Dominance Measuring Method Performance under Incomplete Information about Weights.

In multi-attribute utility theory, it is often not easy to elicit precise values for the scaling weights representing the relative importance of criteria. A very widespread approach is to gather incomplete information. A recent approach for dealing with such situations is to use information about each alternative?s intensity of dominance, known as dominance measuring methods. Different dominancemeasuring methods have been proposed, and simulation studies have been carried out to compare these methods with each other and with other approaches but only when ordinal information about weights is available. In this paper, we useMonte Carlo simulation techniques to analyse the performance of and adapt such methods to deal with weight intervals, weights fitting independent normal probability distributions orweights represented by fuzzy numbers.Moreover, dominance measuringmethod performance is also compared with a widely used methodology dealing with incomplete information on weights, the stochastic multicriteria acceptability analysis (SMAA). SMAA is based on exploring the weight space to describe the evaluations that would make each alternative the preferred one

Modelling and optimizing multiple attribute decisions by using fuzzy sets

The purpose of this paper is to present a coherent perspective of modeling and optimizing multiple attribute decisions by using fuzzy sets. In management practice we face most of the time the situation in which a problem have several possible solutions and each solution can be analyzed using multiple criteria models. In the same time, in real life decision making process there is a given level of uncertainty which makes difficult a clear cut analytical analysis. The object of this article is to build a model approach for making multiple criteria decision using fuzzy sets of objects. Elaborating multiple attribute decisions involves performing an assessment and selecting from a given and finite set of possible alternative courses of action in the presence of a given and finite, and usually conflicting set of attributes and criteria.decision making, fuzzy sets, modeling, multiple criteria optimization.

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

Simulation-based evaluation of defuzzification-based approaches to fuzzy multi-attribute decision making

This paper presents a simulation-based study to evaluate the performance of 12 defuzzification-based approaches for solving the general fuzzy multiattribute decision-making (MADM) problem requiring cardinal ranking of decision alternatives. These approaches are generated based on six defuzzification methods in conjunction with the simple additive weighting (SAW) method and the technique for order preference by similarity to the ideal solution method. The consistency and effectiveness of these approaches are examined in terms of four new objective performance measures, which are based on five evaluation indexes. The Simulation result shows that the approaches, which are capable of using all the available information on fuzzy numbers, effectively in the defuzzification process, produce more consistent ranking outcomes. In particular, the SAW method with the degree of dominance defuzzification is proved to be the overall best performed approach, which is, followed by the SAW method with the area center defuzzification. These findings are of practical significance in real-world settings where the selection of the defuzzification-based approaches is required in solving the general fuzzy MADM problems under specific decision contexts

Development, test and comparison of two Multiple Criteria Decision Analysis(MCDA) models: A case of healthcare infrastructure location

When planning a new development, location decisions have always been a major issue. This paper examines and compares two modelling methods used to inform a healthcare infrastructure location decision. Two Multiple Criteria Decision Analysis (MCDA) models were developed to support the optimisation of this decision-making process, within a National Health Service (NHS) organisation, in the UK. The proposed model structure is based on seven criteria (environment and safety, size, total cost, accessibility, design, risks and population profile) and 28 sub-criteria. First, Evidential Reasoning (ER) was used to solve the model, then, the processes and results were compared with the Analytical Hierarchy Process (AHP). It was established that using ER or AHP led to the same solutions. However, the scores between the alternatives were significantly different; which impacted the stakeholders‟ decision-making. As the processes differ according to the model selected, ER or AHP, it is relevant to establish the practical and managerial implications for selecting one model or the other and providing evidence of which models best fit this specific environment. To achieve an optimum operational decision it is argued, in this study, that the most transparent and robust framework is achieved by merging ER process with the pair-wise comparison, an element of AHP. This paper makes a defined contribution by developing and examining the use of MCDA models, to rationalise new healthcare infrastructure location, with the proposed model to be used for future decision. Moreover, very few studies comparing different MCDA techniques were found, this study results enable practitioners to consider even further the modelling characteristics to ensure the development of a reliable framework, even if this means applying a hybrid approach

Dominance intensity measure within fuzzy weight oriented MAUT: an application

We introduce a dominance intensity measuring method to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision-making problems on the basis of multi-attribute utility theory (MAUT) and fuzzy sets theory. We consider the situation where there is imprecision concerning decision-makers’ preferences, and imprecise weights are represented by trapezoidal fuzzy weights.The proposed method is based on the dominance values between pairs of alternatives. These values can be computed by linear programming, as an additive multi-attribute utility model is used to rate the alternatives. Dominance values are then transformed into dominance intensity measures, used to rank the alternatives under consideration. Distances between fuzzy numbers based on the generalization of the left and right fuzzy numbers are utilized to account for fuzzy weights. An example concerning the selection of intervention strategies to restore an aquatic ecosystem contaminated by radionuclides illustrates the approach. Monte Carlo simulation techniques have been used to show that the proposed method performs well for different imprecision levels in terms of a hit ratio and a rank-order correlation measure

Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

A discriminative analysis of approaches to ranking fuzzy numbers in fuzzy decision making

This paper presents a discriminative analysis of approaches to ranking fuzzy numbers in fuzzy decision making based on a comprehensive review of existing approaches. The consistency and effectiveness of the approaches to ranking fuzzy numbers are examined in terms of two objective measures developed, leading to a better understanding of the relative performance of individual approaches in ranking fuzzy numbers. Representative fuzzy numbers are selected for carrying out the comparative study of several typical approaches in ranking fuzzy numbers. Several interesting findings are identified which may be of practical significance to fuzzy decision making in real situations

Application of Fuzzy Analytic Hierarchy Process (FAHP) to Improve Precision and Certainty on Safety Conformity Evaluation in a Bottling Plant

With the bottling plant facing safety impacts, the commitment toward zero levels of accidents needs to be evaluated. However, the perception and measurement of safety conformity by the safety manager that is subjected to imprecision and uncertainty are hardly evaluated correctly with the present dominant approach of using crisp numeric values. This article presents a fuzzy analytic hierarchy process (FAHP) approach to reduce the imprecision and uncertainty in the safety conformity multicriteria decision-making results. The method establishes and selects the best safety conformity factors in alignment with different criteria within the segments of a Nigerian bottling plant. The fuzzy synthetic extent concerning each alternative, the degree of possibility, prioritizing weights, and the choice of the best criterion were judged based on the maximum weight in the FAHP evaluation process. The average weight criterion was used to distinguish the best from the worst units within each segment. The results reveal the criteria weights as 0.4937 for haulage drillers (warehouse), 0.3038 for palletizers (manufacturing corridor), 0.3333 for syrup mixers/lab technicians for quality assurance, and no choice of the best parameter for the fleet workshop. However, the highest weight for the contractors is 0.3201, which is for contractor 1. To compare the best and worst criteria in the present study and a literature source, the optimal criteria choices of safety conformity conflicted in all the segments. The principal difference between the present method and the analytic hierarchy process approach is integrating fuzzy application to the analytical hierarchy process to provide a more accurate safety conformity assessment, yielding reliable and informative results representing the vagueness of the bottling process decision-making process. This unique approach provides an opportunity for the production workers to work more collaboratively towards attaining new solutions to the uncertainty and imprecision problem in safety conformity for the bottling plant