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The objective of the current paper is to incorporate the new class and concepts of convexity and Hermite–Hadamard inequality with the fuzzy Riemann integral operators because almost all classical single-valued and interval-valued convex functions are special cases of fuzzy-number valued convex mappings. Therefore, a new class of nonconvex mapping in the fuzzy environment has been defined; up and down h -pre-invex fuzzy-number valued mappings (U.D  h -pre-invex F-N∙V∙Ms). With the help of this newly defined class, some new versions of Hermite–Hadamard (HH) type inequalities have been also presented. Moreover, some related inequalities such as HH Fejér- and Pachpatte-type inequalities for U∙D  h -pre-invex F-N∙V∙Ms are also introduced. Some exceptional cases have been discussed, which can be seen as applications of the main results. We have provided some nontrivial examples. Finally, we also discuss some future scopes. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the Riemann–Liouville fractional integral operator for left and right convex interval-valued functions (left and right convex I∙V-F), as well as various related notions and concepts. First, the authors used the Riemann–Liouville fractional integral to prove Hermite–Hadamard type (– type) inequality. Furthermore, – type inequalities for the product of two left and right convex I∙V-Fs have been established. Finally, for left and right convex I∙V-Fs, we found the Riemann–Liouville fractional integral Hermite–Hadamard type inequality (– Fejér type inequality). The findings of this research show that this methodology may be applied directly and is computationally simple and precise. [ABSTRACT FROM AUTHOR]

The main objective of this study is to introduce new versions of fractional integral inequalities in fuzzy fractional calculus utilizing the introduced preinvexity. Due to the behavior of its definition, the idea of preinvexity plays a significant role in the subject of inequalities. The concepts of preinvexity and symmetry have a tight connection thanks to the significant correlation that has developed between both in recent years. In this study, we attain the Hermite-Hadamard (H·H) and Hermite-Hadamard-Fejér (H·H Fejér) type inequalities for preinvex fuzzy-interval-valued functions (preinvex F·I·V·Fs) via Condition C and fuzzy Riemann–Liouville fractional integrals. Furthermore, we establish some refinements of fuzzy fractional H·H type inequality. There are also some specific examples of the reported results for various preinvex functions deduced. To support the newly introduced ideal, we have provided some nontrivial and logical examples. The results presented in this research are a significant improvement over earlier results. This paper's awe-inspiring notions and formidable tools may energize and revitalize future research on this worthwhile and fascinating topic. [ABSTRACT FROM AUTHOR]

The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (I-V·Fs), known as left and right χ -pre-invex interval-valued functions (LR- χ -pre-invex I-V·Fs). For this class of non-convex I-V·Fs, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we'll discuss a few specific examples that may be extrapolated from our primary findings. [ABSTRACT FROM AUTHOR]

Due to its significant influence on numerous areas of mathematics and practical sciences, the theory of integral inequality has attracted a lot of interest. Convexity has undergone several improvements, generalizations, and extensions over time in an effort to produce more accurate variations of known findings. This article's main goal is to introduce a new class of convexity as well as to prove several Hermite–Hadamard type interval-valued integral inequalities in the fractional domain. First, we put forth the new notion of generalized convexity mappings, which is defined as U D - Ԓ -convexity on coordinates with regard to fuzzy-number-valued mappings and the up and down ( U D ) fuzzy relation. The generic qualities of this class make it novel. By taking into account different values for Ԓ , we produce several known classes of convexity. Additionally, we create some new fractional variations of the Hermite–Hadamard ( H H ) and Pachpatte types of inequalities using the concepts of coordinated U D - Ԓ -convexity and double Riemann–Liouville fractional operators. The results attained here are the most cohesive versions of previous findings. To demonstrate the importance of the key findings, we offer a number of concrete examples. [ABSTRACT FROM AUTHOR]

In interval analysis, the fuzzy inclusion relation and the fuzzy order relation are two different concepts. Under the inclusion connection, convexity and non-convexity form a substantial link with various types of inequalities. Moreover, convex fuzzy-interval-valued functions are well known in convex theory because they allow us to infer more exact inequalities than convex functions. Most likely, integral operators play significant roles to define different types of inequalities. In this paper, we have successfully introduced the Riemann–Liouville fractional integrals on coordinates via fuzzy-interval-valued functions (FIVFs). Then, with the help of these integrals, some fuzzy fractional Hermite–Hadamard-type integral inequalities are also derived for the introduced coordinated convex FIVFs via a fuzzy order relation (FOR). This FOR is defined by φ -cuts or level-wise by using the Kulish–Miranker order relation. Moreover, some related fuzzy fractional Hermite–Hadamard-type integral inequalities are also obtained for the product of two coordinated convex fuzzy-interval-valued functions. The main results of this paper are the generalization of several known results. [ABSTRACT FROM AUTHOR]

This study attempts to utilize newly developed machine learning techniques in order to develop a general prediction algorithm for agricultural soils in Saudi Arabia, specifically in the Taif region. Energy dispersive X-ray fluorescence (EDXRF) measurements were used to develop national predictive models that predict the concentrations of 14 micronutrients in soils of Taif rose farms, for providing high-quality data comparable to conventional methods. Machine learning algorithms used in this study included the simple linear model, the multivariate linear regression (MLR); and two nonlinear models, the random forest (RF) and multivariate adaptive regression splines (MARS). Our study proposes a machine learning (ML) strategy for predicting fertility parameters more accurately in agricultural soils using 10 farms of the Taif rose (Rosa damascena) in Taif, Saudi Arabia as a case study. Results demonstrated that MARS provides higher prediction performance when the number of explanatory variables is small, while RF is superior when the number of variables is large. On the other hand, the MLR is recommended as a moderate method for predicting multivariate variables. The study showed that multivariate models can be used to overwhelm the drawbacks of the EDXRF device, such as high detection limits and an element that cannot be directly measured. [ABSTRACT FROM AUTHOR]

Despite being an important economic component of Taif region and the Kingdom of Saudi Arabia (KSA) as a whole, Taif rose experiences challenges because of uncontrolled conditions. In this study, we developed a phenotyping prediction model using deep learning (DL) that used simple and accurate methods to obtain and analyze data collected from ten rose farms. To maintain broad applicability and minimize computational complexity, our model utilizes a complementary learning approach in which both spatial and temporal instances of each dataset are processed simultaneously using three state-of-the-art deep neural networks: (1) convolutional neural network (CNN) to treat the image, (2) long short-term memory (LSTM) to treat the timeseries and (3) fully connected multilayer perceptions (MLPs)to obtain the phenotypes. As a result, this approach not only consolidates the knowledge gained from processing the same data from different perspectives, but it also leverages on the predictability of the model under incomplete or noisy datasets. An extensive evaluation of the validity of the proposed model has been conducted by comparing its outcomes with comprehensive phenotyping measurements taken from real farms. This evaluation demonstrates the ability of the proposed model to achieve zero mean absolute percentage error ( MAPE ) and mean square percentage error (MSPE) within a small number of epochs and under different training to testing schemes. [ABSTRACT FROM AUTHOR]

The purpose of this study is to define a new class of harmonically convex functions, which is known as left and right harmonically convex interval-valued function (LR--convex IV-F), and to establish novel inclusions for a newly defined class of interval-valued functions (IV-Fs) linked to Hermite–Hadamard (H-H) and Hermite–Hadamard–Fejér (H-H-Fejér) type inequalities via interval-valued Riemann–Liouville fractional integrals (IV-RL-fractional integrals). We also attain some related inequalities for the product of two LR--convex IV-Fs. These findings enable us to identify a new class of inclusions that may be seen as significant generalizations of results proved by Iscan and Chen. Some examples are included in our findings that may be used to determine the validity of the results. The findings in this work can be seen as a considerable advance over previously published findings. [ABSTRACT FROM AUTHOR]

The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this paper, our aim is to establish the relation between integral inequalities and interval-valued functions (IV-Fs) based upon the pseudo-order relation. Firstly, we discuss the properties of left and right preinvex interval-valued functions (left and right preinvex IV-Fs). Then, we obtain Hermite–Hadamard (-) and Hermite–Hadamard–Fejér (--Fejér) type inequality and some related integral inequalities with the support of left and right preinvex IV-Fs via pseudo-order relation and interval Riemann integral. Moreover, some exceptional special cases are also discussed. Some useful examples are also given to prove the validity of our main results. [ABSTRACT FROM AUTHOR]

The purpose of this study is to introduce the new class of Hermite–Hadamard inequality for LR-convex interval-valued functions known as LR-interval Hermite–Hadamard inequality, by means of pseudo-order relation (  ≤ p  ). This order relation is defined on interval space. We have proved that if the interval-valued function is LR-convex then the inclusion relation "  ⊆  " coincident to pseudo-order relation "  ≤ p  " under some suitable conditions. Moreover, the interval Hermite–Hadamard–Fejér inequality is also derived for LR-convex interval-valued functions. These inequalities also generalize some new and known results. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area. [ABSTRACT FROM AUTHOR]