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Abstract. Group decision making is part of every organizational life. It is a type of participatory process in which multiple decision makers acting collectively, analyze problems, consider and evaluate several alternatives, and select from among the alternatives a solution. In such a situation, an important issue is the level of agreement or consensus achieved among the group of decision makers before obtaining the solution. In the beginning, consensus was meant as a full and unanimous agreement. Regrettably, this stringent concept of consensus in many cases is a utopia. As a result, and from a pragmatic point of view, it makes more sense to speak about a degree of consensus and, here, the theory of fuzzy sets has delivered new tools for the analysis of such imprecise phenomena like consensus. Given the significance of reaching an accepted solution by all the decision makers, consensus is a major aim of group decision making problems and, in such a way, it has obtained a great attention in the literature. However, there still exist several dares which have to be tackled by the researchers. The purpose of this paper is to bring out several issues that represent challenges that have to be faced.

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Network congestion remains one of the main barriers to the continuing success of the Internet. For Web users, congestion manifests itself in unacceptably long response times. One possible remedy to the latency problem is to use caching at the client, at the proxy server, or within the Internet. However, Web documents are becoming increasingly dynamic (i.e., have short lifetimes), which limits the potential benefit of caching. The performance of a Web caching system can be dramatically increased by integrating document prefetching (a.k.a. "proactive caching") into its design. Although prefetching reduces the response time of a requested document, it also increases the network load, as some documents will be unnecessarily prefetched (due to the imprecision in the prediction algorithm). In this study, we analyze the confluence of the two effects through a tractable mathematical model that enables us to establish the conditions under which prefetching reduces the average response time of a requested document. The model accommodates both passive client and proxy caching along with prefetching. Our analysis is used to dynamically compute the "optimal" number of documents to prefetch in the subsequent client's idle (think) period. In general, this optimal number is determined through a simple numerical procedure. Closed-form expressions for this optimal number are obtained for special yet important cases. We discuss how our analytical results can be used to optimally adapt the parameters of an actual prefetching system. Simulations are used to validate our analysis and study the interactions among various system parameters.

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