A study of triangular membership function and multiple regressions to calculate the MSW compost index

The municipal solid waste compost consists of elements with a varied composition, including light and heavy metal elements. For MSW compost to act as a soil conditioner, and to ensure agricultural stakeholders to believe in its use for crops production, validation of elements is obligatory. The triangular membership function evaluates each element of a fuzzy set for both discrete and continuous values, and regression analysis estimates the relationship between values. In this paper, a triangular membership function (μf) is studied and used to characterize the effect of individual elements available in the compost sample. The characterization determines the variation in the composition of elements in the compost sample and accordingly calculates its scorei. Furthermore, a reinvestigation is done by applying multiple regression analysis, especially on heavy metals, to compare their composition with light mineral nutrients and other supplementary elements. A relationship between R=4.12 and R2=0.067498635 is derived to determine the predicted value and defines the composition of heavy metals as attributed to another mineral nutrients. Furthermore, a correlation (Co) is derived to find the performance of the compost sample todecide whether both light and supplementary mineral nutrients are capable of minimizing the effect of heavy metals. A gratuity score (Gsi) is added to each heavy metal depending on the correlation value to form a composti. The scorei=88.11 and composti = 9.12 obtained, was summated to derive Ci=97.23, stating that the increase in score value declares that the compost sample is mature enough to be used for agriculture and enhance crops productivity.

The Ranking Function for Solving the Fuzzy Hotelling T2 Test

A multivariate control chart is measured by many variables that are correlated in production, using the quality characteristics in any product. In this paper, statistical procedures were employed to find the multivariate quality control chart by utilizing fuzzy Hotelling test. The procedure utilizes the triangular membership function to treat the real data, which were collected from Baghdad Soft Drinks Company in Iraq. The quality of production was evaluated by using a new method of the ranking function.

The Sunn [Eurygaster spp. (Hemiptera: Scutelleridae)] damage in wheat and the effect of seed amount used on yield by fuzzy logic method

Sunn pest (Eurygaster spp.) is a highly harmful insect species for Wheatgrass. Especially with the emphasis it makes in herbal products, it causes the wheat to lose both its bread and pasta qualities. This study presents an example of a model that approximates the wheat yield in the irrigated field in Batman province according to the criteria selected through fuzzy logic. In the modelling, firstly the parameters affecting the wheat yield were determined and input and output variables were defined. In the next step, the membership functions are determined by doing the blurring process. The triangular membership function has been selected for the membership function. Later, fuzzy rule base was determined and fuzzy rules were formed. In the next step, the fuzzy inference mechanism was created. For the rinsing process, the "weight average" method was used. In the study, fuzzy logic toolbox was used in Matlab and the results obtained were seen to be useful in determining wheat yield per decare.

Readiness of Regions for Digitalization of the Construction Complex

The construction industry is high-tech and is one of the key areas for the strategic development of regions in terms of their digitalization. The construction complex provides regions with infrastructure of various levels from design documentation to commissioning, as well as reconstruction and major repairs of buildings. The article adopts an isolated regional approach, which is due to the need to assess specific territories by the level of readiness for digitalization of the construction complex. The purpose of the research is to determine the level of readiness of Russian regions for the digitalization of the construction complex by forming a rating of regions according to the indicator “the level of readiness of the region for digitalization of the construction complex”. To build the rating, the fuzzy sets method was applied using a triangular membership function, which allows to describe the influence of various processes on the formation of digitalization processes in the construction complex of the region. When forming the rating, a scale of fuzzy variable values is set which allows one to classify regions by levels, namely very low, low, medium, high, and very high. The generated rating is illustrated according to the specified scale. Based on the rating, the leading regions and outsider regions are identified by the formed indicator. It was determined that Moscow and Saint Petersburg are highly prepared for the digitalization of their construction complexes, and 53 regions of Russia are potentially prepared. In the future, it will be possible to create a rating of Russian regions on the level of readiness for digitalization of the construction complex with a two-year lag. Then, using the DEA shell analysis method, a quantitative assessment will be carried out that allows you to form performance boundaries and, against the background of four years, adjust the data to identify the most realistic picture. Also, the rating methodology considered by the authors allows us to scale this research to the international level, which will allow us to assess the level of digital development of construction complexes in other countries. The proposed rating algorithm is suitable for other sectors and complexes of the economy. It is enough to determine the main aggregate indicator and select groups of factors.

Optimization by Context Refinement for Development of Incremental Granular Models

Optimization by refinement of linguistic contexts produced from an output variable in the construction of an incremental granular model (IGM) is presented herein. In contrast to the conventional learning method using the backpropagation algorithm, we use a novel method to learn both the cluster centers of Gaussian fuzzy sets representing the symmetry in the premise part and the contexts of the consequent part in the if–then fuzzy rules. Hence, we use the fundamental concept of context-based fuzzy clustering and design with an integration of linear regression (LR) and granular fuzzy models (GFMs). This GFM is constructed based on the association between the triangular membership function produced both in the input–output variables. The context can be established by the system user or using an optimization method. Hence, we can obtain superior performances based on the combination of simple linear regression and local GFMs optimized by context refinement. Experimental results pertaining to coagulant dosing in a water purification plant and automobile miles per gallon prediction revealed that the presented method performed better than linear regression, multilinear perceptron, radial basis function networks, linguistic model, and the IGM.

Triangular Fuzzy-Rough Set Based Fuzzification of Fuzzy Rule-Based Systems

In real-world approximation problems, precise input data are economically expensive. Therefore, fuzzy methods devoted to uncertain data are in the focus of current research. Consequently, a method based on fuzzy-rough sets for fuzzification of inputs in a rule-based fuzzy system is discussed in this paper. A triangular membership function is applied to describe the nature of imprecision in data. Firstly, triangular fuzzy partitions are introduced to approximate common antecedent fuzzy rule sets. As a consequence of the proposed method, we obtain a structure of a general (non-interval) type-2 fuzzy logic system in which secondary membership functions are cropped triangular. Then, the possibility of applying so-called regular triangular norms is discussed. Finally, an experimental system constructed on precise data, which is then transformed and verified for uncertain data, is provided to demonstrate its basic properties.

Proposed α-cut CUSUM and EWMA Control Charts for Fuzzy Response Observations

This research proposesalpha ([Formula: see text]-cut Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts with fuzzy response observations in a manufacturing process under the existence of mean shift utilizing the fuzzy logic. In this research, the replicate’s observation is a fuzzy number represented by a triangular membership function, with the lower, average, and upper observation values. The fuzzy numbers are then normalized and assigned as input to the fuzzy logic, while a common output measure (COM) value is the output. Finally, the original values of the COM values are employed in developing the EWMA and CUSUM control charts with different [Formula: see text]-cut values. Three real case studies are adopted to illustrate the proposed EWMA and CUSUM control charts; including piston inside diameter, cap’s angel, and tablet weight. Results showed that the proposed EWMA and CUSUM control charts efficiently monitor fuzzy observations and detect the shift in process means. Moreover, the amount mean shift and [Formula: see text]-cut values affect the decision on process condition. In conclusion, the proposed approach is found effective in monitoring quality characteristic of fuzzy observations under mean shift which can be applied in a wide range of business applications.

Enhanced Fuzzy Assessment Methodology to Find Overlapping in Membership Function Using K Ratio to Find the Yield of Rice

Fuzzy expert systems are designed based on fuzzy logic and deal with fuzzy sets. Many fuzzy expert systems have been developed for diagnosis. Fuzzy expert systems are developed using fuzzification interface, enhanced fuzzy assessment methodology, and defuzzification interface. Fuzzification helps to convert crisp values into fuzzy values. By applying the enhanced fuzzy assessment methodology for rice, the yield parameters of rice can be diagnosed with number of tillers per hill, number of grains per panicle, and 1000 grain weight. Pest and disease incidence becomes simple for scientists. Enhanced fuzzy assessment methodology for rice uses triangular membership function with Mamdani's inference and K Ratio. Defuzzification interface is adopted to convert the fuzzy values into crisp values. Performance of the system can be evaluated using the accuracy level. Accuracy is the proportion of the total number of predictions that are correct. The proposed algorithm was implemented using MATLAB fuzzy logic tool box to construct fuzzy expert system for rice.