Alireza Chakeri

Fuzzy Nash Equilibriums in Crisp and Fuzzy Games

In this paper, we introduce fuzzy Nash equilibrium to determine a graded representation of Nash equilibriums in crisp and fuzzy games. This interpretation shows the distribution of equilibriums in the matrix form of a game and handles uncertainties in payoffs. In addition, a new method to rank fuzzy values with the users viewpoint is investigated. By this means, the definition of satisfaction function, which provides the result of comparison in the form of real value, is developed when users have preferences regarding the payoffs.

Linguisitc representation of Nash equilibriums in fuzzy games

Fuzzy preference relation has been a useful tool in decision making situations to choose and compare between alternatives. In this paper we show how fuzzy linguistic preference relation can be used in game theory. A fuzzy IF-THEN rule set is constructed to derive preferences according to difference between payoffs. Then using a linguistic choice function, priority of each payoff is derived. We interpret the priorities as the linguistic Nash equilibriums. Also for comparing between fuzzy variables, two measures are introduced including possibility and amount of being greater using fuzzy extension principle.

Fuzzy Nash equilibrium in fuzzy games using ranking fuzzy numbers

In traditional game theory, the players play with policy of maximizing their payoffs. In real world, there are many situations where payoffs have uncertainty and are fuzzy in nature. In this paper, a new method for finding pure strategy Nash equilibriums, to realistically analyze the games with fuzzy payoffs is investigated. Using ranking fuzzy numbers, a fuzzy preference relation is constructed over payoffs. The priorities of payoffs are considered as the degree of being Nash equilibriums.

A cooperative incentive mechanism for recurrent crowd sensing

Crowd sensing (CS) is an approach that consists of collecting many samples of a phenomena of interest by distributing the sampling process across a large number of individuals. In this work, we address the effect of cooperation among individuals by modeling a recurrent CS task as a repeated game. In this game, participants are the players of the corresponding game, and every round of the CS task is considered as a single-shot game which is repeated over time. In this model, participants compete and cooperate with each other in order to sell their samples. We represent the participants evolutionary behaviors by a graph network in which all the individuals make utilities in the long run. We show that although a pure competition approach faces problems such as the continuous drop-out of participants and the raise of prices of samples, this hybrid approach keeps the prices of samples low while maintaining the required number of participants.

Relational data partitioning using evolutionary game theory

This paper presents a new approach for relational data partitioning using the notion of dominant sets. A dominant set is a subset of data points satisfying the constraints of internal homogeneity and external in-homogeneity, i.e. a cluster. However, since any subset of a dominant set cannot be a dominant set itself, dominant sets tend to be compact sets. Hence, in this paper, we present a novel approach to enumerate well distributed clusters where the number of clusters need not be known. When the number of clusters is known, in order to search the solution space appropriately, after finding each dominant set, data points are partitioned into two disjoint subsets of data points using spectral graph image segmentation methods to enumerate the other well distributed dominant sets. For the latter case, we introduce a new hierarchical approach for relational data partitioning using a new class of evolutionary game theory dynamics called InImDynamics which is very fast and linear, in computational time, with the number of data points. In this regard, at each level of the proposed hierarchy, Dunns index is used to find the appropriate number of clusters. Then the objects are partitioned based on the projected number of clusters using game theoretic relations. The same method is applied to each partition to extract its underlying structure. Although the resulting clusters exist in their equivalent partitions, they may not be clusters of the entire data. Hence, they are checked for being an actual cluster and if they are not, they are extended to an existing cluster of the data. The approach can also be used to assign unseen data to existing clusters, as well.

An Incentive Mechanism for Crowdsensing Markets With Multiple Crowdsourcers

In this paper, we design an incentive mechanism for data collection in smart cities. We propose an incentive mechanism for crowdsensing with multiple crowdsourcers. We model the incentive mechanism as a noncooperative game. We consider two different pricing mechanisms when the crowdsourcers fixed the rewards in advance, and when the crowdsourcers dynamically set the rewards in order to maximize their own utilities. A discrete time dynamic inspired by the well known best response dynamic, called elite strategy dynamics, is proposed to compute a Nash equilibrium of the modeled game. Comprehensive simulations were presented to evaluate the performance of the proposed incentive mechanism.

Dempster-Shafer theory of evidence in Single Pass Fuzzy C Means

Clustering large data sets has become very importantas the amount of available unlabeled data increases. Single Pass Fuzzy C Means (SPFCM) is useful when memory is too limited to load the whole data set. The main idea is to divide dataset into several chunks and to apply FCM to each chunk. SPFCM uses the weighted cluster centers of the previous chunk in the next chunks. Although when the number of chunks is increased, the algorithm shows sensitivity to the order the data processed. Hence, we improved SPFCM by recognizing boundary and noisy data in each chunk and using it to influence clustering in the next chunks. In this regard, the proposed approach transfers the boundary and noisy data as well as the weighted cluster centers to the next chunks. We show that our proposed approach is significantly less sensitive to the order in which the data is loaded in each chunk.

Dominant Sets as a Framework for Cluster Ensembles: An Evolutionary Game Theory Approach

Ensemble clustering aggregates partitions obtained from several individual clustering algorithms. This can improve the accuracy of results from individual methods and provide robustness against variability in the methods applied. Theorems show one can find dominant sets (clusters) very efficiently by using an evolutionary game theoretic approach. Experiments on an MRI data set consisting of about 4 million data are detailed. The distributed dominant set framework generates partitions of quality slightly better than clustering all the data using fuzzy C means.

Spectral sparsification in spectral clustering

Graph spectral clustering algorithms have been shown to be effective in finding clusters and generally outperform traditional clustering algorithms, such as k-means. However, they have scalibility issues in both memory usage and computational time. To overcome these limitations, the common approaches sparsify the similarity matrix by zeroing out some of its elements. They generally consider local neighborhood relationships between the data instances such as the k-nearest neighbor method. Although, they eventually work with the Laplacian matrix, there is no evidence about preservation of its spectral properties with approximation guarantees. As a result, in this paper, we adopt the idea of spectral sparsification to sparsify the Laplacian matrix. A spectral sparsification algorithm takes a dense graph G with n vertices and m edges (that is usually O(n2)), and returns a new graph H with the same set of vertices and many fewer edges, on the order of O(n log n), that approximately preserves the spectral properties of the input graph. We study the effect of the spectral sparsification method based on sampling by effective resistance on the spectral clustering outputs. Through experiments, we show that the clustering results obtained from sparsified graphs are very similar to the results of the original non-sparsified graphs.