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This paper proposes a new method for calculating the missing elements of an incomplete matrix of pairwise comparison values for a decision problem. The matrix is completed by minimizing a measure of global inconsistency, thus obtaining a matrix which is optimal from the point of view of consistency with respect to the available judgements. The optimal values are obtained by solving a linear system and unicity of the solution is proved under general assumptions. Some other methods proposed in the literature are discussed and a numerical example is presented

Overtourism problems, anti-tourist movements and negative externalities of tourism are popular research approaches and are key concepts to better understand the sustainable development of tourism destinations. In many of the overtourism narratives, Venice is considered to be one of the most relevant cases of overtourism and therefore has become a laboratory for studying the different conflicts that emerge when tourism numbers continue to grow and the quality of the tourism flow continues to decline. This article is therefore focusing on Venice and on one of the possible solutions to mitigate the negative impacts of tourism represented by the concept of a tourist carrying capacity (TCC) in an urban destination. The aim of this paper is to discuss alternative methodologies regarding the calculation of the TCC, and to apply a fuzzy instead of a ‘crisp’ linear programming model to determine the scenarios of a sustainable number of tourists in the cultural destination of Venice, looking for the optimal compromise between, on the one hand, the wish of maximizing the monetary gain by the local tourism sectors and, on the other, the desire to control the undesirable effects that tourism exerts on a destination by the local population. To solve the problems related to tourism statistics and data availability, some uncertainty in the parameters has been included using fuzzy numbers. The fuzziness in the model was introduced on the basis of questionnaires distributed among both tourists and residents. By applying the fuzzy linear programming model to the emblematic case of Venice, it was shown that this approach can indeed help destinations to understand the challenges of sustainable tourism development better, to evaluate the impact of alternative policies of overtourism on the sustainability of tourism, and hence, to help design a strategy to manage tourist flows more adequately

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