Triangular interval type-2 fuzzy soft set and its application

Comparison Uncertainty of Different Types of Membership Functions in T2FLS: Case of International Financial Market

This article deals with the determination and comparison of different types of functions of the type-2 interval of fuzzy logic, using a case study on the international financial market. The model is demonstrated on the time series of the leading stock index DJIA of the US market. Type-2 Fuzzy Logic membership features are able to include additional uncertainty resulting from unclear, uncertain or inaccurate financial data that are selected as inputs to the model. Data on the financial situation of companies are prone to inaccuracies or incomplete information, which is why the type-2 fuzzy logic application is most suitable for this type of financial analysis. This paper is primarily focused on comparing and evaluating the performance of different types of type-2 fuzzy membership functions with integrated additional uncertainty. For this purpose, several model situations differing in shape and level or degree of uncertainty of membership functions are constructed. The results of this research show that type-2 fuzzy sets with dual membership functions is a suitable expert system for highly chaotic and unstable international stock markets and achieves higher accuracy with the integration of a certain level of uncertainty compared to type-1 fuzzy logic.

A novel approach to optimize the production cost of railway coaches of India using situational-based composite triangular and trapezoidal fuzzy LPP models

This article offers a comparative study of maximizing and modelling production costs by means of composite triangular fuzzy and trapezoidal FLPP. It also outlines five different scenarios of instability and has developed realistic models to minimize production costs. Herein, the first attempt is made to examine the credibility of optimized cost via two different composite FLP models, and the results were compared with its extension, i.e., the trapezoidal FLP model. To validate the models with real-time phenomena, the Production cost data of Rail Coach Factory (RCF) Kapurthala has been taken. The lower, static, and upper bounds have been computed for each situation, and then systems of optimized FLP are constructed. The credibility of each model of composite-triangular and trapezoidal FLP concerning all situations has been obtained, and using this membership grade, the minimum and the greatest minimum costs have been illustrated. The performance of each composite-triangular FLP model was compared to trapezoidal FLP models, and the intense effects of trapezoidal on composite fuzzy LPP models are investigated.

A Robust Interval Type-2 Fuzzy Logic Controller for Variable Speed Wind Turbines Based on a Doubly Fed Induction Generator

This paper presents an implementation of a new robust control strategy based on an interval type-2 fuzzy logic controller (IT2-FLC) applied to the wind energy conversion system (WECS). The wind generator used was a variable speed wind turbine based on a doubly fed induction generator (DFIG). Fuzzy logic concepts have been applied with great success in many applications worldwide. So far, the vast majority of systems have used type-1 fuzzy logic controllers. However, T1-FLC cannot handle the high level of uncertainty in systems (complex and non-linear systems). The amount of uncertainty in a system could be reduced by using type-2 fuzzy logic since it offers better capabilities to handle linguistic uncertainties by modeling vagueness and unreliability of information. A new concept based on an interval type-2 fuzzy logic controller (IT-2 FLC) was developed because of its uncertainty management capabilities. Both these control strategies were designed and their performances compared for the purpose of showing the control most efficient in terms of reference tracking and robustness. We made a comparison between the performance of the type-1 fuzzy logic controller (T1-FLC) and interval type-2 fuzzy logic controller (IT2-FLC). The simulation results clearly manifest the height robustness of the interval type-2 fuzzy logic controller in comparison to the T1-FLC in terms of rise time, settling time, and overshoot value. The simulations were realized by MATLAB/Simulink software.

Representation and application of Fuzzy soft sets in type-2 environment

This paper has represented a soft-set in the type-2 environment by its simplest form as an augmentation to soft-set theories. Furthermore, we have applied the type-2 fuzzy soft set(T2FSS) by using our most straightforward representation to find the solution of a decision-making-problem (DMP) based-on T2FSS as well as weighted type-2 fuzzy soft set (WT2FSS). We have proposed two definitions, namely, Mid-$$\alpha $$ α -threshold fuzzy-set of a T2FSS and Mid-$$\lambda $$ λ -threshold fuzzy-set of a T2FSS. Furthermore, we have presented the definition, namely, level fuzzy-soft-set(LFSS) of a T2FSS. Using this concept, we have prepared two algorithms to select one object in T2FSS as well as WT2FSS based on DMP, which take regret disinclination and expectation preference of decision-makers into consideration in the decision procedure. Also, we have presented two numerical examples at the end.