In this study,the authors envisage the neutrosophic number from various distinct rational perspectives and viewpoints to give it a look of a conundrum.They focused and analysed neutrosophic fuzzy numbers when indeterm...In this study,the authors envisage the neutrosophic number from various distinct rational perspectives and viewpoints to give it a look of a conundrum.They focused and analysed neutrosophic fuzzy numbers when indeterminacy and falsity functions are dependent on each other,which serves an indispensable role for the uncertainty concept.Additionally,the idea of cylindrical neutrosophic single-valued number is focused here,when the indeterminacy and falsity functions are dependent to each other using an influx of different logical and innovative graphical representation.They also developed the score and accuracy function for this particular cylindrical neutrosophic single-valued number and analysed some real-life problems like networking critical path model problem and minimal spanning tree problem of operation research field when the numbers are in cylindrical neutrosophic ambiance.They also introduced a multi-criterion group decision-making problem in this cylindrical neutrosophic domain.This noble thought will help us to solve a plethora of daily life problems in the neutrosophic arena.展开更多
In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain varia...An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.展开更多
To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the result...To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the results,a new ap-proach is proposed based on expected value-standard devi-ation value criterion(C_(ESD) criterion).Firstly,the effective solution to the URMOP problem is defined;then,by applying sequence relationship between the uncertain random variables,the UR-MOP problem is transformed into a single-objective program-ming(SOP)under uncertain random environment(URSOP),which are transformed into a deterministic counterpart based on the C_(ESD) criterion.Then the validity of the new approach is proved that the optimal solution to the SOP problem is also effi-cient for the URMOP problem;finally,a numerical example and a case application are presented to show the effectiveness of the new approach.展开更多
Hot compression tests were conducted on Ti40 burn resistant titanium alloy in the temperature range of 900-1 100 ℃ and strain rate range of 0.01-10 s-1 to investigate its fracture behavior and critical fracture condi...Hot compression tests were conducted on Ti40 burn resistant titanium alloy in the temperature range of 900-1 100 ℃ and strain rate range of 0.01-10 s-1 to investigate its fracture behavior and critical fracture conditions in hot forming. It was observed that the failure of Ti40 alloy is attributed to longitudinal surface cracking due to severe oxidation of element V and the secondary tensile stresses. The critical fracture strain increases with increasing temperature and decreasing strain rate. From these observations and parallel FEM simulations,it was concluded that the critical fracture strain is a function of a single argument Zener-Hollomon parameter,and there is a linear relationship between them. An Oyane criterion successfully predicted the location of crack initiation. The critical fracture values also exhibit a liner relationship with lnZ. Based on these results,a new fracture criterion of Ti40 alloy based on Zener-Hollomon parameter was established.展开更多
文摘In this study,the authors envisage the neutrosophic number from various distinct rational perspectives and viewpoints to give it a look of a conundrum.They focused and analysed neutrosophic fuzzy numbers when indeterminacy and falsity functions are dependent on each other,which serves an indispensable role for the uncertainty concept.Additionally,the idea of cylindrical neutrosophic single-valued number is focused here,when the indeterminacy and falsity functions are dependent to each other using an influx of different logical and innovative graphical representation.They also developed the score and accuracy function for this particular cylindrical neutrosophic single-valued number and analysed some real-life problems like networking critical path model problem and minimal spanning tree problem of operation research field when the numbers are in cylindrical neutrosophic ambiance.They also introduced a multi-criterion group decision-making problem in this cylindrical neutrosophic domain.This noble thought will help us to solve a plethora of daily life problems in the neutrosophic arena.
文摘In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
基金supported by the National Natural Science Foundation of China(71601183 71571190)
文摘An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China(72001213)the basic research program of Natural Science of Shaanxi Province,China(2021JQ-369).
文摘To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the results,a new ap-proach is proposed based on expected value-standard devi-ation value criterion(C_(ESD) criterion).Firstly,the effective solution to the URMOP problem is defined;then,by applying sequence relationship between the uncertain random variables,the UR-MOP problem is transformed into a single-objective program-ming(SOP)under uncertain random environment(URSOP),which are transformed into a deterministic counterpart based on the C_(ESD) criterion.Then the validity of the new approach is proved that the optimal solution to the SOP problem is also effi-cient for the URMOP problem;finally,a numerical example and a case application are presented to show the effectiveness of the new approach.
基金Project(MKPT-01-101) supported by the State Science and Technology Key Projects
文摘Hot compression tests were conducted on Ti40 burn resistant titanium alloy in the temperature range of 900-1 100 ℃ and strain rate range of 0.01-10 s-1 to investigate its fracture behavior and critical fracture conditions in hot forming. It was observed that the failure of Ti40 alloy is attributed to longitudinal surface cracking due to severe oxidation of element V and the secondary tensile stresses. The critical fracture strain increases with increasing temperature and decreasing strain rate. From these observations and parallel FEM simulations,it was concluded that the critical fracture strain is a function of a single argument Zener-Hollomon parameter,and there is a linear relationship between them. An Oyane criterion successfully predicted the location of crack initiation. The critical fracture values also exhibit a liner relationship with lnZ. Based on these results,a new fracture criterion of Ti40 alloy based on Zener-Hollomon parameter was established.
