Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy Parameters: A FGP Approach

The motivation behind this paper is to present multi-level multi-objective quadratic fractional programming (ML-MOQFP) problem with fuzzy parameters in the constraints. ML-MOQFP problem is an important class of non-linear fractional programming problem. These type of problems arise in many fields such as production planning, financial and corporative planning, health care and hospital planning. Firstly, the concept of the -cut and fuzzy partial order relation are applied to transform the set of fuzzy constraints into a common crisp set. Then, the quadratic fractional objective functions in each level are transformed into non-linear objective functions based on a proposed transformation. Secondly, in the proposed model, separate non-linear membership functions for each objective function of the ML-MOQFP problem are defined. Then, the fuzzy goal programming (FGP) approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach

Fuzzy Linear Programming in DSS for Energy System Planning

Energy system planning requires the use of planning tools. The mathematical models of real-world energy systems are usually multiperiod linear optimization programs. In these models, the objective function describes the total discounted costs of covering the demand for final energy or energy services. The demand for various forms of energy or energy services is the driving force of the models. By using such linear programming (LP) formulations, decision makers can elaborate suitable strategies for solving their planning problems, such as the development of emission reduction strategies. Uncertainties that affect the process of energy system planning can be divided into parameter and decision uncertainties. Data or parameter uncertainties can be addressed either by stochastic optimization or by the methodology of fuzzy linear programming (FLP). In addition, FLP allows explicit incorporation of decision uncertainties into a mathematical model. This paper therefore aims at evaluating the methodology of FLP with respect to the support that it offers the decision-making process in energy system planning under uncertainty. Employing the parallels between multi-objective linear programming (MOLP) and FLP, problems of FLP in decision support system applications are pointed out and solutions are offered. The proposed modifications are based on the methodology of aspiration-reservation based decision support and still enable modeling of uncertainties in a fuzzy sense. A case study is documented to show the application of the modified FLP approach

Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships

A Spatial Fuzzy Compromise Approach for Flood Disaster Management

Natural disasters affect regions with different intensity and produce damages that vary in space. Topographical features of the region; location of properties that may be exposed to the peril; level of exposure; impact of different mitigation measures; are all variables with considerable spatial variability. A new method for evaluation of disaster impacts has been presented in this report that takes into consideration spatial variability of variables involved and associated uncertainty. Flood management has been used to illustrate the utility of proposed approach. Floodplain management is a spatial problem. Representation of flood damage mitigation alternatives and objectives in space provides a better insight into the management problem and its characteristics. Protection of a region from floods can be achieved through various structural and non-structural measures. Comparison of different measures and evaluation of their impacts is based on the multiple criteria. If they are described spatially, decision-making problem can be conceptualized as spatial multi criteria decision-making (MCDM). Tkach and Simonovic (1997) introduced spatial Compromise Programming (SPC) technique to account for spatial variability in flood management. Some of the criteria and preferences of the stakeholders involved with flood management are subject to uncertainty that may originate in the data, knowledge of the domain or our ability to adequately describe the decision problem. The main characteristic of flood management is the existence of objective and subjective uncertainty. Fuzzy set theory has been successfully used to address both, objective and subjective uncertainty. Bender and Simonovic (2000) incorporated vagueness and imprecision as sources of uncertainty into multi criteria decision-making in water resources. In this report a new technique named Spatial Fuzzy Compromise Programming (SFCP) has been developed to enhance our ability to address the issues related to uncertainties in spatial environment. A general fuzzy compromise programming technique, when made 2 spatially distributed, proved to be a powerful and flexible addition to the list of techniques available for decision making where multiple criteria are used to judge multiple alternatives. All uncertain variables (subjective and objective) are modeled by way of fuzzy sets. In the present study, fuzzy measures have been introduced to spatial multi criteria decision-making in the GIS environment in order to account for uncertainties. Through a case study of the Red River floodplain near the City of St. Adolphe in Manitoba, Canada, it has been illustrated that the new technique provides measurable improvement in flood management. Final results in the form of maps that shown spatial distribution of the impacts of mitigation measures on the region can be of great value to insurance industry.https://ir.lib.uwo.ca/wrrr/1004/thumbnail.jp

Imprecise WareHouse Space in Aggregate Production Planning Using Fuzzy Goal Programming

Considering the fluctuating market demands with variable storage capacity and available production capacity, this study examines a number of workable techniques for modeling multiproduct aggregate production planning problems with fuzzy numbers. The suggested method makes use of factors including; inventory levels, labor levels, overtime, backordering levels, workforce capacity, machine capacity, and fuzzy warehouse capacity in an effort to reduce operating costs, reduce production waste, and increase capacity utilization rate. With the aid of this formulation and interpretation, a fuzzy multiproduct aggregate production planning model is developed. Finally, the study's conclusions were arrived at using information provided by Rich Pharmaceuticals Ltd. using Lingo version 18 software (RPL).and it uses parametric programming, best balancing, and interactive techniques to give solutions that can be adjusted to fit a variety of decision-making circumstances

A similarity-based cooperative co-evolutionary algorithm for dynamic interval multi-objective optimization problems

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.Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances

An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights

This article proposes an approach to multiattribute decision making with incomplete attribute weight information where individual assessments are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). By employing a series of optimization models, the proposed approach derives a linear program for determining attribute weights. The weights are subsequently used to synthesize individual IVIFN assessments into an aggregated IVIFN value for each alternative. In order to rank alternatives based on their aggregated IVIFN values, a novel method is developed for comparing two IVIFNs by introducing two new functions: the membership uncertainty index and the hesitation uncertainty index. An illustrative investment decision problem is employed to demonstrate how to apply the proposed procedure and comparative studies are conducted to show its overall consistency with existing approaches

Fuzzy uncertainty modelling for project planning; application to helicopter maintenance

Maintenance is an activity of growing interest specially for critical systems. Particularly, aircraft maintenance costs are becoming an important issue in the aeronautical industry. Managing an aircraft maintenance center is a complex activity. One of the difficulties comes from the numerous uncertainties that affect the activity and disturb the plans at short and medium term. Based on a helicopter maintenance planning and scheduling problem, we study in this paper the integration of uncertainties into tactical and operational multiresource, multi-project planning (respectively Rough Cut Capacity Planning and Resource Constraint Project Scheduling Problem). Our main contributions are in modelling the periodic workload on tactical level considering uncertainties in macro-tasks work contents, and modelling the continuous workload on operational level considering uncertainties in tasks durations. We model uncertainties by a fuzzy/possibilistic approach instead of a stochastic approach since very limited data are available. We refer to the problems as the Fuzzy RoughCut Capacity Problem (FRCCP) and the Fuzzy Resource Constraint Project Scheduling Problem (RCPSP).We apply our models to helicopter maintenance activity within the frame of the Helimaintenance project, an industrial project approved by the French Aerospace Valley cluster which aims at building a center for civil helicopter maintenance

Evaluating strategies for implementing industry 4.0: a hybrid expert oriented approach of B.W.M. and interval valued intuitionistic fuzzy T.O.D.I.M.

open access articleDeveloping and accepting industry 4.0 influences the industry structure and customer willingness. To a successful transition to industry 4.0, implementation strategies should be selected with a systematic and comprehensive view to responding to the changes flexibly. This research aims to identify and prioritise the strategies for implementing industry 4.0. For this purpose, at first, evaluation attributes of strategies and also strategies to put industry 4.0 in practice are recognised. Then, the attributes are weighted to the experts’ opinion by using the Best Worst Method (BWM). Subsequently, the strategies for implementing industry 4.0 in Fara-Sanat Company, as a case study, have been ranked based on the Interval Valued Intuitionistic Fuzzy (IVIF) of the TODIM method. The results indicated that the attributes of ‘Technology’, ‘Quality’, and ‘Operation’ have respectively the highest importance. Furthermore, the strategies for “new business models development’, ‘Improving information systems’ and ‘Human resource management’ received a higher rank. Eventually, some research and executive recommendations are provided. Having strategies for implementing industry 4.0 is a very important solution. Accordingly, multi-criteria decision-making (MCDM) methods are a useful tool for adopting and selecting appropriate strategies. In this research, a novel and hybrid combination of BWM-TODIM is presented under IVIF information