized ordered weighted aggregation operator, the ordered weighted geometric operator, the averaging operator, the geometric mean operator, the ordered weighted square root operator, the square root operator, the max operator, the median operator and the rain operator are also the special cases of the OWD measure. Some methods depending on the input arguments are given to determine the weights associated with the OWD measure. The prominent characteristic of the OWD measure is that it can relieve （or intensify） the influence of unduly large or unduly small deviations on the aggregation results by assigning them low （or high） weights. This desirable characteristic makes the OWD measure very suitable to be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. Finally, based on the OWD measure, we develop a group decision making approach, and illustrate it with a numerical example.

DUAL HESITANT FUZZY INFORMATION AGGREGATION WITH EINSTEIN T-CONORM AND T-NORM

Dual hesitant fuzzy set （DHFS） is a new generalization of fuzzy set （FS） consisting of two parts （i.e., the membership hesitancy function and the non-membership hesitancy fimction）, which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set （FS）, intuitionistic fuzzy set （IFS）, and hesitant fuzzy set （HFS） so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-eonorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.

SOME NEW SIMILARITY MEASURES FOR INTUITIONISTIC FUZZY VALUES AND THEIR APPLICATION IN GROUP DECISION MAKING

We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.

AGGREGATION AND DECISION MAKING USING INTUITIONISTIC MULTIPLICATIVE TRIANGULAR FUZZY INFORMATION

The intuitionistic triangular fuzzy set is a generalization of the intuitionistic fuzzy set. In practical applications, we find that the results derived by using the traditional intuitionistic triangular fuzzy aggregation operators based on intuitionistic triangular fuzzy sets are sometimes inconsistent with intuition. To overcome this issue, based on the [1/9, 9] scale, we define the concepts of intuitionistic multiplicative triangular fuzzy set and intuitionistic multiplicative triangular fuzzy number, and then we discuss their operational laws and some desirable properties. Based on the operational laws, we develop a series of aggregation operators for intuitionistic multiplicative triangular fuzzy information, and then apply them to propose an approach to multi-attribute decision making under intuitionistic fuzzy environments. Finally, we use a practical example involving the evaluation of investment alternatives of an investment company to demonstrate our aggregation operators and decision making approach.

UNIFORMIZATION OF MULTIGRANULAR LINGUISTIC LABELS AND THEIR APPLICATION TO GROUP DECISION MAKING

In multiple attribute group decision making （MAGDM） problems based on linguistic information, the granularities of linguistic label sets are usually different due to the differences of thinking modes and habits among decision makers. In order to deal with this inconvenience, the transformation relationships among multigranular linguistic labels （TRMLLs）, which are applied to unify linguistic labels with different granularities into a certain linguistic label set with fixed granularity, are presented in this paper. Furthermore, the reference tables are made according to TRMLLs so that the interrelated calculation will be less complicated, and the method of how to use them is explained in detail. At length, the TRMLLs are illustrated through an application example.

An overview on the applications of the hesitant fuzzy sets in group decision-making: theory, support and methods

Due to the characteristics of hesitant fuzzy sets (HFSs), one hesitant fuzzy element (HFE), which is the basic component of HFSs, can express the evaluation values of multiple decision makers (DMs) on the same alternative under a certain attribute. Thus, the HFS has its unique advantages in group decision making (GDM). Based on which, many scholars have conducted in-depth research on the applications of HFSs in GDM. We have viewed lots of relevant literature and divided the existing studies into three categories: theory, support and methods. In this paper, we elaborate on hesitant fuzzy GDM from these three aspects. The first aspect is mainly about the introduction of HFSs, HFPRs and some hesitant fuzzy aggregation operators. The second aspect describes the consensus process under hesitant fuzzy environment, which is an important support for a complete decision making process. In the third aspect, we introduce seven hesitant fuzzy GDM approaches, which can be applied in GDM under different decision-making conditions. Finally, we summarize the research status of hesitant fuzzy GDM and put forward some directions of future research.

ON PAIRED PRIORITIZATIONS OF CRITERIA IN THE PERSPECTIVE OF DIAGRAPHS

It is not usually independent among criteria in multi-criteria decision making （MCDM）, and various dependences of criteria greatly influence the results of decision making. If an exact decision is desired, we must make clear the role of the dependences of criteria. Prioritizations, a new kind of dependences of criteria proposed recently, imply that the importance weights of criteria with lower priority for an alternative rely on whether the alternative satisfies the decision maker under criteria with higher priority. It has been validated that there exist lots of relevant applications in our daily activities. However, most existing literatures focus on how to deal with the problems of MCDM with ordered prioritizations among criteria （a special form of prioritizations）. The characteristics of prioritizations are not dug deep. This paper constructs a new form of prioritizations, called paired prioritizations, so as to reduce or even avoid imperfect rationality of decision makers hidden in the ordered prioritizations. We first represent binary paired prioritizations as a digraph, based on which we discover two kinds of imperfect rationality （inconsistency and incompleteness） produced in the period that the decision maker supplies the binary paired prioritizations. After the given paired prioritizations are consistent and complete, we develop an approach to transform the paired prioritizations to ordered prioritizations. The latter can be used to handle prioritized MCDM problems. Moreover, uncertainty, another kind of imperfect rationality, is considered when the decision maker provides the fuzzy paired prioritizations based on a set of linguistic labels. We construct a fuzzy digraph whose fuzzy relations are just the fuzzy paired prioritizations. The ordered prioritizations can then be derived with the aid of the fuzzy digraph. Two use cases are taken to show the process of transformations from binary/fuzzy paired prioritizations to ordered prioritizations.

Multiplicative Integral Theory of Generalized Orthopair Fuzzy Sets and Its Applications

There are two main issues of fuzzy multi-attribute decision-making:determine the weight of each attribute and choose an appropriate aggregation method to integrate the evaluation information of different attributes.In order to solve the multi-attribute decision-making problem in generalized orthopair fuzzy environment with unknown attribute weights more effectively,we give a decision-making method based on generalized orthopair fuzzy definite integrals.To be specific,we first introduce the complement operations of q-rung orthopair fuzzy numbers,and then investigate the multiplicative q-rung orthopair fuzzy calculus.Through the complement operations,we establish the mutual conversion formula between additive and multiplicative q-rung orthopair fuzzy calculus theory.Then,we give a multiplicative integral-based q-rung orthopair fuzzy multi-attribute decision-making method,and discuss the relationship between the q-rung orthopair fuzzy definite integrals and the q-rung orthopair fuzzy weighted geometric operator.Compared with traditional decision-making methods,this method does not rely on subjective weight information,which is especially important when dealing with large sample data.Finally,the application of election is studied to verify the feasibility and effectiveness of the proposed method.With the introduction of generalized orthopair fuzzy sets,the expression form of election evaluation information has been expanded.We also provide some examples to compare the obtained results with the results generated by the addition operation and reveal the correlation between them.