Markov chains to determine the probability of climate change for planting selection in the city of Caxias do Sul/Aplicação de cadeias de markov na probabilidade de mudanças climáticas para seleção de plantio na cidade de Caxias do Sul

The Markov stochastic chain model and the analytical hierarchy process (AHP) were used as tools to support decision-making for the best crop-planting choice in the city of Caxias do Sul, Brazil. Temperature and precipitation information were collected from the Meteorological Database for Teaching and Research of the National Institute of Meteorology of Brazil for the period 1997-2017. The stochastic model was applied to obtain the probability of transition between a range of variations for temperature and precipitation. In the second phase of the study, an algebraic model was developed, making it possible to link the probability of the Markov chain transition matrix to the AHP judgment matrix. In the third phase, the AHP was applied as a tool to determine the most beneficial crop that could be planted for the studied city, considering the evaluated criteria: temperature, precipitation, and soil pH. The alternatives for crop planting were carrots, tomatoes, apples, and grapes. These were chosen because they are the most-planted crops in the city of Caxias do Sul. The ranking of the benefit-force results of applying the model for spring was carrots (0.297), apples (0.259), grapes (0.228), and tomatoes (0.215); for summer: grapes (0.261), tomatoes (0.261), apples (0.238), and carrots (0.230); for autumn: carrots (0.316), grapes (0.243), tomatoes (0.228), and apples (0.213); and for winter: carrots (0.327), tomatoes (0.235), apples (0.222), and grapes (0.216). Thus, it was concluded that farmers would have a better chance of success if they planted carrots during the spring, autumn, and winter, and grapes during the summer. Key words: Hierarchical analytical process, operational research, decision-making process, crops, temperature, precipitation, soil pH. O Modelo de Cadeia Estocástica de Markov e o Processo de Hierarquia Analítica (AHP) foram utilizados como ferramentas de apoio à tomada de decisão para a melhor escolha de plantio na cidade de Caxias do Sul, Brasil. As informações de temperatura e precipitação foram coletadas de 1997 a 2017 no Banco de Dados Meteorológicos para Ensino e Pesquisa do Instituto Nacional de Meteorologia do Brasil. O modelo estocástico foi aplicado para obtenção da probabilidade de transição entre faixas de variação para temperatura e precipitação. Na segunda fase do estudo, um modelo algébrico foi desenvolvido, possibilitando vincular a probabilidade da matriz de transição de cadeias de Markov na matriz de julgamento do AHP. Na