There are several methods in the literature to find the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems. However, in all these methods, it is assumed that the product of two trapezoidal (triangular) fuzzy numbers will also be a trapezoidal (triangular) fuzzy number. Fan et al. (“Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach”, Information Sciences, Vol. 241, pp. 12–27, 2013) proposed a method for finding the fuzzy optimal solution of FFLP problems without considering this assumption. In this paper, it is shown that the method proposed by Fan et al. (2013) suffer from errors and to overcome these errors, a new method (named as Mehar method) is proposed for solving FFLP problems by modifying the method proposed by Fan et al. (2013) . To illustrate the proposed method, some numerical problems are solved.

Potassium dihydrogen phosphate, KH2PO4 (KDP) crystal is an excellent electro-optical nonlinear optical crystal with large electro-optical nonlinear coefficient, high laser damage threshold, and laser frequency doubling effect, electro-optical effect , Piezoelectric effects and other special features, widely used in inertial confinement fusion engineering (ICF) and electro-optical switching devices. Therefore, its growth mechanism, growth process and performance have been systematically studied. In the process of KDP crystal growth, it is found that the stability of the growth solution is an important factor affecting the quality of crystal growth. Therefore, in recent years, more and more research on the stability of the solution, such as the study of ph, doping, supersaturation, overheating time on the stability of the solution. Among them, the research on the doping is mostly reported, and the research on this aspect is mainly focused on two aspects. On the one hand, it is the study of the stability of the solution under doping, and the other is the effect of doping on the optical quality of the crystal. In fact, the stability of the growth solution and the quality of crystal growth is directly related to the quality, but the existing research to isolate the two researches. Therefore, the experiment will be carried out in the case of double-doped KDP solution stability, KDP crystal growth and crystal optical quality and other experiments, and in-depth analysis of the impact of solution stability and crystal optical quality of the reasons, while the solution stability and The relationship between the optical quality of the crystal is briefly analyzed.

In the era of rapid information technology development, artificial intelligence (AI) and virtual reality (VR) technologies have gradually infiltrated the field of university English teaching, brought significant applications and impacted to English language learning in listening, speaking, writing, translation, and personalized learning. AI plays a vital role as an auxiliary teaching method in university English instruction, and the integration of VR technology further enhances teaching efficiency. This research will propose relevant recommendations to provide theoretical references for university English education in the age of AI, while also offering insights and guidance to educators in the education industry during the informatization reform of education.

In order to maximize the potential energy utilization of agricultural and forestry waste and sludge, the experimental research on co-pyrolysis was carried out for two kinds of sludge (urban industrial sludge, paper sludge) and a typical biomass straw. The results show that adding biomass can effectively improve sludge pyrolysis characteristics; biomass straw and sludge, there are complex interactive effects between components in the co-pyrolysis process, and the characteristic parameters show nonlinear changes. When industrial sludge is mixed with straw, with the increase of straw content, the initial temperature of pyrolysis gradually decreases, the termination temperature increases, the peak of pyrolysis reaction rate and the corresponding temperature gradually increase, and the pyrolysis index gradually increases; when paper sludge is mixed with straw, with the increase of straw content, the initial temperature of pyrolysis gradually decreases, the termination temperature increases, the peak of pyrolysis reaction rate gradually increases, while the peak corresponding temperature gradually decreases, and the pyrolysis index gradually decreases. Combined with characteristic parameters and reaction kinetics analysis, it is suggested that the straw mixing proportion should be controlled at about 25% during the co-pyrolysis of industrial sludge and straw. During the co-pyrolysis of paper sludge and straw, it is suggested to control the straw blending ratio at about 75%.