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In this paper, we present two new classes of fuzzy negations. They are an extension of a well-known class of fuzzy negations, the Sugeno Class. We use it as a base for our work for the first two construction methods. The first method generates rational fuzzy negations, where we use a second-degree polynomial with two parameters. We investigate which of these two conditions must be satisfied to be a fuzzy negation. In the second method, we use an increasing function instead of the parameter δ of the Sugeno class. In this method, using an arbitrary increasing function with specific conditions, fuzzy negations are produced, not just rational ones. Moreover, we compare the equilibrium points of the produced fuzzy negation of the first method and the Sugeno class. We use the equilibrium point to present a novel method which produces strong fuzzy negations by using two decreasing functions which satisfy specific conditions. We also investigate the convexity of the new fuzzy negation. We give some conditions that coefficients of fuzzy negation of the first method must satisfy in order to be convex. We present some examples of the new fuzzy negations, and we use them to generate new non-symmetric fuzzy implications by using well-known production methods of non-symmetric fuzzy implications. We use convex fuzzy negations as decreasing functions to construct an Archimedean copula. Finally, we investigate the quadratic form of the copula and the conditions that the coefficients of the first method and the increasing function of the second method must satisfy in order to generate new copulas of this form. [ABSTRACT FROM AUTHOR]

The assessment of rocking response is a challenging task due to its high nonlinearity. The present study investigates two methodologies to evaluate finite rocking rotations and overturn of three typical rocking systems. In particular, fuzzy linear regression (FLR) with triangular fuzzy numbers and a hybrid model combining logistic regression and fuzzy logic were adopted. To this end, three typical rocking structures were considered, and nonlinear time history analyses were performed to obtain their maximum response. Eighteen seismic intensity measures (IMs) extracted from recorded seismic accelerograms were considered to predict the responses. In the absence of rocking overturn, the finite rocking rotations and similarity ratios were calculated by adopting the FLR method. Moreover, extensive analysis was performed to evaluate the influence of each IM on the model's predictions. On the other hand, rocking overturn was evaluated by logistic regression to compute the probability of collapse, followed by the FLR method to estimate the similarity between the different rocking-based structural systems. The root mean square error (RMSE) parameter and the log loss function were determined for every model to assess the predictions that emerged from the two fuzzy methods. As indicated, both methods demonstrated satisfactory results, presenting minimal deviations from the observed values. Finally, in the case of finite rocking rotation predictive models, remarkably high similarity ratios were observed among the various structures, with a median value of 0.96. [ABSTRACT FROM AUTHOR]

In this paper, we revisit and study the basic properties of two families of fuzzy implications, the so-called (T , N) − and (N ′ , T , N) − implications. More specific, we study when these fuzzy implications satisfy, or not, the neutrality property (N P) , the exchange principle (E P) , the identity principle (I P) and the ordering property (O P) . Moreover, a study is presented for the law of importation (L I) with respect to a t- norm. Also, we study the relation of Φ − conjugation in (N ′ , T , N) − implications. [ABSTRACT FROM AUTHOR]

The trophic state of an aquatic body is influenced by many biotic and abiotic factors. When lots of parameters affect a phenomenon, such as eutrophication, it is difficult to distinguish which are the ones that affect the ecosystem the most. In this paper, we propose an alternative way for data analysis, in order to avoid complex systems with many variables. For the examined Mediterranean shallow lake, the studied parameters are water temperature (°C), ammonia (NH 4 -N) (mg/L), dissolved oxygen (mg/L), turbidity (NTU), pH, conductivity (mS/cm), and chlorophyll-a (μg/L). We formed groups with the variables above based on fuzzy equivalence relations and from each group we chose the parameter influence the studied phenomenon the most. Numerical results of fuzzy linear regression showed strong agreement with the proposed method above and pH, NH 4 -N, and dissolved oxygen are the variables influence this ecosystem more than the others. PRACTITIONER POINTS: When having many parameters in a studied ecosystem, we propose a way we can distinguish the most representative ones, the parameters that influence more the phenomenon we study each time. Formation of groups in variables can be applied to many case studies in order to have a clear idea of our data and the relevance of each of them in our dependent one. Fuzzy linear regression can be used in order to check the final results and ensure that the equivalence relations are a such a good method used in the data analysis while the researchers save time in long procedures of analyzing parameters not very close involved to the phenomenon investigated every time., (© 2021 Water Environment Federation.)