Narrow Results

Fuzzy mathematics is a generalization in which fuzzy numbers replace real numbers and fuzzy arithmetic replaces real arithmetic. It is an excellent scope for modeling vague and uncertain aspects of the actual environments. In this important area, Dubois and Prade¹ defined a fuzzy matrix as a rectangular array of fuzzy numbers. They have also defined the LR type fuzzy numbers with some useful approximate arithmetic operators. The aim of this paper is to extend some useful aspects of linear algebra e.g. determinant, norm and eigenvalue for fuzzy matrices with LR fuzzy number entries by the use of fuzzy arithmetic. Finally, applications in fuzzy analytical hierarchy process (AHP) are investigated.

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

In this paper, a method for solving Riccati fuzzy differential equations is studied in great detail. To obtain the solution of Riccati fuzzy differential equations (RFDEs), we study the fuzzy differential equations (FDEs) using the concept of generalized $H$-differentiability.