Fuzzy Multi-objective Programming Problem Research Articles

A fuzzy multi-objective programming model for the delivery and distribution of humanitarian relief materials

Disaster relief presents many unique logistics challenges, including damaged transportation infrastructure, multiple conflicting goals, and secondary disasters caused by spontaneous disaster relief. The delivery and distribution of humanitarian relief materials faced by nonprofit organizations (NPOs) poses a critical challenge due to the highly unpredictable nature of disasters, conflicting missions, and the need to navigate government regulations in disaster management. In this paper, we propose a novel multi-objective disaster relief modeling system for NPOs, considering (1) prioritization (providing medical services to seriously injured victims), (2) effectiveness (degree of satisfaction), (3) efficiency (operational costs), and (4) equity (cost of maintaining order). To incorporate the practical constraints of disaster relief operations, we include factors such as road damage, transportation capacity limitations, and route flow saturation as part of the model formulation. We then utilize fuzzy multi-objective programming to optimize the proposed disaster relief model, considering two relief distribution schemes: a common NPOs' spontaneous relief scheme and a newly designed traffic control scheme with government regulation. Based on the real-world scenario of the 2008 Wenchuan earthquake, we demonstrate that the designed traffic control scheme exhibited remarkable improvement among the NPOs' four objectives compared to the spontaneous relief scheme. Moreover, in the process of solving fuzzy multi-objective programming problems, artificial intelligence technology is employed to handle the fuzziness in multi-objective and automatically adjust parameters, making the solution results better and in line with practical situations. And we also validate the proposed model can be solved in polynomial time, meeting the engineering practice requirements, and can be easily extend to most disaster relief distribution scenarios.

Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems

The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp . Some basic notions in the problem under the pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is presented for obtaining a subset of the parametric space that has the same pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

Multi-Objective Non-Linear Programming Problems in Linear Diophantine Fuzzy Environment

Due to various unpredictable factors, a decision maker frequently experiences uncertainty and hesitation when dealing with real-world practical optimization problems. At times, it’s necessary to simultaneously optimize a number of non-linear and competing objectives. Linear Diophantine fuzzy numbers are used to address the uncertain parameters that arise in these circumstances. The objective of this manuscript is to present a method for solving a linear Diophantine fuzzy multi-objective nonlinear programming problem (LDFMONLPP). All the coefficients of the nonlinear multi-objective functions and the constraints are linear Diophantine fuzzy numbers (LDFNs). Here we find the solution of the nonlinear programming problem by using Karush-Kuhn-Tucker condition. A numerical example is presented.

Fuzzy goal programming approach to solve fully fuzzy multi-objective quadratic programming problem

Fuzzy goal programming approach to solve fully fuzzy multi-objective quadratic programming problem

A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets

In this paper, we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions.

Approaches for Solving Fully Fuzzy Rough Multi-Objective Nonlinear Programming Problems

Practical nonlinear programming problem often encounters uncertainty and indecision due to various factors that cannot be controlled. To overcome these limitations, fully fuzzy rough approaches are applied to such a problem. In this paper, an effective two approaches are proposed to solve fully fuzzy rough multi-objective nonlinear programming problems (FFRMONLP) where all the variables and parameters are fuzzy rough triangular numbers. The first, based on a slice sum technique, a fully fuzzy rough multi-objective nonlinear problem has turned into five equivalent multi-objective nonlinear programming (FFMONLP) problems. The second proposed method for solving FFRMONLP problems is α-cut approach, where the triangular fuzzy rough variables and parameters of the FFRMONLP problem are converted into rough interval variables and parameters by α-level cut, moreover the rough MONLP problem turns into four MONLP problems. Furthermore, the weighted sum method is used in both proposed approaches to convert multi-objective nonlinear problems into an equivalent nonlinear programming problem. Finally, the effectiveness of the proposed procedure is demonstrated by numerical examples.

Some Approaches for Fuzzy Multiobjective Programming Problems

In this paper we discuss two approaches to bring a balance between effectiveness and efficiency while solving a multiobjective programming problem with fuzzy objective functions. To convert the original fuzzy optimization problem into deterministic terms, the first approach makes use of the Nearest Interval Approximation Operator (Approximation approach) for fuzzy numbers and the second one takes advantage of an Embedding Theorem for fuzzy numbers (Equivalence approach). The resulting optimization problem related to the first approach is handled via Karush- Kuhn-Tucker like conditions for Pareto Optimality obtained for the resulting interval optimization problem. A Galerkin like scheme is used to tackle the deterministic counterpart associated to the second approach. Our approaches enable both faithful representation of reality and computational tractability. They are thus in sharp contrast with many existing methods that are either effective or efficient but not both. Numerical examples are also supplemented for the sake of illustration.

On optimistic, pessimistic and mixed approaches under different membership functions for fully intuitionistic fuzzy multiobjective nonlinear programming problems

The concept of measuring the membership degree along with a non-membership degree, gives rise to the intuitionistic fuzzy set theory. The present study formulates a nonlinear programming problem with multiple objectives, including all the parameters and decision variables as intuitionistic fuzzy numbers. The problem is further investigated subject to optimistic, pessimistic and mixed approaches under linear, exponential and hyperbolic membership functions. The article redefines pessimistic and mixed point of view to be in the true spirit compatible with the definition of an intuitionistic fuzzy number. Accuracy function is used to reduce the problem to an equivalent crisp multiobjective nonlinear programming problem and then optimal compromise solution is obtained under different approaches using various membership/non-membership functions. At appropriate places, theorems have also been proved to establish the equivalence between the original formulation and its crisp counterparts under each approach. Further, practical applications in production planning and transportation problem are illustrated to explain the optimistic, pessimistic and mixed approaches using the proposed algorithm and finally a comparison is also drawn.

A Bibliography Survey on Fuzzy Multi Objective Programming Problems

This paper presents Bibliography of Research Papers/Books/Articles on the applications of Operations Research related to Fuzzy Multi Objective Programming Problems between 2000 -2010. In this paper we represent the Fuzzy problems as a four major categories. We analyze the operations research applications to Fuzzy multi objective in different ways. We summarize the significant trends in this field and we identified areas that need to be addressed in the future. This paper covers 95 articles between 2000 –2010.

Multi objective programming problem in the hesitant fuzzy environment

In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the evaluation information provided by the decision makers is expressed in a hesitant fuzzy environment. For this purpose a new solution concept, namely hesitant fuzzy Pareto optimal solution to the problem is introduced, and two methods are proposed to obtain it. Then it is shown that the optimal solutions of these methods are the hesitant fuzzy Pareto optimal solutions. Finally, these methods are implemented on some illustrative examples and comparative analysis of our methodology is taken with other extensions of fuzzy sets.

Fuzzy multi-objective programming problem for revenue management in food industry

Food industry is one of the fastest growing industry. With the development of varieties in this industry, the need for revenue management is vital. Revenue management is a technique to optimize the income by selling the right product to right customer at right time which is done by using data driven tactics and strategies. In this paper, a revenue management problem is formulated as multi-objective programming problem in an uncertain environment. As in real life situations most of the parameters are generally uncertain, therefore cost parameter considered as triangular fuzzy numbers. Fuzzy problem is converted into deterministic problem by alpha-cut method and then the algorithm is developed to solve the multi-objective linear programming problem to optimize revenue as well as cost simultaneously. To demonstrate and justify the formulated problem a numerical illustration has been considered and solved. All the mathematical problems are solved through an optimisation software LINGO-13.

A modified fuzzy approach for the fully fuzzy multi-objective and multi-level integer quadratic programming problems based on a decomposition technique

A modified fuzzy approach for the fully fuzzy multi-objective and multi-level integer quadratic programming problems based on a decomposition technique

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.

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.

Solving intuitionistic fuzzy multi-objective nonlinear programming problem

This paper presents intuitionistic fuzzy multi-objective nonlinear programming problem (IFMONLPP). All the coefficients of the multi-objective nonlinear programming problem (MONLPP) and the constraints are taken to be intuitionistic fuzzy numbers (IFN). The IFMONLPP has been transformed into crisp one and solved by using Kuhn-Tucker condition. Numerical example is provided to illustrate the approach.

Some new solution concepts in generalized fuzzy multiobjective optimization problems

Some new solution concepts to a general fuzzy multiobjective nonlinear programming problem are introduced in this research, and four scalarization techniques are proposed to obtain them. Then, the relation between the set of defined optimal solutions and the set of optimal solutions of the scalarized problems are studied. Moreover, a general scalarized problem is given and shown that these four techniques can be drawn from this problem. Adequate number of numerical examples have been solved to illustrate the techniques.

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.

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.

Solution of Fuzzy Multi-objective Nonlinear Programming Problem Using Fuzzy Programming Techniques Based on Hyperbolic Membership Functions

The main objective of this paper is three folds: (i) introduction of hyperbolic membership function in Zimmerman’s fuzzy programming technique to handle multi-objective nonlinear programming problems (ii) reduction of fuzzy multi objective nonlinear programming problem to crisp one using ranking function (iii) reduction of complexity of nonlinear problem occurring in course of application of Zimmerman’s technique by the process of linearization.

Multi-objective fuzzy mathematical modelling of closed-loop supply chain considering economical and environmental factors

The growing concern for sustainability has forced the researchers and managers to incorporate the environmental and social factors along with the economical factors in the design of supply chains. This paper presents the design and optimization of a multi-objective closed-loop supply chain considering the economical and environmental factors with uncertainty in parameters. The proposed network is modeled as fuzzy multi-objective mixed integer linear programming problem considering multi-customer zones, multi-collection centers, multi-disassembly centers, multi-refurbishing centers, multi-external suppliers, and different product recovery processes; to take care for purchasing cost, transportation cost, processing cost, set-up cost, and capacity constraints simultaneously. The model is solved using an interactive $$\upvarepsilon $$ -constraint method. A case example is solved using LINGO 14.0 to demonstrate the significance and applicability of the developed fuzzy optimization model for closed-loop supply chain.