Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy Preference Relations

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.Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods

Comparison of different Multiple-criteria decision analysis methods in the context of conceptual design: application to the development of a solar collector structure

At each stage of the product development process, the designers are facing an important task which consists of decision making. Two cases are observed: the problem of concept selection in conceptual design phases and, the problem of pre-dimensioning once concept choices are made. Making decisions in conceptual design phases on a sound basis is one of the most difficult challenges in engineering design, especially when innovative concepts are introduced. On the one hand, designers deal with imprecise data about design alternatives. On the other hand, design objectives and requirements are usually not clear in these phases. The greatest opportunities to reduce product life cycle costs usually occur during the first conceptual design phases. The need for reliable multi-criteria decision aid (MCDA) methods is thus greatest at early conceptual design phases. Various MCDA methods are proposed in the literature. The main criticism of these methods is that they usually yield different results for the same problem. In this work, an analysis of six MCDA methods (weighed sum, weighted product, Kim & Lin, compromise programming, TOPSIS, and ELECTRE I) was conducted. Our analysis was performed via an industrial case of solar collector structure development. The objective is to define the most appropriate MCDA methods in term of three criteria: (i) the consistency of the results, (ii) the ease of understanding and, (iii) the adaptation of the decision type. The results show that TOPSIS is the most consistent MCDA method in our case

Critical review of multi-criteria decision aid methods in conceptual design phases: application to the development of a solar collector structure

At each stage of the product development process, the designers are facing an important task which consists of decision making. Two cases are observed: the problem of concept selection in conceptual design phases and, the problem of pre-dimensioning once concept choices are made. Making decisions in conceptual design phases on a sound basis is one of the most difficult challenges in engineering design, especially when innovative concepts are introduced. On the one hand, designers deal with imprecise data about design alternatives. On the other hand, design objectives and requirements are usually not clear in these phases. The greatest opportunities to reduce product life cycle costs usually occur during the first conceptual design phases. The need for reliable multi-criteria decision aid (MCDA) methods is thus greatest at early conceptual design phases. Various MCDA methods are proposed in the literature. The main criticism of these methods is that they usually yield different results for the same problem [22,23,25]. In this work, an analysis of six MCDA methods (weighed sum, weighted product, Kim & Lin, compromise programming, TOPSIS, and ELECTRE I) was conducted. Our analysis was performed via an industrial case of solar collector structure development. The objective is to define the most appropriate MCDA methods in term of three criteria: (i) the consistency of the results, (ii) the ease of understanding and, (iii) the adaptation of the decision type. The results show that TOPSIS is the most consistent MCDA method in our case

A Compact Representation of Preferences in Multiple Criteria Optimization Problems

[EN] A critical step in multiple criteria optimization is setting the preferences for all the criteria under consideration. Several methodologies have been proposed to compute the relative priority of criteria when preference relations can be expressed either by ordinal or by cardinal information. The analytic hierarchy process introduces relative priority levels and cardinal preferences. Lexicographical orders combine both ordinal and cardinal preferences and present the additional difficulty of establishing strict priority levels. To enhance the process of setting preferences, we propose a compact representation that subsumes the most common preference schemes in a single algebraic object. We use this representation to discuss the main properties of preferences within the context of multiple criteria optimization.Salas-Molina, F.; Pla Santamaría, D.; Garcia-Bernabeu, A.; Reig-Mullor, J. (2019). A Compact Representation of Preferences in Multiple Criteria Optimization Problems. Mathematics. 7(11):1-16. https://doi.org/10.3390/math7111092S116711Ahmadi, A., Ahmadi, M. R., & Nezhad, A. E. (2014). A Lexicographic Optimization and Augmented ϵ-constraint Technique for Short-term Environmental/Economic Combined Heat and Power Scheduling. Electric Power Components and Systems, 42(9), 945-958. doi:10.1080/15325008.2014.903542González-Arteaga, T., Alcantud, J. C. R., & de Andrés Calle, R. (2016). A new consensus ranking approach for correlated ordinal information based on Mahalanobis distance. Information Sciences, 372, 546-564. doi:10.1016/j.ins.2016.08.071Miettinen, K., & M�kel�, M. M. (2002). On scalarizing functions in multiobjective optimization. OR Spectrum, 24(2), 193-213. doi:10.1007/s00291-001-0092-9Ignizio, J. P. (1983). Generalized goal programming An overview. Computers & Operations Research, 10(4), 277-289. doi:10.1016/0305-0548(83)90003-5Sitorus, F., Cilliers, J. J., & Brito-Parada, P. R. (2019). Multi-criteria decision making for the choice problem in mining and mineral processing: Applications and trends. Expert Systems with Applications, 121, 393-417. doi:10.1016/j.eswa.2018.12.001Zyoud, S. H., & Fuchs-Hanusch, D. (2017). A bibliometric-based survey on AHP and TOPSIS techniques. Expert Systems with Applications, 78, 158-181. doi:10.1016/j.eswa.2017.02.016Erdoğan, M., & Kaya, İ. (2016). A combined fuzzy approach to determine the best region for a nuclear power plant in Turkey. Applied Soft Computing, 39, 84-93. doi:10.1016/j.asoc.2015.11.013Chen, Y., Liu, R., Barrett, D., Gao, L., Zhou, M., Renzullo, L., & Emelyanova, I. (2015). A spatial assessment framework for evaluating flood risk under extreme climates. Science of The Total Environment, 538, 512-523. doi:10.1016/j.scitotenv.2015.08.094Zammori, F. (2010). The analytic hierarchy and network processes: Applications to the US presidential election and to the market share of ski equipment in Italy. Applied Soft Computing, 10(4), 1001-1012. doi:10.1016/j.asoc.2009.07.013Carter, C. R., & Rogers, D. S. (2008). A framework of sustainable supply chain management: moving toward new theory. International Journal of Physical Distribution & Logistics Management, 38(5), 360-387. doi:10.1108/09600030810882816Ignizio, J. P. (1976). An Approach to the Capital Budgeting Problem with Multiple Objectives. The Engineering Economist, 21(4), 259-272. doi:10.1080/00137917608902798Lonergan, S. C., & Cocklin, C. (1988). The use of lexicographic goal programming in economic/ecolocical conflict analysis. Socio-Economic Planning Sciences, 22(2), 83-92. doi:10.1016/0038-0121(88)90020-1González-Pachón, J., & Romero, C. (2014). Properties underlying a preference aggregator based on satisficing logic. International Transactions in Operational Research, 22(2), 205-215. doi:10.1111/itor.1211

Revealed cardinal preference

I prove that as long as we allow the marginal utility for money lamda to vary between purchases (similarly to the budget) then the quasi-linear and the ordinal budget-constrained models rationalize the same data. However, we know that lamda is approximately constant. I provide a simple constructive proof for the necessary and sufficient condition for the constant lambda rationalization, which I argue should replace the Generalized Axiom of Revealed Preference in empirical studies of consumer behavior.

Group aggregation of pairwise comparisons using multi-objective optimization

AbstractIn group decision making, multiple decision makers (DMs) aim to reach a consensus ranking of alternatives in a decision problem. The differing expertise, experience and, potentially conflicting, interests of the DMs will result in the need for some form of conciliation to achieve consensus. Pairwise comparisons are commonly used to elicit values of preference of a DM. The aggregation of the preferences of multiple DMs must additionally consider potential conflict between DMs and how these conflicts may result in a need for compromise to reach group consensus.We present an approach to aggregating the preferences of multiple DMs, utilizing multi-objective optimization, to derive and highlight underlying conflict between the DMs when seeking to achieve consensus. Extracting knowledge of conflict facilitates both traceability and transparency of the trade-offs involved when reaching a group consensus.Further, the approach incorporates inconsistency reduction during the aggregation process to seek to diminish adverse effects upon decision outcomes. The approach can determine a single final solution based on either global compromise information or through utilizing weights of importance of the DMs.Within multi-criteria decision making, we present a case study within the Analytical Hierarchy Process from which we derive a richer final ranking of the decision alternatives

A Local Adjustment Method to Improve Multiplicative Consistency of Fuzzy Reciprocal Preference Relations

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.Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identification and modification (IIM) method to detect and rectify only the most inconsistent elements of an inconsistent FPR. As such, the proposed IIM can be considered a local adjustment method to improve multiplicative consistency (MC) of FPRs. The case of inconsistent FPRs with missing values, i.e., incomplete FPRs, is addressed with the estimation of the missing preferences with a constrained nonlinear optimization model by the application of the IIM method. The implementation process of the proposed algorithms is illustrated with numerical examples. Simulation experiments and comparisons with existent methods are also included to show that the new method requires fewer iterations than existent methods to improve the MC of FPRs and achieves better MC level, while preserving the original preference information as much as possible than the existent methods. Thus, the results presented in this article demonstrate the correctness, effectiveness, and robustness of the proposed method