Solving fully neutrosophic linear programming problem with application to stock portfolio selection

Neutrosophic set is considered as a generalized of crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about the real world problems. In this paper, a neutrosophic linear programming (NLP) problem with single-valued trapezoidal neutrosophic numbers is formulated and solved. A new method based on the so-called score function to find the neutrosophic optimal solution of fully neutrosophic linear programming (FNLP) problem is proposed. This method is more flexible than the linear programming (LP) problem, where it allows the decision maker to choose the preference he is willing to take. A stock portfolio problem is introduced as an application. Also, a numerical example is given to illustrate the utility and practically of the method

A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem

We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number of α-level sets. By using α-level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for each α-level set. The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function. Based on the Kth-best algorithm, the two subproblems can be solved sequentially. Based on a series of α-level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem. Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach

Lexicographic Methods for Fuzzy Linear Programming

Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution methods are still being proposed. Among the existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables for handling inexactness and vagueness in data have experienced a remarkable development in recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is to present an updated review of advances in this particular area. Consequently, the paper briefly examines well-known models and methods for FLP, and expands on methods for fuzzy single- and multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical relevance. For this case, computer codes are provided that can be used to reproduce results presented in the paper and for practical applications. The paper demonstrates that FLP that is focused on lexicographic methods is an active area with promising research lines and practical implications.Spanish Ministry of Economy and CompetitivenessEuropean Union (EU) TIN2017-86647-

A New Method for Solving Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers

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 method as compared to the existing method for solving the same type of fuzzy linear programming problems

Utilizing a new approach for solving fully fuzzy linear programming problems

This paper deals with fully fuzzy linear programming (FFLP) problem in which all parameters and variables are characterized by L-R fuzzy numbers. By a proposed approach, the FFLP problem is converted into the triple objective functions, and hence a single objective using the weighting method. Through this approach the problem is not transformed into the crisp linear programming problem (LPP) that is enable for obtaining fuzzy optimal solution and the corresponding fuzzy optimal solution which is more realistic to the real world problems. Then a numerical example is taken to the utility and clarify the practically and the efficiency of the approach.</p

A Novel Technique for Solving Multiobjective Fuzzy Linear Programming Problems

This study considers multiobjective fuzzy linear programming (MFLP) problems in which the coefficients in the objective functions are triangular fuzzy numbers. The study proposing a new technique to transform MFLP problems into the equivalent single fuzzy linear programming problem and then solving it via linear ranking function using the simplex method, supported by numerical example

A Constructive Proof of Fundamental Theory for Fuzzy Variable Linear Programming Problems

Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generalize the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof using a numerical example

Fuzzy Efficiency Measures in Data Envelopment Analysis Using Lexicographic Multiobjective Approach

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.There is an extensive literature in data envelopment analysis (DEA) aimed at evaluating the relative efficiency of a set of decision-making units (DMUs). Conventional DEA models use definite and precise data while real-life problems often consist of some ambiguous and vague information, such as linguistic terms. Fuzzy sets theory can be effectively used to handle data ambiguity and vagueness in DEA problems. This paper proposes a novel fully fuzzified DEA (FFDEA) approach where, in addition to input and output data, all the variables are considered fuzzy, including the resulting efficiency scores. A lexicographic multi-objective linear programming (MOLP) approach is suggested to solve the fuzzy models proposed in this study. The contribution of this paper is fivefold: (1) both fuzzy Constant and Variable Returns to Scale models are considered to measure fuzzy efficiencies; (2) a classification scheme for DMUs, based on their fuzzy efficiencies, is defined with three categories; (3) fuzzy input and output targets are computed for improving the inefficient DMUs; (4) a super-efficiency FFDEA model is also formulated to rank the fuzzy efficient DMUs; and (5) the proposed approach is illustrated, and compared with existing methods, using a dataset from the literature

On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers

The paper presents a new method for solving fully fuzzy linear programming problems with inequality constraints and parameterized fuzzy numbers, by means of solving multiobjective linear programming problems. The equivalence is proven between the set of nondominated solutions of the fully fuzzy linear programming problem and the set of weakly efficient solutions of the considered and related multiobjective linear problem. The whole set of nondominated solutions for a fully fuzzy linear programming problem is explicitly obtained by means of a finite generator set.The first author was partially supported by the research project MTM2017-89577-P (MINECO, Spain), and the second author was partially supported by Spanish Ministry of Economy and Competitiveness through grants AYA2016-75931-C2-1-P, AYA2015-68012-C2-1, AYA2014-57490-P, AYA2013-40611-P, and from the Consejería de Educación y Ciencia (Junta de Andalucía) through TIC-101, TIC-4075 and TIC-114