Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics, fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.Comment: 10 pages, 17 reference

Oczekiwana stopa zwrotu z portfela finansowego – przypadek trójkątnych rozmytych wartości bieżących

The main aim of this article is to present an uncomplicated method of estimating return rate on a portfolio of securities with Present Values presented as triangular fuzzy numbers. Determined return rates on the securities are not triangular fuzzy numbers. Despite this, we achieved a solution that is based on the arithmetic of triangular fuzzy numbers. The whole considerations are illustrated by a numerical example.Głównym celem artykułu jest przedstawienie nieskomplikowanej metody szacowania stopy zwrotu z portfela instrumentów finansowych o wartościach bieżących przedstawionych jako trójkątne liczby rozmyte. Wyznaczone stopy zwrotu z poszczególnych składników nie są trójkątnymi liczbami rozmytymi. Pomimo tego uzyskano takie rozwiązanie, które bazuje na arytmetyce trójkątnych liczb rozmytych. Całość rozważań zilustrowano przykładem numerycznym

An enhanced fuzzy linguistic term generation and representation for time series forecasting

This paper introduces an enhancement to linguistic forecast representation using Triangular Fuzzy Numbers (TFNs) called Enhanced Linguistic Generation and Representation Approach (ElinGRA). Since there is always an error margin in the predictions, there is a need to define error bounds in the forecast. The interval of the proposed presentation is generated from a Fuzzy logic based Lower and Upper Bound Estimator (FLUBE) by getting the models of forecast errors. Thus, instead of a classical statistical approaches, the level of uncertainty associated with the point forecasts will be defined within the FLUBE bounds and these bound can be used for defining fuzzy linguistic terms for the forecasts. Here, ElinGRA is proposed to generate triangular fuzzy numbers (TFNs) for the predictions. In addition to opportunity to handle the forecast as linguistic terms which will increase the interpretability, ElinGRA improved forecast accuracy of constructed TFNs by adding an extra correction term. The results of the experiments, which are conducted on two data sets, show the benefit of using ElinGRA to represent the uncertainty and the quality of the forecast

Research on VIKOR group decision making using WOWA operator based on interval Pythagorean triangular fuzzy numbers

A new decision-making method based on interval Pythagorean triangular fuzzy numbers is proposed for fuzzy information decision-making problems, taking the advantages of interval Pythagorean fuzzy numbers and triangular fuzzy numbers into account. The VIse Kriterijumski Optimizacioni Racun (VIKOR) group decision-making method is based on the Weighted Ordered Weighted Average (WOWA) operator of interval Pythagorean triangular fuzzy numbers (IVPTFWOWA). First, this article provides the definition of the IVPTFWOWA operator and proves its degeneracy, idempotence, monotonicity, and boundedness. Second, the decision steps of the VIKOR decision method using the IVPTFWOWA operator are presented. Finally, the scientificity and effectiveness of the proposed method were verified through case studies and comparative discussions. The research results indicate that the following: (1) the IVPTFWOWA operator combines interval Pythagorean fuzzy numbers and triangular fuzzy numbers, complementing the shortcomings of the two fuzzy numbers, and can characterize fuzzy information on continuous geometry, thereby reducing decision errors caused by inaccurate and fuzzy information; (2) the VIKOR decision-making method based on the IVPTFWOWA operator applies comprehensive weights, fully considering the positional weights of the scheme attributes and the weights of raters, and fully utilizing the attribute features of decision-makers and cases; and (3) compared to other methods, there is a significant gap between the decision results obtained using this method, making it easier to identify the optimal solution

A Novel Technique for Solving Multiobjective Fuzzy Linear Programming Problems

This study considers multiobjective fuzzy linear programming (MFLP) problems in which the coefficients in the objective functions are triangular fuzzy numbers. The study proposing a new technique to transform MFLP problems into the equivalent single fuzzy linear programming problem and then solving it via linear ranking function using the simplex method, supported by numerical example