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For checking the optimality of the objective function, we introduce a lexicographic order relation to compare two arbitrary triangular fuzzy numbers. Based on the order relation, the multi-objective fully fuzzy linear programming problem is converted into a crisp multi-level multi-objective linear programming problem, which may be solved by using the Min operator step by step. A numerical example...
This work introduces a study about vectors and matrices of fuzzy numbers, in particular, stochastic vectors and matrices, including the study of related properties, the arithmetical operations and other concepts, such as the distance. We also present several examples for the analyzed concepts.
The idea screening of a new product concept is perhaps the most critical activity in new product development (NPD). This paper presents a fuzzy synthetic evaluation method (FSEM) for selecting an optimum design alternatives based on fuzzy set theory. The process involves constructing a hierarchical objective, setting evaluation criteria, establishing a fuzzy judgment matrix and weight vector, and...
In this paper, we talk about the solution of fuzzy linear systems, prove a necessary and sufficient condition, and give an exact numerical example, then provide a condition for one solution to be a fuzzy vector.
In this paper, we study the problems with respect to means and pre-orders for fuzzy n - cell numbers. Firstly, we introduce some concepts of vector-valued means and weight number-valued means of fuzzy n - cell numbers, and investigate their properties. And then, bases on these means, we define some binary relations on fuzzy n - cell number space, study their properties, and point out they are weak...
This paper proposes a method for solving fuzzy linear programming problems where all the coefficients are fuzzy numbers. Firstly, this paper use the expected value of fuzzy variable presented by Baoding Liu to compare two fuzzy numbers. Secondly, this paper offer the acceptable solution of fuzzy linear programming for the decision-maker in different degrees of feasiblity. Lastly, we solve one numerical...
In this paper, the characteristic index vectors, positive and negative ideal characteristic index vector of fuzzy numbers are defined, based on the characteristic quantity of fuzzy number.Then, the ranking index is proposed according to the given fuzzy numberpsilas linear weighted distance between characteristic index vector and positive /negative ideal characteristic index vector, respectively.Finally,...
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