The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor when the inputs variable of the model crisp, output variable, and parameters are fuzzed. The results were compared usin

Laser is a powerful device that has a wide range of applications in fields ranging from materials science and manufacturing to medicine and fibre optic communications. One remarkable

   Nanoparticles (NPs) have unique capabilities that make them an eye-opener opportunity for the upstream oil industry. Their nano-size allows them to flow within reservoir rocks without the fear of retention between micro-sized pores. Incorporating NPs with drilling and completion fluids has proved to be an effective additive that improves various properties such as mud rheology, filtration, thermal conductivity, and wellbore stability. However, the biodegradability of drilling fluid chemicals is becoming a global issue as the discharged wetted cuttings raise toxicity concerns and environmental hazards. Therefore, it is urged to utilize chemicals that tend to break down and susceptible to biodegradation. This research presents the pra

Reverse Osmosis (RO) has already proved its worth as an efficient treatment method in chemical and environmental engineering applications. Various successful RO attempts for the rejection of organic and highly toxic pollutants from wastewater can be found in the literature over the last decade. Dimethylphenol is classified as a high-toxic organic compound found ubiquitously in wastewater. It poses a real threat to humans and the environment even at low concentration. In this paper, a model based framework was developed for the simulation and optimisation of RO process for the removal of dimethylphenol from wastewater. We incorporated our earlier developed and validated process model into the Species Conserving Genetic Algorithm (SCG

In this paper, we apply the notion of a bipolar fuzzy n-fold KU-ideal of KU- algebras. We introduce the concept of a bipolar fuzzy n-fold KU-ideal and investigate several properties. Also, we give relations between a bipolar fuzzy n- fold KU-ideal and n-fold KU-ideal. The image and the pre-image of bipolar fuzzy n-fold KU-ideals in KU-algebras are defined and how the image and the pre- image of bipolar fuzzy n-fold KU-ideals in KU-algebras become bipolar fuzzy n- fold KU-ideals are studied. Moreover, the product of bipolar fuzzy n-fold KU- ideals in Cartesian product KU-algebras is given.

In thisˑ paperˑ, we apply the notion ofˑ intuitionisticˑ fuzzyˑ n-fold KU-ideal of KU-algebra. Some types of ideals such as intuitionistic fuzzy KU-ideal, intuitionisticˑ fuzzy closed idealˑ and intuitionistic fuzzy n-fold KU-ideal are studied. Also, the relations between intuitionistic fuzzy n-fold KU-ideal and intuitionistic fuzzy KU-ideal are discussed. Furthermore, aˑ fewˑ results of intuitionisticˑ fuzzyˑ n-ˑfold KU-ideals of a KU-algebra underˑ homomorphismˑ are discussed.

In real-life problems, we use square roots in natural distributions such as (the probability density function), distances and lengths in the Pythagorean theorem, and quadratic formulas in (the height of falling objects), radius of circles, harmonic movements (pendulum and springs), and standard deviation in statistics. We have observed that using fuzzy sets in real-life problems is more convenient than ordinary sets. Therefore, they are important in algebraic structures. As a result, more effort has been made to study square root structures in fuzzy sets. This paper introduces the notion of square roots fuzzy of QS-ideals on QS-algebras and some important characteristics. Some illustrative examples have been provided which prove tha

The notion of interval value fuzzy k-ideal of KU-semigroup was studied as a generalization of afuzzy k-ideal of KU-semigroup. Some results of this idea under homomorphism are discussed. Also, we presented some properties about the image (pre-image) for interval~ valued fuzzy~k-ideals of a KU-semigroup. Finally, the~ product of~ interval valued fuzzyk-ideals is established.

In this paper, Min-Max composition fuzzy relation equation are studied. This study is a generalization of the works of Ohsato and Sekigushi. The conditions for the existence of solutions are studied, then the resolution of equations is discussed.