Fuzzy Programming Problems Research Articles

Multi-objective fuzzy probabilistic quadratic programming problem

The aim of the paper is to present a multi-choice multi-objective fuzzy probabilistic quadratic programming problem and its solution methodology. The mathematical programming problem suggested here is difficult to solve directly. Therefore, three major steps are suggested to solve the proposed mathematical programming problem. In first step, fuzzy chance constraint is transformed to its equivalent chance constraint programming problem using α-cut technique. Chance constraint technique is used to obtain a crisp multi-choice multi-objective quadratic programming problem. In the next step, importance is given to handle multi-choice parameter using least square approximation technique. At the end of second step, a multi-objective quadratic mathematical programming is obtained. Finally, goal programming approach is used to solve the transformed multi-objective quadratic mathematical programming. Using existing methodology and software, the final solution of the proposed model is obtained. The proposed method is implemented with a numerical example.

A joint maxmin-lexicographic maximisation approach in fuzzy goal programming using dominance possibility and necessity criteria

In this paper, a new approach for solving fuzzy goal programming problems is introduced. The coefficients and the aspiration level of each fuzzy goal are considered either trapezoidal or triangular fuzzy numbers. Four dominance criteria (dominance possibility, strict dominance possibility, dominance necessity, and strict dominance necessity) are utilised for comparing the fuzzy numbers. The proposed approach is based on merging the maxmin approach and the lexicographic approach in a two-phase process. The first phase applies the maxmin technique by maximising the minimum achievement degree of the fuzzy goals. The second phase lexicographically maximises the achievement degrees of the fuzzy goals according to their preemptive priorities. This methodology provides the decision maker with the advantage of improving the results of his preemptive priority structure model by initially maximising the lowest achievement of the fuzzy goals, and hence guarantee that the ultimate achievement of any fuzzy goal will never be lower than a specific percentage of the achieved maxmin value. The suggested approach is illustrated by a numerical example.

On differentiable harmonic univex fuzzy mappings and its applications to fuzzy mathematical programming problem

In this paper, harmonic preunivex (H-preunivex) and harmonic preunicave (H-preunicave) fuzzy mappings have been introduced and several interesting results have been obtained related to generalised convexity. By using the concept of differentiability with H-preunivex and H-preunicave fuzzy mappings, harmonic univex (H-univex) and harmonic unicave (Hunicave) fuzzy mappings have been obtained respectively. Furthermore, H-univex and pseudo H-univex fuzzy mappings have been applied to study the sufficient optimality conditions and the duality results for Harmonic univex fuzzy programming problem (HUFP). Moreover, KKT conditions for the HUFP have been studied by using the H-univex fuzzy mappings. Suitable examples have been given to illustrate the results.

On differentiable harmonic univex fuzzy mappings and its applications to fuzzy mathematical programming problem

In this paper, harmonic preunivex (H-preunivex) and harmonic preunicave (H-preunicave) fuzzy mappings have been introduced and several interesting results have been obtained related to generalised convexity. By using the concept of differentiability with H-preunivex and H-preunicave fuzzy mappings, harmonic univex (H-univex) and harmonic unicave (Hunicave) fuzzy mappings have been obtained respectively. Furthermore, H-univex and pseudo H-univex fuzzy mappings have been applied to study the sufficient optimality conditions and the duality results for Harmonic univex fuzzy programming problem (HUFP). Moreover, KKT conditions for the HUFP have been studied by using the H-univex fuzzy mappings. Suitable examples have been given to illustrate the results.

Forward and reverse flows pricing decisions for two competing supply chains with common collection centers in an intuitionistic fuzzy environment

This paper studies the selling and the acquisition price decisions for the products of two partially overlapping competing supply chains in an intuitionistic fuzzy environment. In the forward flows, the supply chains are assumed to produce substitutable products and sell them in a duopoly marketplace. The reverse flows are also concentrated on collecting and recycling the used products. While regularly it is assumed that the structures of the competing supply chains are completely separated, this paper assumes that the supply chains benefit from the services of the same collection centers. Considering the collection centers and the two supply chains to act as three integrated entities having enough bargaining powers to affect the decisions of each other, this paper concentrates on investigating the effects of different power structure scenarios on the optimal pricing decisions made by all of the parties involved in the problem. Another important feature of this study is that it employs the concept of intuitionistic fuzzy sets to integrate uncertainties and impressions inevitable in real-world situations into the decision-making process. To achieve this purpose, first, a new credibility-based definition for the concept of intuitionistic fuzzy variables is provided. This concept is then employed in the process of developing the intuitionistic fuzzy pricing models. A new expected value operator is also defined which is employed to transform the credibility-based intuitionistic fuzzy programming problems into their crisp equivalents. A numerical example is employed to discuss the properties of the introduced concepts, providing some interesting managerial implications regarding the defined problem.

A New Algorithm for Solving Fully Fuzzy Bi-Level Quadratic Programming Problems

A New Algorithm for Solving Fully Fuzzy Bi-Level Quadratic Programming Problems

An Efficient Algorithm for Solving Fuzzy Linear Programming Problems

In this article, we consider some well-known approaches for solving fuzzy linear programming (FLP) problems. We present some of the difficulties of these approaches. Then, crisp linear programming problems are suggested for solving FLP problems. A new algorithm is also given. The proposed approach has advantages over the other methods. For example, we can achieve higher membership degrees for objective function and constraints. Moreover, we show that the fuzzy optimal solutions obtained by the proposed approach are efficient enough. Also, we see that unlike the previous methods, our method finds efficient solutions by solving only one crisp linear problem instead of solving two or three crisp problems. Finally some numerical examples are presented to show the efficiency of the given approach over the other approaches.

On duality of fuzzy multiobjective optimisation problems: application to a multiplicative search technique

In this paper, we present a new study to minimise the expected value of the first meeting time between one of the searchers and the randomly moving target in the space (case of the multiplicative search technique) from a viewpoint of computational optimisation. We introduce the dual problem for the fuzzy multiobjective nonlinear programming problem (FMONLP) with inequality constraints which is obtained in El-Hadidy [International Journal of Computational Methods, Vol. 13, No. 6 (2016) 1650038 (38 pages)]. For this problem, we generalise the following classes of the vector-valued functions for fuzzy sets: weak strictly pseudo-quasi type I, strong pseudo-quasi type I, weak quasi strictly type I and weak strictly pseudo type I. We provide the fuzzy forms of Mond-Weir and general Mond-Weir duals for the involved problem and consequently various duality results are derived.

Multi-objective fuzzy quadratic probabilistic programming problem involving fuzzy Cauchy random variable

Multi-objective fuzzy quadratic probabilistic programming problem involving fuzzy Cauchy random variable

Multi-objective fuzzy quadratic probabilistic programming problem involving fuzzy Cauchy random variable

In this paper, we have proposed a method for solving a multi-objective quadratic probabilistic programming problem, where the objective functions are multi-objective and quadratic in nature. The right hand side parameters are fuzzy Cauchy distributed independent random variable with location parameter δ and scale parameter β. The proposed mathematical programming problem is solved using two steps. First, the fuzziness is removed by using alpha cut technique and randomness is removed by chance constrained method. In second step, weighting method is used to solve the transformed multi-objective quadratic mathematical programming. This mathematical model is solved by existing methodology or software. A numerical example is presented to illustrate the efficiency and feasibility of the proposed method.

An analytic method based on plane decomposition for solving two-stage fuzzy EV programming problem

An analytic method based on plane decomposition for solving two-stage fuzzy EV programming problem

Intuitionistic fuzzy multi-objective linear programming problem with various membership functions

This study addresses intuitionistic fuzzy multi-objective linear programming problems using triangular intuitionistic fuzzy numbers with mixed constraints. We convert the problem into single objective fuzzy programming problem. Then using different types of membership functions (linear and nonlinear), we transform the problem into crisp linear/non-linear programming problem, which is solved by suitable crisp programming approaches. The methodology is demonstrated with the help of a numerical example and the usefulness of various membership functions is discussed.

Fuzzy multi-objective optimization for optimum allocation in multivariate stratified sampling with quadratic cost and parabolic fuzzy numbers

ABSTRACTThis article deals with the uncertainties in a multivariate stratified sampling problem. The uncertain parameters of the problem, such as stratum standard deviations, measurement costs, travel costs and total budget of the survey, are considered as parabolic fuzzy numbers and the problem is formulated as a fuzzy multi-objective nonlinear programming problem with quadratic cost function. Using α-cut, parabolic fuzzy numbers are defuzzified and then the compromise allocations of the problem are obtained by fuzzy programming for a prescribed value of α. To demonstrate the utility of the proposed problem a numerical example is solved with the help of [LINGO User?s Guid. Lindo Systems Inc., 1415 North Dayton Street, Chicago,Illinois-60622, (USA), 2013] software and the derived compromise optimum allocation is compared with deterministic and proportional allocations.

English

English

A modified approach for solving a fuzzy multi-objective programming problem

Based on ranking of fuzzy numbers which deals with fuzzy-valued multi-objective programming problem and the modified crisp model, a modified approach is proposed. Also, two algorithms that play a pivotal role in the proposed method are introduced. The first one returns a ranking function to a given fuzzy number and the second algorithm uses the modified crisp model to deliver a Pareto optimal solution. Moreover, we investigate the stability of the first kind of the solution which is obtained using these algorithms. Finally, a numerical example is given to illustrate our modified approach, using Maple program.

A method to solve separable fuzzy nonlinear programming problem

This paper formulates piecewise fuzzy linear approximation of fuzzy nonlinear function of a single variable. First, we construct the equation of fuzzy line segment through two fuzzy points using -cuts of two fuzzy points. Now the fuzzy nonlinear function is represented by a set of connected fuzzy line segments. Fuzzy line segments have been defined by partitioning the domain of a fuzzy nonlinear function. Then formulation of approximating fuzzy linear programming problem has been given to find the solution of fuzzy nonlinear separable programming problem. An illustrative example is given to demonstrate the methodology.

A method to solve separable fuzzy nonlinear programming problem

A method to solve separable fuzzy nonlinear programming problem

Genetic algorithm approach for solving multi-objective fuzzy stochastic programming problem

This paper is concerned with the solution procedure of a multi-objective fuzzy stochastic optimisation problem by simulation-based genetic algorithm. In this article, a multi-objective fuzzy chance constrained programming problem is considered with continuous fuzzy random variables. The uncertain parameters are considered as fuzzy normal and fuzzy log-normal random variables. The feasibilities of the fuzzy chance constraints are checked by the fuzzy stochastic programming with the genetic process without deriving the deterministic equivalents. The proposed procedure is illustrated by a numerical example.

An Improvement for Fuzzy Stochastic Goal Programming Problems

We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.

Expected Solving Model of Constrained Particle Swarm Optimization in Fuzzy Programming Problem

Expected Solving Model of Constrained Particle Swarm Optimization in Fuzzy Programming Problem