Fuzzy Preference Programming Research Articles

Developing an integrated model for the selection of strategic alliance partners in the airline industry

This study proposes a hybrid model to help airlines select suitable partners for strategic alliances. The model addresses the interdependency and feedback effects between criteria and alternatives by using the Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Analytic Network Process (ANP). Decision-makers may hold diverse opinions and preferences due to incomplete information, differences in knowledge or simply inherent conflicts between various departments. This can make it difficult to judge the importance of the selection criteria. To remedy the problem we further apply Fuzzy Preference Programming (FPP) to integrate the different expert opinions. The proposed model can help practitioners improve their decision making process, especially when criteria and alternatives are numerous and inter-related. The method is demonstrated using data from a Taiwanese airline. Specific companies can easily extend this generic model to address their individual needs.

WEIGHTED PRIORITIZATION MODELS IN THE FUZZY ANALYTIC HIERARCHY PROCESS

The paper deals with the group prioritization problem in the fuzzy analytic hierarchy process. We extend the fuzzy preference programming method to fuzzy group prioritization by introducing important weights of decision-makers (DMs). The modified prioritization problem is represented as a weighted fuzzy goal programming model. Additionally, we represent the uncertain DMs' importance weights as fuzzy numbers and modify the goal programming model by a possibilistic approach. Both proposed models transform the initial prioritization problems with fuzzy or crisp important weights into equivalent crisp linear programs. Unlike the known fuzzy prioritization methods, the proposed approach does not require an additional defuzzification procedure for final ranking of alternatives and can deal with incomplete set of comparison judgments.

A hybrid model for selection of an outsourcing provider

Outsourcing is a good strategy for firms that need to reduce operating costs and improve competitiveness and it is important that firms scientifically select appropriate outsourcing providers. Some efforts have been made to find systematic ways to deal with outsourcing problems, but these efforts incorrectly assumed that the criteria used in the decision process are independent, which is not true in the real world. In this study, we propose a new hybrid multiple criteria decision-making (MCDM) model, which addresses the dependent relationships between the various criteria. The relations-structure among the criteria is built with the aid of the decision-making trial and evaluation laboratory (DEMATEL) method. Decision-makers tend to hold diverse opinions about their preferences due to incomplete information and knowledge, or inherent conflict between various departments. We further used the fuzzy preference programming and the analytic network process (ANP) to form a model for the selection of partners for outsourcing providers. The proposed model can help practitioners improve their decision making process, especially when criteria are numerous and inter-related. The method is demonstrated using data from a Taiwanese airline.

A hybrid ANP model in fuzzy environments for strategic alliance partner selection in the airline industry

Strategic airline alliances are an increasingly common strategy for enhancing airline competitiveness and satisfying customer needs, especially in an era characterized by blurring industry boundaries, fast-changing technologies, and global integration. Airlines have been very active in utilizing this form of strategic development. However, the selection of a suitable partner for a strategic alliance is not an easy decision, involving a host of complex considerations by different departments. Furthermore the decision-makers may hold diverse opinions and preferences arising due to incomplete information and knowledge or inherent conflict between various departments. In this study fuzzy preference programming and the analytic network process (ANP) are combined to form a model for the selection of partners for strategic alliances. The effects of uncertainty and disagreement between decision-makers as well as the interdependency and feedback that arise from the use of different criteria and alternatives are also addressed. This generic model can be easily extended to fulfill the specific needs of a variety of companies.

Fuzzy analytic hierarchy process: A logarithmic fuzzy preference programming methodology

Fuzzy analytic hierarchy process (AHP) proves to be a very useful methodology for multiple criteria decision-making in fuzzy environments, which has found substantial applications in recent years. The vast majority of the applications use a crisp point estimate method such as the extent analysis or the fuzzy preference programming (FPP) based nonlinear method for fuzzy AHP priority derivation. The extent analysis has been revealed to be invalid and the weights derived by this method do not represent the relative importance of decision criteria or alternatives. The FPP-based nonlinear priority method also turns out to be subject to significant drawbacks, one of which is that it may produce multiple, even conflict priority vectors for a fuzzy pairwise comparison matrix, leading to entirely different conclusions. To address these drawbacks and provide a valid yet practical priority method for fuzzy AHP, this paper proposes a logarithmic fuzzy preference programming (LFPP) based methodology for fuzzy AHP priority derivation, which formulates the priorities of a fuzzy pairwise comparison matrix as a logarithmic nonlinear programming and derives crisp priorities from fuzzy pairwise comparison matrices. Numerical examples are tested to show the advantages of the proposed methodology and its potential applications in fuzzy AHP decision-making.

Integration of fuzzy AHP and FPP with TOPSIS methodology for aeroengine health assessment

This paper models the aeroengine health assessment problem as a multi-criteria decision-making (MCDM) problem and proposes a three-step evaluation model, which combines the techniques of fuzzy analytic hierarchy process (fuzzy AHP), fuzzy preference programming (FPP) and technique for order performance by similarity to ideal solution (TOPSIS). Fuzzy AHP and FPP methods are used to determine the relative weights of multiple evaluation criteria and synthesize the ratings of candidate aeroengines. Aggregated the evaluators’ attitude toward preference, then TOPSIS is employed to obtain a crisp overall performance value for each alternative to make a final decision. To illustrate how the approach is used for the aeroengine health assessment problem, an empirical study of a real case involving eleven evaluation criteria and ten initial commercial aeroengines of Air China Ltd. is conducted. The case study demonstrates the effectiveness and feasibility of the proposed evaluation procedure.

Selection of vendor using analytical hierarchy process based on fuzzy preference programming

Modern businesses face a more severe and challenging environment than before. Selection of vendor and evaluating its performance are decisions of strategic importance from business point of view. Selecting vendors involve those that perform optimally on the desired multicriteria dimensions like cost, quality, delivery performance, etc. In this paper we identify the major criteria for selecting vendors and develop a hierarchy through which decision maker can examine the relationship among these criteria. Some of these criteria possess characteristics of fuzziness. By applying analytical hierarchy process (AHP) based on fuzzy preference programming (FPP) a pair wise comparison is made between criteria. The whole process of fuzzy AHP involves decomposition, pairwise comparison, interval comparison, derive priorities using optimization technique of FPP. An overall crisp priority is obtained for ranking the best vendor. A numerical example illustrates our methodology.

Validating AHP, fuzzy alpha cut and fuzzy preference programming method using clustering technique

Fuzzy multicriteria analysis (MA) methods suitable for a given decision problem usually differ in aggregation processes for handling the alternatives’ performance ratings and criteria weights. Due to their structural differences, these methods often produce inconsistent ranking results for the same fuzzy MA problem. This paper presents a validation procedure using fuzzy clustering for selecting among inconsistent ranking results produced by analytical hierarchy process (AHP), fuzzy alpha cut and fuzzy preference programming (FPP) methods for a given problem. The procedure compares the ranking results obtained by fuzzy MA methods using different aggregation algorithms with the clustering results of the alternatives by fuzzy clustering. An empirical study of evaluating major port trusts of India is conducted to demonstrate the effectiveness of the validation procedure.

Supplier selection in electronic marketplaces using satisficing and fuzzy AHP

Supplier selection is a critical and demanding task for companies that participate in electronic marketplaces to find suppliers and to execute electronically their transactions. This paper is aimed to suggest a fresh approach for decision support enabling effective supplier selection processes in electronic marketplaces. We introduce an evaluation method with two stages: initial screening of the suppliers through the enforcement of hard constraints on the selection criteria and final supplier evaluation through the application of a modified variant of the Fuzzy Preference Programming (FPP) method. The proposed method alleviates the information overload effect that is inherent in the environment of electronic marketplaces, facilitates an easier elicitation of user preferences through the reduction of necessary user input (i.e. pairwise comparisons) and reduces computational complexity, in terms of the number of linear programs to be solved, in comparison with the original FPP method. The FPP method is adopted and modified accordingly in order to tackle the issue of inconsistency/uncertainty of human preference models. Our approach is demonstrated with the example of a hypothetical metal manufacturing company that finds and selects suppliers in the environment of an electronic marketplace.

On the order of the preference intensities in fuzzy AHP

We show that a recently discovered fundamental problem with the Analytic Hierarchy Process (AHP) concerning the meaning of the resultant preference intensities is also evident for the fuzzy AHP. We prove that if there is a judgmental inconsistency in the fuzzy pair-wise comparisons, it is impossible to ensure the preservation of the order regarding to preference intensities in the resultant priority vector. Further, it is shown with an example from the published literature that the order of the preference intensities may not be preserved even there is no inconsistency in the judgment set, albeit it is possible to comply with this order via using fuzzy preference programming (FPP) methodology. Finally, it is proved that if the interval judgments regarding to the decompositions of original judgments to α- level sets are consistent, FPP guarantees the preservation of the order of the preference intensities at those levels.

Fuzzy analytic hierarchy process based group decision support system to select and evaluate new manufacturing technologies

Manufacturing organizations often make complex decisions in regards to investment in new manufacturing technologies (NMT). These NMT are assessed based on attributes such as flexibility, quality etc., which are hard to quantify. This fact calls upon the need for a structured decision support systems that can adequately represent qualitative and subjective assessments. The gist of this paper is to propose an integrated fuzzy analytic hierarchy process (AHP) based approach to facilitate the selection and evaluation of NMT in the presence of intangible attributes and uncertainty. Three important issues that are pertinent and critical to fuzzy AHP, namely contradiction in user preferences, deriving priorities from inconsistent fuzzy judgment matrices, and group decision-making are addressed in detail. Also, an attempt is made to compare fuzzy preference programming (FPP) and two-stage logarithmic goal programming (TLGP) based fuzzy prioritization methods. Based on the comparative study, it is concluded that FPP is preferred over TLGP to select and evaluate NMT. Numerical examples are provided to illustrate the aforementioned issues.

Applying consistent fuzzy preference relations to partnership selection

Partnership selection has been important to the formation of a virtual enterprise. Based on the fuzzy preference programming (FPP) method proposed by Mikhailov [Fuzzy analytical approach to partnership selection in formation of virtual enterprises. Omega 2002;30:393–401], this investigation presents a consistent fuzzy preference relations method to select partners. Human thoughts are full of uncertainty, so the decision-makers cannot make exact pairwise comparisons. The FPP method solves this problem using an interval value instead of Saaty's 1–9 scale. In this study, the FPP method is reviewed, and then the consistent fuzzy preference relations method is elucidated. Finally, the presented method is applied to the example addressed by Mikhailov [Fuzzy analytical approach to partnership selection in formation of virtual enterprises. Omega 2002;30:393–401]. This study reveals that the proposed method yields consistent decision rankings from only n - 1 pairwise comparisons—the same number as in Mikhailov's research. Briefly, the presented consistent fuzzy preference relations method is an easy and practical way to provide rankings of partnership in making decision.

Combining different prioritization methods in the analytic hierarchy process synthesis

A multicriteria approach for combining prioritization methods within the analytic hierarchy process (AHP) is proposed. The leading assumption is that for each particular decision problem and related hierarchy, AHP must not necessarily employ only one prioritization method (e.g. eigenvector method). If more available methods are used to identify the best estimates of local priorities for each comparison matrix in the hierarchy, then the estimate of final alternatives’ priorities should also be the best possible, which is in natural concordance with an additive compensatory structure of the AHP synthesis. The most popular methods for deriving priorities from comparison matrices are identified as candidates (alternatives) to participate in AHP synthesis: additive normalization, eigenvector, weighted least-squares, logarithmic least-squares, logarithmic goal programming and fuzzy preference programming. Which method will be used depends on the result of multicriteria evaluation of their priority vectors’ performance with regard to suggested deviation and rank reversal measures. Two hierarchies with matrices of size 3–6 are used to illustrate an approach.

Analysis of the optimal configuration of energy transportation infrastructure in Asia with a linear programming energy system model : Fujii, Y. et al. International Journal of Global Energy Issues, 2002, 18, (1), 22–43

Fuzzy analytic hierarchy process (AHP) proves to be a very useful methodology for multiple criteria decision-making in fuzzy environments, which has found substantial applications in recent years. The vast majority of the applications use a crisp point estimate method such as the extent analysis or the fuzzy preference programming (FPP) based nonlinear method for fuzzy AHP priority derivation. The extent analysis has been revealed to be invalid and the weights derived by this method do not represent the relative importance of decision criteria or alternatives. The FPP-based nonlinear priority method also turns out to be subject to significant drawbacks, one of which is that it may produce multiple, even conflict priority vectors for a fuzzy pairwise comparison matrix, leading to entirely different conclusions. To address these drawbacks and provide a valid yet practical priority method for fuzzy AHP, this paper proposes a logarithmic fuzzy preference programming (LFPP) based methodology for fuzzy AHP priority derivation, which formulates the priorities of a fuzzy pairwise comparison matrix as a logarithmic nonlinear programming and derives crisp priorities from fuzzy pairwise comparison matrices. Numerical examples are tested to show the advantages of the proposed methodology and its potential applications in fuzzy AHP decision-making.

Group prioritization in the AHP by fuzzy preference programming method

In this paper we propose a new group fuzzy preference programming (GFPP) method for deriving group priorities from crisp pairwise comparison judgements, provided by multiple decision makers. The assessment of the group priorities is formulated as a fuzzy linear programming problem, maximizing the group's overall satisfaction with the group solution. The GFPP method combines the group synthesis and prioritization stages into a coherent integrated framework, which does not need additional aggregation procedures. The method can easily deal with missing judgements and provides a meaningful indicator for measuring the level of group satisfaction and group consistency. Scope and purpose The increasing complexity of decision-making problems in modern organizations requires the development of innovative decision support tools, which integrate theoretical methods of operations research and recent advancements of computing science. The main objective of this paper is to present a new approach for group decision making with the analytic hierarchy process (AHP), suitable for the development of group decision support systems. We focus on the problem of deriving local group priorities (weights of criteria and scores of alternatives), which is the most important stage of the AHP. The main characteristics of our method for prioritization and its possibilities for group decision-making support are illustrated through detailed examples.

Fuzzy analytic network process and its application to the development of decision support systems

In this paper we propose a fuzzy extension of the analytic network process (ANP) that uses uncertain human preferences as input information in the decision-making process. Instead of the classical Eigenvector prioritization method, employed in the prioritization stage of the ANP, a new fuzzy preference programming method, which obtains crisp priorities from inconsistent interval and fuzzy judgments is applied. The resulting fuzzy ANP enhances the potential of the ANP for dealing with imprecise and uncertain human comparison judgments. It allows for multiple representations of uncertain human preferences, as crisp, interval, and fuzzy judgments and can find a solution from incomplete sets of pairwise comparisons. An important feature of the proposed method is that it measures the inconsistency of the uncertain human preferences by an appropriate consistency index. A prototype decision support system realizing the proposed method is developed, and its performance is illustrated by examples.

Deriving priorities from fuzzy pairwise comparison judgements

A new approach for deriving priorities from fuzzy pairwise comparison judgements is proposed, based on α-cuts decomposition of the fuzzy judgements into a series of interval comparisons. The assessment of the priorities from the pairwise comparison intervals is formulated as an optimisation problem, maximising the decision-maker's satisfaction with a specific crisp priority vector. A fuzzy preference programming method, which transforms the interval prioritisation task into a fuzzy linear programming problem is applied to derive optimal crisp priorities. Aggregating the optimal priorities, which correspond to different α-cut levels enables overall crisp scores of the prioritisation elements to be obtained. A modification of the linear fuzzy preference programming method is also proposed to derive priorities directly from fuzzy judgements, without applying α-cut transformations. The formulation of the prioritisation problem as an optimisation task is similar to the previous approach, but it requires the solution of a non-linear optimisation program. The second approach also derives crisp priorities and has the advantage that it does not need additional aggregation and ranking procedures. Both proposed methods are illustrated by numerical examples and compared to some of the existing fuzzy prioritisation methods.

Fuzzy assessment of priorities with application to competitive bidding

ABSTRACT This paper presents a new fuzzy preference programming method for deriving priorities from inconsistent interval pairwise comparison matrices in the Analytical Hierarchy Process (AHP). The preference programming method of Arbel for elicitation of the priorities from interval matrices transforms the prioritisation problem into a linear program, which is attractive from a computational point of view, however it cannot deal with inconsistent decision—maker judgements. The proposed fuzzy preference programming method represents the inconsistent interval judgements as fuzzy linear constraints and defines a convex non—empty fuzzy feasible area. The assessment of the priorities is stated as an optimisation problem, maximising the decision-maker's satisfaction with the solution of an approximate fuzzy programming problem. The new method is applicable for both crisp and interval inconsistent judgements and can be considered as a generalisation of the classical prioritisation methods in the AHP. An application of this method for the modelling of uncertain judgements and the assessment of priorities in competitive bidding is described.