Solving matrix games with hesitant fuzzy pay-offs

In this paper, we present a multi-objective fractional probabilistic programming problem where the parameters in the objective functions and right-hand side constraints are multi-choice in nature. Multi-choice multi-objective objective fractional probabilistic programming problem is formulated. The multi-choice parameters in the right-hand side of constraints are random variables following Cauchy distribution. Multi-choice multi-objective fractional probabilistic programming problem is transformed to deterministic equivalent multi-choice multi-objective fractional programming problem using chance-constrained programming problem. Lagrange interpolating polynomial approach is proposed to deal with multi-choice parameters. The multi-choice multi-objective fractional programming problem is transformed to non-linear mixed integer multi-objective programming problem. An \(\epsilon -\) constrained method is applied to find the compromise solutions of non-linear mixed integer multi-objective programming problem using different values of \(\epsilon \). LINGO software is applied to find the optimal solution of single objective non-linear mixed integer programming problem. Finally, a numerical example is given to illustrate the proposed programming problem.KeywordsMulti-choice programming problemMulti-objective programming problemProbabilistic programming problemFractional programming problem\(\epsilon \)-constraint method

In this paper, we focus on multiobjective nonlinear programming problems with fuzzy parameters and introduce new solution concepts by assuming that the decision maker may have fuzzy goals for each of the objective functions with fuzzy parameters. In order to deal with multiobjective nonlinear programming problems with fuzzy parameters, two types of feasibility and two types of Pareto optimality are introduced by making use of several indices for ranking two fuzzy numbers proposed by Dubois and Prade. Then new solution concepts are defined by considering both two types of feasibility and Pareto optimality, and it is shown that new solutions proposed here can be obtained on the basis of nonlinear programming for appropriate satisficing levels.

Stability of multiobjective nonlinear programming problems with fuzzy parameters

The fuzziness induced in the decision making in the actual system in general, comprises fuzziness in the formulation of the problem and that in the judgments of the decision maker (DM) as a human being. This paper proposes an interactive fuzzy satisficing method, which takes into consideration the fuzziness in problem formulation as well as that in the judgments of DM. The multiobjective nonlinear programming problem containing fuzzy parameters is transformed into the α ‐multiobjective nonlinear programming problem. After determining the fuzzy goal of DM for each objective function by eliciting the membership function, the following reference values are set: the fuzziness index α of DM for the fuzzy parameter; and the reference membership values, which are reference for the membership functions. For the specified α and the reference membership values, the corresponding augmented minimax problem is solved, and DM is supplied with the α‐Pareto optimal, together with the trade‐off ratios among membership functions and the trade‐off ratios between α and the membership functions. Obtaining the result, the DM takes the information concerning current α‐Pareto optimal solution and the trade‐off ratios into consideration, and respond by updating the reference membership values and the value of α if necessary. In this way the satisficing solution finally is derived for DM, thereby ensuring the α‐Pareto optimality. This is the proposed interactive fuzzy satisficing method. The interactive process is demonstrated for a numerical example by the interactive computer program.

Particle swarm optimization (PSO) was proposed by Kennedy et al. as a general approximate solution method for nonlinear programming problems. Its efficiency has been shown, but there have been left some shortcomings of the method. Thus, the authors proposed a revised PSO (rPSO) method incorporating the homomorphous mapping and the multiple stretching in order to cope with these shortcomings. In this paper, we construct an interactive fuzzy satisficing method for multiobjective nonlinear programming problems based on the rPSO. Furthermore, in order to obtain better solutions in consideration of the property of multiobjective programming problems, we incorporate the direction to nondominated solutions into the rPSO. Finally, we show the efficiency of the proposed method by applying it to numerical examples

The sufficient optimality conditions and duality results have recently been given for the following generalised convex programming problem:where the funtion f and g satisfyfor some η: X0 × X0 → ℝnIt is shown here that a relaxation defining the above generalised convexity leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar case, and avoids the major difficulty of verifying that the inequality holds for the same function η(. , .). Further, this relaxation allows one to treat certain nonlinear multi-objective fractional programming problems and some other classes of nonlinear (composite) problems as special cases.

A method for optimal design of automotive body assembly using multi-material construction

Stability of possibilistic multiobjective nonlinear programming problems without differentiability

Here, we propose a mathematical model to analyze the multi-objective bimatrix game under entropy environment. In this new approach, the entropy function of each player is considered as an objective to the multi-objective bimatrix game. This model is named as multi-objective entropy bimatrix game model. The formulated model is a multi-objective non-linear programming problem. To solve this model, we have introduced a solution procedure, which determines the feasibility of multi-objective non-linear programming problem using fuzzy programming approach and revised Genetic Algorithm (GA). By a real coded GA we have obtained the bounds of the objectives of the said model. Then we have determined the solutions of our proposed model. Finally, numerical examples are presented to illustrate the methodology.

In this paper, we propose a generalisation of convexity, namely higher order semilocally strong convexity for a nonlinear multiobjective programming problem, where the function involved are semidifferentiable. The generalised Karush-Kuhn-Tucker necessary and sufficient optimality conditions are derived. Moreover, a general Mond-Weir type dual problem is presented for nonlinear multiobjective programming problem involving higher order semilocally strong convexity and usual duality theorems are discussed.

Warner (1965) introduced the randomized response model as an alternative survey technique for socially undesirable or incriminating behaviour questions in order to reduce response error, protect a respondent’s privacy, and increase response rates. In multivariate stratified surveys with multiple randomised response data the choice of optimum sample sizes from various strata may be viewed as a multi-objective nonlinear programming problem. The allocation thus obtained may be called a “compromise allocation” in sampling literature.In this paper, we have formulated two stage stratified Warner’s Randomised Response model (RRM) as a multi-objective integer non-liner optimization problem. In this problem of RRM we have minimized the square root of coefficient of variations instead of variations for different characteristics because the coefficient of variation is unit free, subject to the linear and quadratic cost constraint. The multi-objective optimization problem of RRM has been solved by lexicographic goal programming integrated with fixed priority - distance method. The solution obtained by lexicographic goal programming Integrated with fixed priority - distance have been compared with various existing approaches namely the value function approach, goal programming techniques, - constraint method and distance-based method and Khuri & Cornel distance based method. A numerical example is also been presented to illustrate the computational details.https://doi.org/10.28919/jmcs/3376

Converting general nonlinear programming problems into separable programming problems with feedforward neural networks

A multi-objective discounted Markov decision process (MDP) with expectation and variance criteria is discussed. First, difficulties in variance minimization are discussed and it is shown that variance minimization is much more difficult than the expectation optimization. Then, the multi-objective MDP with expectation and variance criteria is formulated as a multi-objective non-linear programming problem. An algorithm for finding a stationary satisfactory Pareto policy is proposed by applying the satisficing trade-off method of Nakayama. In the proposed algorithm, a decision-maker need not have a high degree of judgment and it is easy to take the balance of expectation and variance criteria and furthermore, the number of auxiliary optimization problems to be solved is quite small. Numerical examples show the efficiency of the proposed algorithm.

<p>There exist several methods for solving fuzzy linear or nonlinear programming problems under positivity fuzzy variables and restricted fuzzy coefficients. Due to the limitation of these methods, they can’t be applied for solving fully fuzzy linear or non- linear programming problems with unrestricted fuzzy coefficients and fuzzy variables. In this paper an efficient method to find the fuzzy optimal solution for fully fuzzy quadratic programming (FFQP) problem with unrestricted variables and parameters has been proposed. All the coefficients and decision variables of both objective functions and the constraints are triangular fuzzy numbers. The proposed method is based on converted FFQP problem into crisp quadratic programming (CQP) problem. Finally an illustrative numerical example has been given to clarify the proposed solution method.</p>

Characterization of vector strict global minimizers of order 2 in differentiable vector optimization problems under a new approximation method