A fuzzy additive regression model with exact predictors and fuzzy responses

Coordinating Qualitative Predictor Variables in an Applied Linear Model: Analysis and Application for Applied Sciences

Background In applied sciences, statistical models are pivotal for uncovering relationships in complex datasets. The applied linear model establishes associative links between variables. While qualitative predictors are essential, their integration into linear models poses challenges. The dummy variable approach transforms qualitative variables into binary ones for regression analysis. Multilayer Feedforward Neural Networks (MLFFNN) offer validation of regression models, and fuzzy regression offers alternative methods to address the ambiguity of qualitative predictors. This study aims to enhance the integration of qualitative predictors in applied linear models through statistical methodologies. Material and methods This study design involves the transformation of qualitative predictors into dummy variables, the bootstrapping technique to improve the parameter estimates, the Multilayer Feedforward Neural Network, and fuzzy regression. This study uses the programming language R as an analysis tool. Results The multiple linear regression model demonstrates precision and a significant fit (p<0.05), with an R-squared value of 0.95 and mean square error (MSE) of 9.97. Comparing actual and predicted values, fuzzy regression exhibits superior predictability over linear regression. The MLFFNN yields a reduced MSE net of 0.362, indicating enhanced prediction precision for derived models. Conclusion This study presents a precise methodology for integrating qualitative variables into linear regression, supported by the combination of specific statistical methodologies to enhance predictive modeling. By integrating fuzzy linear regression, MLFF neural networks, and bootstrapping, the proposed technique emerges as the most effective approach for modeling and prediction. These findings underscore the efficacy of this method in seamlessly integrating qualitative variables into linear models, ultimately enhancing accuracy and prediction capabilities.

Linking river flow modification with wetland hydrological instability, habitat condition, and ecological responses

Flow modification pursuing dams is widely found. Some works also focused on its impact on floodplain wetland hydrology. However, how this change can pose an impact on habitat conditions, ecological conditions, and trophic state is also a matter of investigation. The very least attention has been paid to this so far. Therefore, the present study focused on these, taking the dam-induced Lower Tangon river basin of India and Bangladesh as a case. The degree of flow alteration in the river was presented in a heat map. Multi-parametric machine learning (ML) approaches were applied to model hydrological instability and habitat condition. The ecological consequences like evaluating eco-deficit using flow duration curve (FDC) approach, trophic state using trophic state index (TSI), fish habitat zone using image-based hydrological parameters, etc. were measured. The study exhibited that after damming, the degree of river flow modification was about 41%. Consequently, the wetland hydrological instability and habitat conditions were degraded. In the post-dam period, > 50% of wetland area was lost, and hydrological instability was enhanced considerably over wider parts of the wetland. Habitat conditions of the existing wetland also witnessed fragility (poor and very poor areas increased by about 22.23 and 9.34%). As a result of this, adverse ecological responses were found. For instance, the eco-deficit area was increased by 36.19%, a good proportion (100%) of wetlands was witnessed the transformation of TSI from oligotrophic to mesotrophic state, and optimum fish habitat area was declined. The ecological strength map integrating all the cause-effect model parameters showed that good ecological strength was reduced from 49 to 2% in the post-dam. The result of the study would be very useful for wetland restoration for ecological and human well-being.

Hesitant Fuzzy Linear Regression Model for Decision Making

An expert may experience difficulties in decision making when evaluating alternatives through a single assessment value in a hesitant environment. A fuzzy linear regression model (FLRM) is used for decision-making purposes, but this model is entirely unreasonable in the presence of hesitant fuzzy information. In order to overcome this issue, in this paper, we define a hesitant fuzzy linear regression model (HFLRM) to account for multicriteria decision-making (MCDM) problems in a hesitant environment. The HFLRM provides an alternative approach to statistical regression for modelling situations where input–output variables are observed as hesitant fuzzy elements (HFEs). The parameters of HFLRM are symmetric triangular fuzzy numbers (STFNs) estimated through solving the linear programming (LP) model. An application example is presented to measure the effectiveness and significance of our proposed methodology by solving a MCDM problem. Moreover, the results obtained employing HFLRM are compared with the MCDM tool called technique for order preference by similarity to ideal solution (TOPSIS). Finally, Spearman’s rank correlation test is used to measure the significance for two sets of ranking.

Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces.