Triangular interval type-2 fuzzy soft set and its application

Abstract

Decision-making is an essential task in Science and Engineering. Since most of the real-world problems have uncertainty in nature, making the decision is challengeable one for the decision makers. Soft set has the advantage of free from the deficiency of the parameterization tools of existing theories, namely probability, fuzzy theory and the theory of rough sets. Linguistic terms mean different things to different people, so variability in expert's acceptance degree is possible. Here usage of type-1 fuzzy leads to noisy and uncertain, and the parameters also may be noisy and hence type-2 fuzzy sets may be used to address the mentioned issues. Therefore, a triangular interval type-2 fuzzy soft set has been considered in the present work by combining triangular interval type-2 fuzzy set and soft set. In this paper, a triangular interval type-2 fuzzy soft weighted arithmetic operator (TIT2FSWA) has been proposed with its desired mathematical properties; also applied the proposed methodology in a decision-making problem for profit analysis. Further comparative analysis has been made with the existing methods to show the effectiveness of the proposed method.

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

“…The authors use triangular MF, because according to their knowledge and experience they provide better performance than Gaussian. Authors [25] use T2FLS to form a profit analysis decision support model. The authors apply type-2 fuzzy sets because type-1 is too noisy.…”

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

“…But that criticism is ended with the invention of the type-2 fuzzy set concept in 1975 by Zadeh [24]. Many researchers work on [17,[25][26][27][28][29][30][31]35,37] the properties, operations, and applications of type 2 fuzzy sets and its soft set extensions. Here we have represented type 2 fuzzy sets and type 2 fuzzy soft sets in the simplest form and used it in decision-making.…”

“…Mendel [36] proposed a high-level retrospective of type-2 fuzzy sets and fuzzy logic systems. Lathamaheswari et al [37] studied the application of triangular interval type-2 fuzzy soft sets. Melin and Castillo [38] presented a brief review of type-2 fuzzy logic applications in various fields.…”

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

“…Additionally, various components of triangular fuzzy numbers [27,28] are used to design the reliability parameters to build industrial systems. Lathamaheswari et al [59] proposed to the soft-weighted arithmetic operator a threeway type-2 interval with their demanded mathematical characteristics and also applied the proposed methodology in a profit-assessed decision-making problem. The symmetric fuzzy numbers were used in the objective and right-hand side constraints of the fuzzy linear programming problem [29][30][31].…”