Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analysis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers

The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method) is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems

Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

Weighted Constraints in Fuzzy Optimization

Many practical optimization problems are characterized by someflexibility in the problem constraints, where this flexibility canbe exploited for additional trade-off between improving theobjective function and satisfying the constraints. Especially indecision making, this type of flexibility could lead to workablesolutions, where the goals and the constraints specified bydifferent parties involved in the decision making are traded offagainst one another and satisfied to various degrees. Fuzzy setshave proven to be a suitable representation for modeling this typeof soft constraints. Conventionally, the fuzzy optimizationproblem in such a setting is defined as the simultaneoussatisfaction of the constraints and the goals. No additionaldistinction is assumed to exist amongst the constraints and thegoals. This report proposes an extension of this model forsatisfying the problem constraints and the goals, where preferencefor different constraints and goals can be specified by thedecision-maker. The difference in the preference for theconstraints is represented by a set of associated weight factors,which influence the nature of trade-off between improving theoptimization objectives and satisfying various constraints.Simultaneous weighted satisfaction of various criteria is modeledby using the recently proposed weighted extensions of(Archimedean) fuzzy t-norms. The weighted satisfaction of theproblem constraints and goals are demonstrated by using a simplefuzzy linear programming problem. The framework, however, is moregeneral, and it can also be applied to fuzzy mathematicalprogramming problems and multi-objective fuzzy optimization.wiskundige programmering;fuzzy sets;optimalisatie

Optimal Solution of a Fully Fuzzy Linear Fractional Programming Problem by Using Graded Mean Integration Representation Method

In the present paper, the study of fully fuzzy linear fractional programming problem (FFLFPP) using graded mean integration representation method is discussed where all the parameters and variables are characterized by trapezoidal fuzzy numbers. A computational algorithm has been presented to obtain an optimal solution by applying simplex method. To demonstrate the applicability of the proposed approach, one numerical example is solved. Also to check the efficiency and feasibility of the proposed approach, we compare the results of examples by applying crisp numbers, triangular fuzzy numbers and trapezoidal fuzzy numbers

Applying nonlinear MODM model to supply chain management with quantity discount policy under complex fuzzy environment

Purpose: The aim of this paper is to deal with the supply chain management (SCM) with quantity discount policy under the complex fuzzy environment, which is characterized as the bi-fuzzy variables. By taking into account the strategy and the process of decision making, a bi-fuzzy nonlinear multiple objective decision making (MODM) model is presented to solve the proposed problem. Design/methodology/approach: The bi-fuzzy variables in the MODM model are transformed into the trapezoidal fuzzy variables by the DMs's degree of optimism ?1 and ?2, which are de-fuzzified by the expected value index subsequently. For solving the complex nonlinear model, a multi-objective adaptive particle swarm optimization algorithm (MO-APSO) is designed as the solution method. Findings: The proposed model and algorithm are applied to a typical example of SCM problem to illustrate the effectiveness. Based on the sensitivity analysis of the results, the bi-fuzzy nonlinear MODM SCM model is proved to be sensitive to the possibility level ?1. Practical implications: The study focuses on the SCM under complex fuzzy environment in SCM, which has a great practical significance. Therefore, the bi-fuzzy MODM model and MO-APSO can be further applied in SCM problem with quantity discount policy. Originality/value: The bi-fuzzy variable is employed in the nonlinear MODM model of SCM to characterize the hybrid uncertain environment, and this work is original. In addition, the hybrid crisp approach is proposed to transferred to model to an equivalent crisp one by the DMs's degree of optimism and the expected value index. Since the MODM model consider the bi-fuzzy environment and quantity discount policy, so this paper has a great practical significance.Peer Reviewe

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 novel framework for predicting patients at risk of readmission

Uncertainty in decision-making for patients’ risk of re-admission arises due to non-uniform data and lack of knowledge in health system variables. The knowledge of the impact of risk factors will provide clinicians better decision-making and in reducing the number of patients admitted to the hospital. Traditional approaches are not capable to account for the uncertain nature of risk of hospital re-admissions. More problems arise due to large amount of uncertain information. Patients can be at high, medium or low risk of re-admission, and these strata have ill-defined boundaries. We believe that our model that adapts fuzzy regression method will start a novel approach to handle uncertain data, uncertain relationships between health system variables and the risk of re-admission. Because of nature of ill-defined boundaries of risk bands, this approach does allow the clinicians to target individuals at boundaries. Targeting individuals at boundaries and providing them proper care may provide some ability to move patients from high risk to low risk band. In developing this algorithm, we aimed to help potential users to assess the patients for various risk score thresholds and avoid readmission of high risk patients with proper interventions. A model for predicting patients at high risk of re-admission will enable interventions to be targeted before costs have been incurred and health status have deteriorated. A risk score cut off level would flag patients and result in net savings where intervention costs are much higher per patient. Preventing hospital re-admissions is important for patients, and our algorithm may also impact hospital income

A fuzzy multi-criteria decision making approach for managing performance and risk in integrated procurement-production planning

Nowadays in Supply Chain (SC) networks, a high level of risk comes from SC partners. An effective risk management process becomes as a consequence mandatory, especially at the tactical planning level. The aim of this article is to present a risk-oriented integrated procurement–production approach for tactical planning in a multi-echelon SC network involving multiple suppliers, multiple parallel manufacturing plants, multiple subcontractors and several customers. An originality of the work is to combine an analytical model allowing to build feasible scenarios and a multi-criteria approach for assessing these scenarios. The literature has mainly addressed the problem through cost or profit-based optimisation and seldom considers more qualitative yet important criteria linked to risk, like trust in the supplier, flexibility or resilience. Unlike the traditional approaches, we present a method evaluating each possible supply scenario through performance-based and risk-based decision criteria, involving both qualitative and quantitative factors, in order to clearly separate the performance of a scenario and the risk taken if it is adopted. Since the decision-maker often cannot provide crisp values for some critical data, fuzzy sets theory is suggested in order to model vague information based on subjective expertise. Fuzzy Technique for Order of Preference by Similarity to Ideal Solution is used to determine both the performance and risk measures correlated to each possible tactical plan. The applicability and tractability of the proposed approach is shown on an illustrative example and a sensitivity analysis is performed to investigate the influence of criteria weights on the selection of the procurement–production plan

A fuzzy multi-criteria decision making approach for managing performance and risk in integrated procurement-production planning

Nowadays in Supply Chain (SC) networks, a high level of risk comes from SC partners. An effective risk management process becomes as a consequence mandatory, especially at the tactical planning level. The aim of this article is to present a risk-oriented integrated procurement–production approach for tactical planning in a multi-echelon SC network involving multiple suppliers, multiple parallel manufacturing plants, multiple subcontractors and several customers. An originality of the work is to combine an analytical model allowing to build feasible scenarios and a multi-criteria approach for assessing these scenarios. The literature has mainly addressed the problem through cost or profit-based optimisation and seldom considers more qualitative yet important criteria linked to risk, like trust in the supplier, flexibility or resilience. Unlike the traditional approaches, we present a method evaluating each possible supply scenario through performance-based and risk-based decision criteria, involving both qualitative and quantitative factors, in order to clearly separate the performance of a scenario and the risk taken if it is adopted. Since the decision-maker often cannot provide crisp values for some critical data, fuzzy sets theory is suggested in order to model vague information based on subjective expertise. Fuzzy Technique for Order of Preference by Similarity to Ideal Solution is used to determine both the performance and risk measures correlated to each possible tactical plan. The applicability and tractability of the proposed approach is shown on an illustrative example and a sensitivity analysis is performed to investigate the influence of criteria weights on the selection of the procurement–production plan