In this paper, a Multi-criteria De Novo Linear programming (F-MDNLP) problem has been developed under consideration of the ambiguity of parameters. These fuzzy parameters are characterized by fuzzy numbers. A fuzzy goal programming approach is applied for the corresponding multi-criteria De Novo linear programming (   MDNLP) problem by defining suitable membership functions and aspiration levels. The advantage of the approach is that the decision maker's role is only the specification of the level and hence evaluate the   efficient solution for limitation of his/ her incomplete knowledge about the problem domain. A numerical example is given for illustration.

In this paper we have investigated a fuzzy linear programming problem with fuzzy quantities which are LR triangular fuzzy numbers. The given linear programming problem is rearranged according to the satisfactory level of constraints using breaking point method. By considering the constraints, the arranged problem has been investigated for all optimal solutions connected with satisfactory level of quantities on all intervals that constituted from breaking points of the constraints. Optimal solution could be obtained on the constructed [gp-1, gp] intervals for p=1, 2… Here the fuzzy primal simplex algorithm is designed based on revised TSAO’s ranking method.

A Fully fuzzy Linear programming (FFLP) formulation for the reservoir operation of a multipurpose reservoir in presented in the ongoing paper. In the real world, water resources systems usually have complexities among social, economic, natural resources and environmental aspects, which lead to multi-objective problems of significant uncertainties in system parameters, objectives and in their interactions. These uncertainties in FFLP reservoir operation model are considered by being treated as fuzzy sets. In the present study, an FFLP reservoir operation model is developed where all parameters and decision variables are fuzzy numbers. The developed model is demonstrated through a case study of Jayakwadi reservoir stage-II, Maharashtra, India with the objectives of maximization of annual releases for irrigation and hydropower generation. The FFLP reservoir operation model is solved to obtain a compromised solution by simultaneously optimizing the fuzzified objectives and the corresponding degree of truthfulness, using linear membership function. The degree of correspondence (Correspondence) obtained is equal to 0.78 and the corresponding annual releases for irrigation amount of 367 Mm3 and while annual releases for hydropower generation being 216 Mm3. the present study clearly demonstrates that, use of FFLP in multipurpose reservoir system optimization presents a potential alternative to attain an optimal operating policy.

Quadratic programming has been widely applied to solve real-world problems. This paper describes a solution method for solving a special class of fuzzy quadratic programming problems with fuzziness in relations. Then the method is generalized to a more general fuzzy quadratic programming problem, where the cost coefficients, the matrix of the quadratic form, constraints coefficients, and the right-hand sides are all fuzzy numbers. Finally, some examples are taken to the utility of our proposed method.

Today, human decisions are more than ever based on information. But most of this information is not definitive, and in this situation, logical decision making is very difficult based on this uncertainty. Different methods are used to represent this uncertainty, including the fuzzy numbers. The fuzzy linear programming problem is one of the interesting concepts to be addressed in fuzzy optimization. Fully fuzzy Linear programming Problems (FFLP) are issues in which all parameters of the coefficients of the variables in the target functions, the coefficients of the variables in the constraints, the right-hand side of the constraints, and the decision variables in them are fuzzy. In this paper, we show that Definition 2. 6 which is used by Ezzati et al. [1], failed to compare any arbitrary triangular fuzzy numbers. We demonstrate that their presented method is not well in general, thus the proposed method finds the fuzzy optimal solution of Fully fuzzy linear programming problems by Ezzati et al. [1]. Then a new approach is proposed for solving this FFLP problem. An example is also presented to demonstrate the new method.