Optimal Solution of Neutrosophic Linear Fractional Programming Problems With Mixed Constraints

In this paper, Linear Fractional Programming (LFP) problems have been extended to neutrosophic sets (NSs) and the operations and functionality of these laws are studied. Moreover, the new algorithm is based on aggregation ranking function and arithmetic operations of triangular neutrosophic sets (TNSs). Furthermore, for the first time, in this paper, we take up a problem where the constraints are both equality and inequality neutrosophic triangular fuzzy number. Lead from genuine issue, a few numerical models are considered to survey the legitimacy, profitability and materialness of our technique. At last, some numerical trials alongside one contextual analysis are given to show the novel techniques are better than the current strategies.

A study on multiplication operation on triangular fuzzy numbers

The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and further are approximation methods. In this paper we, compare the multiplication operation on triangular fuzzy number between α-cut method and standard approximation method and give some examples.

Fuzzy-Based Investigation of Challenges for the Deployment of Renewable Energy Power Generation

Studying and analyzing the challenges that the renewable energy sector faces can help evaluate the risks and improve the planning. This research is done by considering the challenges in the implementation of sustainable generation of electricity through RESs in India, based on factors, including technical, financial, involvement, support, and others. The triangular fuzzy number (TFN) method, based on fuzzy logic concept, is used to analyze the challenges in this study. In general, TFN comprises of three numbers, likewise Gaussian fuzzy numbers, trapezoidal fuzzy numbers also exist. The classified sets of numbers are denotations to decision-makers’ perspective or a choice towards the criterion preference. Although alternatives are many to design a fuzzy set depending on elements count, the TFNs are the ones considered as actual representations of a fuzzy number. On the other hand, cases the Gaussian or trapezoidal, are manifestations of fuzzy intervals. Another argument is that the membership function shape corresponding to the number of fuzzy set elements is largely dependent on the study. The challenges identified along with analysis in this paper will help the industry, governments, and policymakers focus and tackle essential issues to facilitate further the deployment of RESs in India towards a more sustainable country.

A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers

Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method.

Fuzzy Finite Element Analysis for Static Responses of Plane Structures

In this paper, a fuzzy finite element algorithm is investigated to determine static responses of plane structures. This algorithm concerns finite element method, fuzzy sets theory, and response surface method. Firstly, the notion of a standardized triangular fuzzy number is developed and utilized to replace original fuzzy numbers in the surrogate models. Then, the error estimations between the training and the test sets are performed to select the suitable response surface model amongst the regression models. Lastly, a good performance combination of complete and non-complete quadratic polynomial regression models is proposed to define the responses of structures. The merits of the proposed algorithm are illustrated via numerical examples.

Computing the Number of Failures for Fuzzy Weibull Hazard Function

The number of failures plays an important factor in the study of maintenance strategy of a manufacturing system. In the real situation, this number is often affected by some uncertainties. Many of the uncertainties fall into the possibilistic uncertainty, which are different from the probabilistic uncertainty. This uncertainty is commonly modeled by applying the fuzzy theoretical framework. This paper aims to compute the number of failures for a system which has Weibull failure distribution with a fuzzy shape parameter. In this case two different approaches are used to calculate the number. In the first approach, the fuzziness membership of the shape parameter propagates to the number of failures so that they have exactly the same values of the membership. While in the second approach, the membership is computed through the α-cut or α-level of the shape parameter approach in the computation of the formula for the number of failures. Without loss of generality, we use the Triangular Fuzzy Number (TFN) for the Weibull shape parameter. We show that both methods have succeeded in computing the number of failures for the system under investigation. Both methods show that when we consider the function of the number of failures as a function of time then the uncertainty (the fuzziness) of the resulting number of failures becomes larger and larger as the time increases. By using the first method, the resulting number of failures has a TFN form. Meanwhile, the resulting number of failures from the second method does not necessarily have a TFN form, but a TFN-like form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification (GMVD) method. The results show that for certain weighting factor of the GMVD, the cores of these fuzzy numbers of failures are identical.

Computer-Based Fuzzy Numerical Method for Solving Engineering and Real-World Applications

The nonlinear equation is a fundamentally important area of study in mathematics, and the numerical solutions of the nonlinear equations are also an important part of it. Fuzzy sets introduced by Zedeh are an extension of classical sets, which have several applications in engineering, medicine, economics, finance, artificial intelligence, decision-making, and so on. The most special types of fuzzy sets are fuzzy numbers. The important fuzzy numbers are trapezoidal fuzzy and triangular fuzzy numbers, which have several applications. In this research article, we propose an efficient numerical iterative method for estimating roots of fuzzy nonlinear equations, which are based on the special type of fuzzy number called triangular fuzzy number. Convergence analysis proves that the order of convergence of the numerical method is three. Some real-life applications are considered as numerical test problems from engineering, which contain fuzzy quantities in the parametric form. Engineering models include fractional conversion of nitrogen-hydrogen feed into ammonia and Van der Waal’s equation for calculating the volume and pressure of a gas and motion of the object under constant force of gravity. Numerical illustrations are given to show the dominance efficiency of the newly constructed iterative schemes as compared to existing methods in the literature.

Neutrosophic Triangular Fuzzy Travelling Salesman Problem Based on Dhouib-Matrix-TSP1 Heuristic

In this paper, the Travelling Salesman Problem is considered in neutrosophic environment which is more realistic in real-world industries. In fact, the distances between cities in the Travelling Salesman Problem are presented as neutrosophic triangular fuzzy number. This problem is solved in two steps: At first, the Yager’s ranking function is applied to convert the neutrosophic triangular fuzzy number to neutrosophic number then to generate the crisp number. At second, the heuristic Dhouib-Matrix-TSP1 is used to solve this problem. A numerical test example on neutrosophic triangular fuzzy environment shows that, by the use of Dhouib-Matrix-TSP1 heuristic, the optimal or a near optimal solution as well as the crisp and fuzzy total cost can be reached.