A fuzzy regression model based on distances and random variables with crisp input and fuzzy output data: a case study in biomass production

Abstract

Least-squares technique is well-known and widely used to determine the coefficients of a explanatory model from observations based on a concept of distance. Traditionally, the observations consist of pairs of numeric values. However, in many real-life problems, the independent or explanatory variable can be observed precisely (for instance, the time) and the dependent or response variable is usually described by approximate values, such as ''about £300'' or ''approximately $500'', instead of exact values, due to sources of uncertainty that may affect the response. In this paper, we present a new technique to obtain fuzzy regression models that consider triangular fuzzy numbers in the response variable. The procedure solves linear and non-linear problems and is easy to compute in practice and may be applied in different contexts. The usefulness of the proposed method is illustrated using simulated and real-life examples.

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

“…Some interrelationships among these fuzzy metric structures can be found in [24]. Fuzzy metrics have been demonstrated to be a very consistent notion, leading to significant improvements in many fields (for instance, in fuzzy regression theory; see [25][26][27][28][29][30]).…”

On the Notion of Fuzzy Dispersion Measure and its Application to Triangular Fuzzy Numbers

“…Those definitions of variance of fuzzy numbers can be in turn divided into two main blocks, which respectively correspond to the two main interpretations of fuzzy sets, namely the "ontic interpretation" and the "epistemic interpretation". According to the "ontic interpretation" of fuzzy sets, the variance of fuzzy numbers is defined as a crisp number representing the mean of the squared (crisp) distances between the corresponding fuzzy numbers and their arithmetic mean (see [14][15][16][17][18][19][20][21][22]). According to the "epistemic interpretation", the (fuzzy) variance of a collection of 𝑛 fuzzy numbers is defined as a fuzzy set.…”