Non-linear Neutrosophic Numbers and Its Application to Multiple Criteria Performance Assessment

[EN] The concept of fuzzy set has been extended by neutrosophic fuzzy sets to represent sets whose elements have different degrees of membership characterized by a truth-membership function, an indeterminacy-membership function and a falsity-membership function. It is usually assumed that these functions are linear, hence excluding the possibility of non-linearity in many decision-making situations. From an alternative definition of non-linear neutrosophic numbers, we develop the concepts of (alpha, beta, gamma)-cuts, possibility mean, variance, skewness and a new possibility score function. These concepts are useful to deal with multiple criteria decision making problems. We illustrate the practical use of these concepts by means of a real case study in supply chain risk management in the motor industry. Due to the fact that neutrosophic sets have been used in several areas of decision-making, finance and economics, we argue that our proposal contributes to enhance the application of neutrosophic numbers.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Reig-Mullor, J.; Salas-Molina, F. (2022). Non-linear Neutrosophic Numbers and Its Application to Multiple Criteria Performance Assessment. International Journal of Fuzzy Systems. 24(6):2889-2904. https://doi.org/10.1007/s40815-022-01295-y2889290424

The evaluation performance for commercial banks by intuitionistic fuzzy numbers: the case of Spain

In a globalized world, the banking sector has been forced to advance not only in financial performance, but also in non-financial performance, especially in sustainability criteria. For this purpose, multicriteria decision methods are especially suited to evaluate efficiency and to make a stable ranking of the most outstanding banks in the Spanish financial system. However, we are aware of the difficulties involved due to the inherent uncertainty and subjectivity of this process. For this reason, the use of fuzzy models is proposed, especially intuitionistic fuzzy numbers combined with the Analytic Hierarchy Process and the TOPSIS. The combination of financial criteria based on the CAMELS rating system with non-financial sustainability criteria makes it possible to order the Spanish banking system based on global efficiency. The most relevant contributions are: first, the use of intuitionistic fuzzy numbers in the performance evaluation process, whereby the quality of the information available can be quantified; and the most important one, a simplification of the process in the implementation of the intuitionistic fuzzy TOPSIS. Finally, through a sensibility analysis, it is possible to isolate the relevance of the sustainability process to obtain the global performance evaluation

A novel approach to improve the bank ranking process: an empirical study in Spain

In this paper, a novel approach to the bank ranking process based on the possibilistic theory is proposed. Through this new method, the sensitivity of the results can be improved. Several methods are applied in order to rank the financial performance of Spanish Banks. Methods such as the Fuzzy Analytic Hierarchy Process (FAHP) and fuzzy TOPSIS are integrated in the proposed model. Criteria and sub-criteria weights are computed based on the judgments of experts using FAHP. These weights and financial indicators are inputs of the fuzzy TOPSIS methods for ranking the banks. The financial ratios are based on the CAMEL rating system criteria. Moreover, the results from the application of several distance measurements (Vertex, Hamming and Euclidean) in fuzzy TOPSIS as well as a new measure based on the possibilistic theory are compared. Finally, the results obtained applying fuzzy TOPSIS show that they vary depending on the separate measure, so it is necessary to have different measures to be able to correct decision making

Extended Fuzzy Analytic Hierarchy Process (E-FAHP): A General Approach

[EN] Fuzzy analytic hierarchy process (FAHP) methodologies have witnessed a growing development from the late 1980s until now, and countless FAHP based applications have been published in many fields including economics, finance, environment or engineering. In this context, the FAHP methodologies have been generally restricted to fuzzy numbers with linear type of membership functions (triangular numbers-TN-and trapezoidal numbers-TrN). This paper proposes an extended FAHP model (E-FAHP) where pairwise fuzzy comparison matrices are represented by a special type of fuzzy numbers referred to as (m,n)-trapezoidal numbers (TrN (m,n)) with nonlinear membership functions. It is then demonstrated that there are a significant number of FAHP approaches that can be reduced to the proposed E-FAHP structure. A comparative analysis of E-FAHP and Mikhailov's model is illustrated with a case study showing that E-FAHP includes linear and nonlinear fuzzy numbers.Reig-Mullor, J.; Pla Santamaría, D.; Garcia-Bernabeu, A. (2020). Extended Fuzzy Analytic Hierarchy Process (E-FAHP): A General Approach. Mathematics. 8(11):1-14. https://doi.org/10.3390/math8112014S114811Chai, J., Liu, J. N. K., & Ngai, E. W. T. (2013). Application of decision-making techniques in supplier selection: A systematic review of literature. Expert Systems with Applications, 40(10), 3872-3885. doi:10.1016/j.eswa.2012.12.040Tavana, M., Zareinejad, M., Di Caprio, D., & Kaviani, M. A. (2016). An integrated intuitionistic fuzzy AHP and SWOT method for outsourcing reverse logistics. Applied Soft Computing, 40, 544-557. doi:10.1016/j.asoc.2015.12.005Medasani, S., Kim, J., & Krishnapuram, R. (1998). An overview of membership function generation techniques for pattern recognition. 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Fuzzy AHP approach to selection problems in process engineering involving quantitative and qualitative aspects. Process Safety and Environmental Protection, 92(5), 467-475. doi:10.1016/j.psep.2013.11.005Rezaei, J., Fahim, P. B. M., & Tavasszy, L. (2014). Supplier selection in the airline retail industry using a funnel methodology: Conjunctive screening method and fuzzy AHP. Expert Systems with Applications, 41(18), 8165-8179. doi:10.1016/j.eswa.2014.07.005Song, Z., Zhu, H., Jia, G., & He, C. (2014). Comprehensive evaluation on self-ignition risks of coal stockpiles using fuzzy AHP approaches. Journal of Loss Prevention in the Process Industries, 32, 78-94. doi:10.1016/j.jlp.2014.08.002Dong, M., Li, S., & Zhang, H. (2015). Approaches to group decision making with incomplete information based on power geometric operators and triangular fuzzy AHP. Expert Systems with Applications, 42(21), 7846-7857. doi:10.1016/j.eswa.2015.06.007Mangla, S. K., Kumar, P., & Barua, M. K. (2015). Risk analysis in green supply chain using fuzzy AHP approach: A case study. Resources, Conservation and Recycling, 104, 375-390. doi:10.1016/j.resconrec.2015.01.001Mosadeghi, R., Warnken, J., Tomlinson, R., & Mirfenderesk, H. (2015). Comparison of Fuzzy-AHP and AHP in a spatial multi-criteria decision making model for urban land-use planning. Computers, Environment and Urban Systems, 49, 54-65. doi:10.1016/j.compenvurbsys.2014.10.001Lupo, T. (2016). A fuzzy framework to evaluate service quality in the healthcare industry: An empirical case of public hospital service evaluation in Sicily. Applied Soft Computing, 40, 468-478. doi:10.1016/j.asoc.2015.12.010Tuljak-Suban, D., & Bajec, P. (2018). The Influence of Defuzzification Methods to Decision Support Systems Based on Fuzzy AHP with Scattered Comparison Matrix: Application to 3PLP Selection as a Case Study. 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Sustainability performance assessment with intuitionistic fuzzy composite metrics and its application to the motor industry

The performance assessment of companies in terms of sustainability requires to find a balance between multiple and possibly conflicting criteria. We here rely on composite metrics to rank a set of companies within an industry considering environmental, social and corporate governance criteria. To this end, we connect intuitionistic fuzzy sets and composite programming to propose novel composite metrics. These metrics allow to integrate important environmental, social and governance principles with the gradual membership functions of fuzzy set theory. The main result of this paper is a sustainability assessment method to rank companies within a given industry. In addition to consider multiple objectives, this method integrates two important social principles such as maximum utility and fairness. A real-world example is provided to describe the application of our sustainability assessment method within the motor industry. A further contribution of this paper is a multicriteria generalization of the concept of magnitude of a fuzzy number

A multicriteria approach to manage credit risk under strict uncertainty

Assessing the ability of applicants to repay their loans is generally recognized as a critical task in credit risk management. Credit managers rely on financial and market information, usually in the form of ratios, to estimate the quality of credit applicants. However, there is no guarantee that a given set of ratios contains the information needed for credit classification. Decision rules under strict uncertainty aim to mitigate this drawback. In this paper, we propose the use of a moderate pessimism decision rule combined with dimensionality reduction techniques and compromise programming. Moderate pessimism ensures that neither extreme optimistic nor pessimistic decisions are taken. Dimensionality reduction from a set of ratios facilitates the extraction of the relevant information. Compromise programming allows to find a balance between quality of debt and risk concentration. Our model produces two critical outputs: a quality assessment and the optimum allocation of funds. To illustrate our multicriteria approach, we include a case study on 29 firms listed in the Spanish stock market. Our results show that dimensionality reduction contributes to avoid redundancy and that quality-diversification optimization is able to produce budget allocations with a reduced number of firms

A multidimensional approach to rank fuzzy numbers based on the concept of magnitude

Ranking fuzzy numbers have become of growing importance in recent years, especially as decision-making is increasingly performed under greater uncertainty. In this paper, we extend the concept of magnitude to rank fuzzy numbers to a more general definition to increase in flexibility and generality. More precisely, we propose a multidimensional approach to rank fuzzy numbers considering alternative magnitude definitions with three novel features: multidimensionality, normalization, and a ranking based on a parametric distance function. A multidimensional magnitude definition allows us to consider multiple attributes to represent and rank fuzzy numbers. Normalization prevents meaningless comparison among attributes due to scaling problems, and the use of the parametric Minkowski distance function becomes a more general and flexible ranking approach. The main contribution of our multidimensional approach is the representation of a fuzzy number as a point in a $n$-dimensional normalized space of attributes in which the distance to the origin is the magnitude value. We illustrate our methodology and provide further insights into different normalization approaches and parameters through several numerical examples. Finally, we describe an application of our ranking approach to a multicriteria decision-making problem within an economic context in which the main goal is to rank a set of credit applicants considering different financial ratios used as evaluation criteria

A multicriteria approach to manage credit risk under strict uncertainty

[EN] Assessing the ability of applicants to repay their loans is generally recognized as a critical task in credit risk management. Credit managers rely on financial and market information, usually in the form of ratios, to estimate the quality of credit applicants. However, there is no guarantee that a given set of ratios contains the information needed for credit classification. Decision rules under strict uncertainty aim to mitigate this drawback. In this paper, we propose the use of a moderate pessimism decision rule combined with dimensionality reduction techniques and compromise programming. Moderate pessimism ensures that neither extreme optimistic nor pessimistic decisions are taken. Dimensionality reduction from a set of ratios facilitates the extraction of the relevant information. Compromise programming allows to find a balance between quality of debt and risk concentration. Our model produces two critical outputs: a quality assessment and the optimum allocation of funds. To illustrate our multicriteria approach, we include a case study on 29 firms listed in the Spanish stock market. Our results show that dimensionality reduction contributes to avoid redundancy and that quality-diversification optimization is able to produce budget allocations with a reduced number of firms.Pla Santamaría, D.; Bravo Selles, M.; Reig-Mullor, J.; Salas-Molina, F. (2021). A multicriteria approach to manage credit risk under strict uncertainty. Top. 29(2):494-523. https://doi.org/10.1007/s11750-020-00571-0S494523292Abdi H, Williams LJ (2010) Principal component analysis. Wiley Interdiscip Reviews Comput Stat 2(4):433–459Adams W, Einav L, Levin J (2009) Liquidity constraints and imperfect information in subprime lending. Am Econ Rev 99(1):49–84Altman EI (1968) Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. 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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

Inverse Malthusianism and Recycling Economics: The Case of the Textile Industry

[EN] The current use of natural resources in the textile industry leads us to introduce a new economic concept called inverse Malthusianism describing a context in which population grows linearly and resource consumption grows exponentially. Inverse Malthusianism implies an exponential increase in environmental impact that recycling may contribute to reduce. Our main goal is to extend the analysis of materials selection under the principle of equimarginality proposed by Jevons. As a first result, we show the particular circumstances under which policies excluding recycled supplies are never optimal. We also aim to overcome the difficulties of reducing environmental aspects to monetary units. To this end, we propose a multicriteria approach to solve the conventional-recycled materials dilemma considering not only economic but also environmental criteria. Then, we allow producers to enrich their decision-making process with relevant information about the environmental impact of materials selection. Although we use examples of the textile industry to illustrate our results, most of the insights in this paper can be extended to other industries.Salas-Molina, F.; Pla Santamaría, D.; Vercher-Ferrandiz, ML.; Reig-Mullor, J. (2020). Inverse Malthusianism and Recycling Economics: The Case of the Textile Industry. Sustainability. 12(14):1-20. https://doi.org/10.3390/su12145861S1201214Chapagain, A. K., Hoekstra, A. Y., Savenije, H. H. G., & Gautam, R. (2006). The water footprint of cotton consumption: An assessment of the impact of worldwide consumption of cotton products on the water resources in the cotton producing countries. Ecological Economics, 60(1), 186-203. doi:10.1016/j.ecolecon.2005.11.027Esteve-Turrillas, F. A., & de la Guardia, M. (2017). Environmental impact of Recover cotton in textile industry. Resources, Conservation and Recycling, 116, 107-115. doi:10.1016/j.resconrec.2016.09.034McInerney, J. (1976). THE SIMPLE ANALYTICS OF NATURAL RESOURCE ECONOMICS. Journal of Agricultural Economics, 27(1), 31-52. doi:10.1111/j.1477-9552.1976.tb00964.xRomero, C. (2012). Short communication. Economics of natural resources: in search of a unified theoretical framework. Spanish Journal of Agricultural Research, 10(1), 29. doi:10.5424/sjar/2012101-329-11Sandin, G., & Peters, G. M. (2018). Environmental impact of textile reuse and recycling – A review. Journal of Cleaner Production, 184, 353-365. doi:10.1016/j.jclepro.2018.02.266Leal Filho, W., Ellams, D., Han, S., Tyler, D., Boiten, V. J., Paço, A., … Balogun, A.-L. (2019). A review of the socio-economic advantages of textile recycling. Journal of Cleaner Production, 218, 10-20. doi:10.1016/j.jclepro.2019.01.210Hotelling, H. (1931). The Economics of Exhaustible Resources. Journal of Political Economy, 39(2), 137-175. doi:10.1086/254195Solow, R. M. (1974). Intergenerational Equity and Exhaustible Resources. The Review of Economic Studies, 41, 29. doi:10.2307/2296370Thampapillai, D. J. (1985). Trade-offs for conflicting social objectives in the extraction of finite energy resources. International Journal of Energy Research, 9(2), 179-192. doi:10.1002/er.4440090209Stahel, W. R. (2016). The circular economy. Nature, 531(7595), 435-438. doi:10.1038/531435aGeissdoerfer, M., Savaget, P., Bocken, N. M. P., & Hultink, E. J. (2017). The Circular Economy – A new sustainability paradigm? Journal of Cleaner Production, 143, 757-768. doi:10.1016/j.jclepro.2016.12.048Ayres, R. U. (1997). Metals recycling: economic and environmental implications. Resources, Conservation and Recycling, 21(3), 145-173. doi:10.1016/s0921-3449(97)00033-5Ljungberg, L. Y. (2007). Materials selection and design for development of sustainable products. Materials & Design, 28(2), 466-479. doi:10.1016/j.matdes.2005.09.006Garcia-Bernabeu, A., Hilario-Caballero, A., Pla-Santamaria, D., & Salas-Molina, F. (2020). A Process Oriented MCDM Approach to Construct a Circular Economy Composite Index. Sustainability, 12(2), 618. doi:10.3390/su12020618Scott, A. D. (1953). Notes on User Cost. The Economic Journal, 63(250), 368. doi:10.2307/2227129Romero, C. (1997). Multicriteria decision analysis and environmental economics: An approximation. European Journal of Operational Research, 96(1), 81-89. doi:10.1016/s0377-2217(96)00118-xLaitala, K., Klepp, I., & Henry, B. (2018). Does Use Matter? Comparison of Environmental Impacts of Clothing Based on Fiber Type. Sustainability, 10(7), 2524. doi:10.3390/su10072524Materials Sustainability Indexhttps://msi.higg.orgAlcott, B. (2005). Jevons’ paradox. Ecological Economics, 54(1), 9-21. doi:10.1016/j.ecolecon.2005.03.020Roy, J. (2000). The rebound effect: some empirical evidence from India. Energy Policy, 28(6-7), 433-438. doi:10.1016/s0301-4215(00)00027-6Cambra‐Fierro, J., & Ruiz‐Benitez, R. (2009). Advantages of intermodal logistics platforms: insights from a Spanish platform. Supply Chain Management: An International Journal, 14(6), 418-421. doi:10.1108/1359854091099518