We prove that some important properties of convex subsets of vector topological spaces remain valid in the space of fuzzy numbers endowed with the Euclidean distance. We use these results to obtain a characterization of fuzzy number-valued Lipschitz functions. This fact helps us to find the best Lipschitz constant of the trapezoidal approximation operator preserving the value and ambiguity intr...

In this paper, a new concept called Trident Fuzzy Aggregation Operators in which the operation is made by grouping of numerous Trapezoidal Numbers (TTriFN) to become solitary trapezoidal trident fuzzy numeral for parallel computing application introduced. This proposed operator architecture applicable development networking and ranking concepts. Also, geometric mean over ‘n’ TTriFN on left-side...

This study is devoted to address the notion of duality in Fully Intuitionistic Fuzzy Linear Programming Problems (FIFLP). The problem is addressed by using a revised simplex method with the Gaussian elimination process in fully intuitionistic fuzzy environment. Intuitionistic Fuzzy Trapezoidal Numbers (IFTrpN), along with the basic arithmetic techniques defined on them help in solving the (FIFL...

In this paper, we present a solution of an arbitrary general fully fuzzy linear systems (FFLS) in the form Ã⊗ x̃ = b̃. Where coefficient matrix à is anm×n fuzzy matrix and all of this system are elements of LR type fuzzy numbers. Our method discuss a general FFLS (square or rectangle fully fuzzy linear systems with trapezoidal or triangular LR fuzzy numbers). To do this, we transform fully fuzzy ...

Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose...

To make the analysis more consistent and logical according to real life situations, in thispaper, the concept of trapezoidal vague set is extended by the idea of trapezoidal vaguesets of type-II. Also we have introduced: definition of trapezoidal vague set of type-IIand arithmetic operations between two trapezoidal vague sets of type-II. Further, a newmethod has been developed f...

Ganesan and Veeramani [Fuzzy linear programs with trapezoidal fuzzy numbers, Annals of Operations Research 143 (2006) 305-315.] proposed a new method for solving a special type of fuzzy linear programming problems. In this paper a new method, named as Mehar’s method, is proposed for solving the same type of fuzzy linear programming problems and it is shown that it is easy to apply the Mehar’s m...

Risk assessment is a popular and important tool in decision making process. Risk assessment is generally performed using models and model is a function of some parameters which are usually affected by uncertainty. Here, we consider that model parameters are affected by epistemic uncertainty. To represent epistemic uncertainty in general triangular fuzzy number or trapezoidal fuzzy numbers are u...

In every field of our real life situations, we deal with a replacement problem, when some items such as machines, medical equipment, military tank, electric bulb etc. or workers need to replace due to their decreased efficiency, failure or break down. To get a more realistic view of a replacement problem, here, we consider that the capital cost ( C ~ ), scrap value or resale value ( S ~ ), main...