Matrix-based reduction approach for one-sided fuzzy three-way concept lattices

Three-way concept analysis is a mathematical model of the combination of formal concept analysis and three-way decision, and knowledge discovery plays a significant impact on formal fuzzy contexts since such datasets are frequently encountered in real life. In this paper, a novel type of one-sided fuzzy three-way concept lattices is presented in a given formal fuzzy context with its complement, in which a ternary classification is available. In such case, we comprehensively explore the connections between the proposed models and classical fuzzy concept lattices among elements, sets, and orders. Furthermore, approaches to granular matrix-based reductions are investigated, by which granular consistent sets, and granular reducts via discernibility Boolean matrices are tectonically put forward. At last, the demonstrated results are performed by several experiments which enrich the research of three-way concept analysis.

Evaluation of time response of GMS for soil suction measurement

The Granular Matrix Sensor (GMS) is an indirect method for soil suction measurement. Since GMS is comparatively inexpensive, robust and usually provide continuous soil suction data, it is a natural candidate for civil engineering practice. The sensor has been used mainly for irrigation purposes, and also for some civil engineering activities. Questions about its effectiveness and reliability are still posed, making studies about this topic desirable. This study presents a laboratory comparison between Watermark and an ordinary tensiometer during an equilibrium period and for a wetting procedure performed in a compacted sandy silt soil (residual soil of gneiss). The results yielded that GMS may provide tensiometer equivalent suction values in a context of no significant water content variation. However, it takes a longer time to obtain stabilized suction values. During the wetting procedure, GMS presented a delay of about 2 h in detecting water while tensiometer detection was almost instantaneous.

Within-Field Variability in Granular Matrix Sensor Data and its Implications for Irrigation Scheduling

Highlights Within-field variability was larger for individual depths than for the profile average across multiple depths. Distributions of the profile average were approximately normal, with increasing variances as the soil was drying. Probability theory was applied to quantify the effect of sensor set number on irrigation scheduling. The benefit of additional sensors sets may decrease for longer irrigation cycles and for more heterogeneous fields. Abstract. Even when located within the same field, multiple units of the same soil moisture sensor rarely report identical values. Such within-field variability in soil moisture sensor data is caused by natural and manmade spatial heterogeneity and by inconsistencies in sensor construction and installation. To better describe this variability, daily soil water tension values from 14 to 23 sets of granular matrix sensors during the middle part of four soybean site-years in the Mississippi Delta were analyzed. The soil water tension data were found to follow approximately normal distributions, to exhibit moderately high temporal rank stability, and to show strong positive correlation between mean and variance. Based on these observations and the existing literature, a probabilistic conceptual framework was proposed for interpreting within-field variability in granular matrix sensor data. This framework was then applied to investigate the impact of sensor set number (i.e., number of replicates) and irrigation triggering threshold on the scheduling of single-day and multi-day irrigation cycles. If a producer’s primary goal of irrigation scheduling is to keep soil water adequate in a particular fraction of land on average, the potential benefit from increasing sensor set number may be smaller than traditionally expected. Improvement, expansion, and validation of this probabilistic framework are welcomed for developing a practical and robust approach to selecting the sensor set number and the irrigation triggering threshold for diverse soil moisture sensor types in diverse contexts. Keywords: Irrigation scheduling, Probability, Sensors, Soil moisture, Soil water tension, Variability, Watermark.