A fuzzy MCDM approach for stock selection

A fuzzy MCDM approach is applied to the stock selection problem, where the proposed approach can deal with qualitative information in addition to quantitative information. A hierarchy of major–sub criteria is then established to reduce the dependence between criteria. The ratings of alternatives versus qualitative sub-criteria and the weights of major- and sub-criteria are assessed in linguistic terms represented by fuzzy numbers. Each sub-criterion is in a benefit, cost, or balanced nature. New standardization methods for fuzzy numbers in the cost and balanced nature are presented. The algorithms of membership functions of the final aggregation are completely developed instead of approximation. The final aggregations in fuzzy numbers are then defuzzified to crisp values in order to rank the performance of alternatives. Moreover, the ratio of market price to performance (PP) is suggested to filter the over/under-pricing of alternatives. A set of buying/selling strategies are recommended according to the performance and PP. An empirical example then demonstrates the processing of the proposed approach.     

Optimal selection of a landfill disposal site using a modified fuzzy utility approach

The present paper develops an integrated fuzzy based model to select an optimal landfill site among the given alternative sites by using the concept of fuzzyutility method and multi-nomial logit theory. The suitability of different landfill sites are evaluated based on some important criteria involved in the process such as accessibility and transportation; environmental, geological and climatic conditions; socioeconomic conditions; land use pattern; and safety at the selected site. These criteria are assessed qualitatively by the decision makers based on their relative degree of importance. The importance weights and ratings of each criterion have been defined in the form of triplets of triangular fuzzy numbers by taking opinion of the decision makers. The corresponding triplets of ratings of each site are used to derive the utility value of the alternative sites. A multi-nomial logit model has been applied to calculate the probability of selection of each alternative site which can help policy makers to take appropriate decisions. Finally, the proposed methodology has been applied to allocate suitable landfill sites for disposing off municipal solid waste for Pilani town which is located in Jhunjhunu district of Rajasthan. The results evaluated by the modified fuzzy utility are also compared to the outputs of a direct method which is basically based on certain linguistic aggregation operators for group decision making. Computational results clearly demonstrate that the results obtained by the proposed method are coinciding very well and prepares a basis to adopt an overall strategy for selecting appropriate landfill site for proper solid waste disposal and its management.     

A QFD-based fuzzy MCDM approach for supplier selection

Supplier selection is a highly important multi-criteria group decision making problem, which requires a trade-off between multiple criteria exhibiting vagueness and imprecision with the involvement of a group of experts. In this paper, a fuzzy multi-criteria group decision making approach that makes use of the quality function deployment (QFD) concept is developed for supplier selection process. The proposed methodology initially identifies the features that the purchased product should possess in order to satisfy the company’s needs, and then it seeks to establish the relevant supplier assessment criteria. Moreover, the proposed algorithm enables to consider the impacts of inner dependence among supplier assessment criteria. The upper and the lower bounds of the weights of supplier assessment criteria and ratings of suppliers are computed by using the fuzzy weighted average (FWA) method. The FWA method allows for the fusion of imprecise and subjective information expressed as linguistic variables or fuzzy numbers. The method produces less imprecise and more realistic overall desirability levels, and thus it rectifies the problem of loss of information. A fuzzy number ranking method that is based on area measurement is used to obtain the final ranking of suppliers. The computational procedure of the proposed framework is illustrated through a supplier selection problem reported in an earlier study.     

An intuitionistic fuzzy projection-based approach for partner selection

The partner selection is an important decision problem in the formation of a new virtual enterprise. Using the projection technique, this study introduces an approach to partner selection with linguistic values and intuitionistic fuzzy information under a group decision-making environment. To avoid information loss, there is no aggregations of decision information in this model except ideal decisions as auxiliary decision tools. Comparisons of the suggested methodology with other methods are also made. A numerical example and an experimental analysis are proposed to illustrate the application of the proposed model.     

Order selection and pricing methods using flexible quantity and fuzzy approach for buyer evaluation

This paper presents the methods for order selection and pricing of manufacturer (supplier) with make-to-order basis when orders exceed production capacity. By quoting the concepts of triangular fuzzy numbers and linguistic variables, a fuzzy approach to evaluating buyers by taking into account both positive and negative criteria is proposed. According to the classified results of buyers, the orders will be produced with priority, declined, or determined by MIP model. The fixed quantity MIP model and flexible quantity MIP model are employed to determine the produced orders along with the production quantity and the reference amount for price reduction. By applying the concept of TOPSIS, the closeness coefficients for satisfaction grades of orders and for ranking values of buyers are used as the adjusting rates in the final pricing MIP model to set segmented price.     

A portfolio selection model using fuzzy returns

We study a static portfolio selection problem, in which future returns of securities are given as fuzzy sets. In contrast to traditional analysis, we assume that investment decisions are not based on statistical expectation values, but rather on maximal and minimal potential returns resulting from the so-called α-cuts of these fuzzy sets. By aggregating over all α-cuts and assigning weights for both best and worst possible cases we get a new objective function to derive an optimal portfolio. Allowing for short sales and modelling α-cuts in ellipsoidal shape, we obtain the optimal portfolio as the unique solution of a simple optimization problem. Since our model does not include any stochastic assumptions, we present a procedure, which turns the data of observable returns as well as experts’ expectations into fuzzy sets in order to quantify the potential future returns and the investment risk.     

Product design and selection using fuzzy QFD and fuzzy MCDM approaches

Quality function deployment (QFD) is a useful analyzing tool in product design and development. To solve the uncertainty or imprecision in QFD, numerous researchers have applied the fuzzy set theory to QFD and developed various fuzzy QFD models. Three issues are investigated by examining their models. First, the extant studies focused on identifying important engineering characteristics and seldom explored the subsequent prototype product selection issue. Secondly, the previous studies usually use fuzzy number algebraic operations to calculate the fuzzy sets in QFD. This approach may cause a great deviation in the result from the correct value. Thirdly, few studies have paid attention to the competitive analysis in QFD. However, it can provide product developers with a large amount of valuable information. Aimed at these three issues, this study integrates fuzzy QFD and the prototype product selection model to develop a product design and selection (PDS) approach. In fuzzy QFD, the α-cut operation is adopted to calculate the fuzzy set of each component. Competitive analysis and the correlations among engineering characteristics are also considered. In prototype product selection, engineering characteristics and the factors involved in product development are considered. A fuzzy multi-criteria decision making (MCDM) approach is proposed to select the best prototype product. A case study is given to illustrate the research steps for the proposed PDS method. The proposed method provides product developers with more useful information and precise analysis results. Thus, the PDS method can serve as a helpful decision-aid tool in product design.     

An interactive fuzzy goal programming approach for multi-period multi-product production planning problem

This study addresses an interactive multiple fuzzy goal programming (FGP) approach to the multi-period multi-product (MPMP) production planning problem in an imprecise environment. The proposed model attempts to simultaneously minimize total production costs, rates of changes in labor levels, and maximizing machine utilization, while considering individual production routes of parts, inventory levels, labor levels, machine capacity, warehouse space, and the time value of money. Piecewise linear membership functions are utilized to represent decision maker’s (DM’s) overall satisfaction levels. A numerical example demonstrates the feasibility of applying the proposed model to the MPMP problem. Furthermore, the proposed interactive approach facilitates the DM with a systematic framework of decision making process which enables DM to modify the search direction to reach the most satisfactory results during solving process.     

A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

A health status index model using a fuzzy approach

In order to derive an operational health status index, it is necessary to develop the concept of health status. An individual belongs to one of several alternative health statuses, but it is difficult to clearly identify which, because the boundaries of statuses are not sharply defined. In this paper a fuzzy approach is proposed for use in expressing the health status and its index. We deal with health status as an intrinsically ambiguous and multi-dimensional expression which is determined through some subjective judgement. We introduce the concept of fuzziness and fuzzy set in order to study the ambiguous health status. Some concepts and properties of group fuzzy measures are clarified so that we may obtain the common measure to express the health statuses. Two examples using the researched data are presented for explaining the concept of health status, the group fuzzy measures and the health status index model.     

Aggregating multiple classification results using fuzzy integration and stochastic feature selection

Classifying magnetic resonance spectra is often difficult due to the curse of dimensionality; scenarios in which a high-dimensional feature space is coupled with a small sample size. We present an aggregation strategy that combines predicted disease states from multiple classifiers using several fuzzy integration variants. Rather than using all input features for each classifier, these multiple classifiers are presented with different, randomly selected, subsets of the spectral features. Results from a set of detailed experiments using this strategy are carefully compared against classification performance benchmarks. We empirically demonstrate that the aggregated predictions are consistently superior to the corresponding prediction from the best individual classifier.     

A combined approach for fuzzy multi-objective multiple knapsack problems for defence project selection

In this study, a model representing military requirements as scenarios and capabilities is offered. Pair-wise comparisons of scenarios are made according to occurrence probabilities by using the Analytical Hierarchy Process (AHP). The weights calculated from AHP are used as the starting weights in a Quality Function Deployment (QFD) matrix. QFD is used to transfer war fighter requirements into the benefit values of projects. Two levels of QFD matrices are used to evaluate new capability areas versus capabilities and capabilities versus projects. The benefit values of the projects are used in a multi-objective problem (multi-objective multiple knapsack problem) that considers the project benefit, implementation risks and environmental impact as multiple objectives. Implementation risk and environmental impact values are also calculated using the same combined AHP and QFD methodology. Finally, the results of the fuzzy multi-objective goal programming suggest a list of projects that offers optimal benefit when carried out within multiple budgets.     

An interactive approach for Bayesian network learning using domain/expert knowledge

Using domain/expert knowledge when learning Bayesian networks from data has been considered a promising idea since the very beginning of the field. However, in most of the previously proposed approaches, human experts do not play an active role in the learning process. Once their knowledge is elicited, they do not participate any more. The interactive approach for integrating domain/expert knowledge we propose in this work aims to be more efficient and effective. In contrast to previous approaches, our method performs an active interaction with the expert in order to guide the search based learning process. This method relies on identifying the edges of the graph structure which are more unreliable considering the information present in the learning data. Another contribution of our approach is the integration of domain/expert knowledge at different stages of the learning process of a Bayesian network: while learning the skeleton and when directing the edges of the directed acyclic graph structure.     

Multi-criteria optimization model integrated with AHP for evaluation and selection of COTS components

This paper deals with COTS evaluation and selection for developing a modular software system under single application development task. We consider both quantitative and qualitative criteria which fulfils the specific needs of a software system. We use analytical hierarchy process (AHP) technique for evaluating the fitness of COTS components based upon various criteria and sub-criteria thereby providing overall score of each COTS component. We develop optimization models integrating AHP and multi-criteria decision-making, which aim at: (i) maximize the total value of purchasing (TVP) subject to budget, compatibility and reliability constraints, and (ii) maximize TVP and minimize the total cost of purchase simultaneously subject to compatibility and reliability constraints. The efficiency of the models is illustrated by means of numerical illustrations.     

An interactive dynamic approach based on hybrid swarm optimization for solving multiobjective programming problem with fuzzy parameters

Real engineering design problems are generally characterized by the presence of many often conflicting and incommensurable objectives. Naturally, these objectives involve many parameters whose possible values may be assigned by the experts. The aim of this paper is to introduce a hybrid approach combining three optimization techniques, dynamic programming (DP), genetic algorithms and particle swarm optimization (PSO). Our approach integrates the merits of both DP and artificial optimization techniques and it has two characteristic features. Firstly, the proposed algorithm converts fuzzy multiobjective optimization problem to a sequence of a crisp nonlinear programming problems. Secondly, the proposed algorithm uses H-SOA for solving nonlinear programming problem. In which, any complex problem under certain structure can be solved and there is no need for the existence of some properties rather than traditional methods that need some features of the problem such as differentiability and continuity. Finally, with different degree of α we get different α-Pareto optimal solution of the problem. A numerical example is given to illustrate the results developed in this paper.     

A fuzzy approach to using expert knowledge for tuning paper machines

Paper machines are very complex production systems, but their scope is simple: they consume materials and resources, called factors, to produce paper, which in turn can be described by its characteristics. In this paper, a decision support system is developed in cooperation with an industrial partner to help them with operational decision making when tuning a paper machine. The decision support system was developed in two phases. Firstly, the knowledge of experts is collected and stored in the form of a fuzzy ontology. Secondly, this knowledge is made usable so that a user of the decision support system can specify what characteristics of the produced paper to increase or to decrease and be returned with a recommendation on what factors to change. In this paper, we will work out the optimization problems on which the system is based. Additionally to a basic goal programming model, two extensions are explored, accounting for uncertainty and non-linearity, respectively.     

Supplier selection and order allocation problem using a two-phase fuzzy multi-objective linear programming

The aim of this paper is to solve a supplier selection problem under multi-price level and multi-product using interactive two-phase fuzzy multi-objective linear programming (FMOLP) model. The proposed model attempts to simultaneously minimize total purchasing and ordering costs, a number of defective units, and late delivered units ordered from suppliers. The piecewise linear membership functions are applied to represent the decision maker’s fuzzy goals for the supplier selection and order allocation problem, and can be resulted in more flexibility via an interactive decision-making process. To demonstrate effectiveness of the proposed model, results of applying the proposed model are shown by a numerical example. The analytical results show that the proposed approach is effective in uncertain environments and provide a reliable decision tool for integrated multi-objective supplier selection problems.     

Dynamic programming: An interactive approach

An interactive approach to the formulation, modeling, analysis, and solution of discrete deterministic dynamic programming problems is presented. The approach utilizes APL both as the mathematical and the programming language. The interactive capabilities of APL and the simple one-to-one correspondence between the programming and the mathematical language provide an extremely convenient environment for dynamic programming investigations in general and for teaching/learning purposes in particular. The approach is illustrated by a simple model and a numerical example.