Conventional data envelopment analysis (DEA) for measuring the relative efficiency of a set of decisionmaking units (DMUs) requires the observations to have precise values. When observations are imprecise and represented by interval values, the efficiencies are also expected to reflect interval values. Several methods exist to calculate the interval overall and technical efficiencies, but such ...

To my Parents Whose guidance, care, love, and support has proven extremely valuable to me ACKNOWLEDGEMENTS First and foremost I would like to thank my advisor, Dr. Nader Sadegh, for giving me the opportunity to carry out this research. I feel privileged to work alongside him for the last two years. He has been a guiding light, supporting me at all times and giving me the right advice. His words...

In previous studies, it is pointed out that in several situations it is better to use interval-valued fuzzy numbers instead of triangular or trapezoidal fuzzy numbers. But till now, there is no method that deals with the sensitivity analysis of such linear programming problems in which all the parameters are represented by interval-valued fuzzy numbers. In this paper, a new method is proposed f...

Determining the set of all optimal solutions of a linear program with interval data is one of the main problems discussed in interval optimization. We review two methods based on duality in linear programming, which are used to approximate the optimal set. Additionally, another decomposition method based on complementary slackness is proposed. This method provides the exact description of the o...

This paper presents an interval version of the Geometric Machine Model (GMM) and the programming language induced by its structure. The GMM is an abstract machine model, based on Girard’s coherence space, capable of modelling sequential, alternative, parallel (synchronous) and non-deterministic computations on a (possibly infinite) shared memory. The processes of the GMM are inductively constru...

The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We propo...

In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in Σ∀,∃([A], [b]) = {x ∈R | ∀A ∈ [A], ∃b ∈ [b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors inΣ∀,∃([A], [b]), and we provide a new definition of the optimality of an interval vector included in Σ∀,∃([A], [b])....

In this paper, we introduce a class of fuzzy linear programming problems and de ne the concepts of feasible and satis cing solutions—the necessary tools for dealing with such problems. In this way, we show that the class of crisp (classical) LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems we de ne the concept of duality and prove the weak and strong duality th...

Given a set of n points (nodes) on a line and a set of m weighted intervals defined on the nodes, we consider a particular dynamic programming (DP) problem on these intervals. If the weight function of the DP has convex or concave property, we can solve this DP problem efficiently by using matrix searching in Monge matrices, together with a new query data structure, which we call the consecutiv...