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.

A study on product-sum of triangular fuzzy numbers

We study the problem: if a˜i, i ∈ N are fuzzy numbers of triangular form, then what is the membership function of the infinite (or finite) sum -˜a1 + a˜2 + · · · (defined via the sub-product-norm convolution)

Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations

In this article, we are concerned with the VIP of fractional fuzzy evolution equations in the space of triangular fuzzy numbers. The continuous dependence of two kinds of fuzzy mild solutions on initial values and orders for the studied problem is obtained. The results obtained in this paper improve and extend some related conclusions on this topic.

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.

Enhanced Fuzzy Delphi Method in Forecasting and Decision-Making

The Delphi method is a process where subjective data are transformed into quasi-objective data using statistical analysis and are converged to stable points. The Delphi method was developed by the RAND Corporation at Santa Monica, California, and is widely used for long-range forecasting in management science. It is a method by which the subjective data of experts are made to converge using some statistical analyses. This article proposes a variation of the Delphi method using triangular fuzzy numbers, where the communication method with the experts is the same, but the estimation procedure is different. The utility of the method is illustrated by a numerical example.

An approach to optimize the cost of transportation problem based on triangular fuzzy programming problem

In this article, we address a fully fuzzy triangular linear fractional programming (FFLFP) problem under the condition that all the parameters and decision variables are characterized by triangular fuzzy numbers. Utilizing the computation of triangular fuzzy numbers and Lexicographic order (LO), the FFLFP problem is changed over to a multi-objective function. Consequently, the problem is changed into a multi-objective crisp problem. This paper outfits another idea for diminishing the computational complexity, in any case without losing its viability crisp LFP issues. Lead from real-life problems, a couple of mathematical models are considered to survey the legitimacy, usefulness and applicability of our method. Finally, some mathematical analysis along with one case study is given to show the novel strategies are superior to the current techniques.

An Improved Fuzzy TOPSIS Method with a New Ranking Index

Owing to vague concepts frequently represented in decision data, the crisp values are inadequate to model real-life situations. In this paper, the rating of each alternative and the weight of each criterion is described by linguistic terms which can be expressed in triangular fuzzy numbers. Next, we focus on fuzzy TOPSIS (FTOPSIS) method. We show that, however, the conventional FTOPSIS is interesting, but it suffers from some flaws. The shortcomings of classical FTOPSIS are shown and some solutions are given. Further, a new similarity index is proposed and then is illustrated using numerical examples. By treating the separations of an alternative from the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS) as “cost” criterion and “benefit” criterion, respectively, we reduce the original fuzzy multiple criteria decision making (FMCDM) problem to a new one with two criteria. Illustrative examples are given to show the advantages of the proposed approach.

Fuzzy Sawi Decomposition Method for Solving Nonlinear Partial Fuzzy Differential Equations

The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition method. For this purpose, two new theorems for fuzzy Sawi transformation regarding fuzzy partial gH-derivatives are introduced. The use of convex symmetrical triangular fuzzy numbers creates symmetry between the lower and upper representations of the fuzzy solution. To demonstrate the effectiveness of the method, a numerical example is provided.