Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system

The fuzzy operations on fuzzy numbers of type L-R are much easier than general fuzzy numbers. It would be interesting to approximate a fuzzy number by a fuzzy number of type L-R. In this paper, we state and prove two significant application inequalities in the monotonic functions set. These inequalities show that under a condition, the nearest fuzzy number of type L-R to an arbitrary fuzzy number exists and is unique. After that, the nearest fuzzy number of type L-R can be obtained by solving a linear system. Note that the trapezoidal fuzzy numbers are a particular case of the fuzzy numbers of type L-R. The proposed method can represent the nearest trapezoidal fuzzy number to a given fuzzy number. Finally, to approximate fuzzy solutions of a fuzzy linear system, we apply our idea to construct a framework to find solutions of crisp linear systems instead of the fuzzy linear system. The crisp linear systems give the nearest fuzzy numbers of type L-R to fuzzy solutions of a fuzzy linear system. The proposed method is illustrated with some examples

A new lexicographical approach for ranking fuzzy numbers

In the literature many ranking methods have been proposed for comparing the fuzzy numbers, most of them suffer from plenty of shortcomings such as complex calculations, inconsistency with human intuition. To overcome such shortcomings, a new ranking method is proposed for L-R flat fuzzy numbers which is based on the lexicographical ordering approach. It is shown that proposed ranking method satisfies all the reasonable properties of the ordering fuzzy quantities proposed by Wang & Kerre (Fuzzy Sets and Systems 118(2001) 375-385). Finally a comprehensive comparison is done between the existing ranking methods with the proposed one to demonstrate the effectiveness of the proposed ranking method. Keywords: Ranking method, L-R flat fuzzy number

Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy Numbers

In this article we present the following definition which is natural combination of the definition for asymptotically equivalent and lacunary statistical convergence of fuzzy numbers. Let =(k_{r}) be a lacunary sequence. The two sequnces X = (X_{k}) and Y=(Y_{k}) of fuzzy numbers are said to be asymptotically lacunary statistical equivalent to multiple L provided that for every >0lim_{r}(1/(h_{r}))|{k∈I_{r}:d(((X_{k})/(Y_{k})),L)≥}|=0

Comparison of two kinds of fuzzy arithmetic, LR and OFN, applied to fuzzy observation of the cofferdam water level

This paper presents certain important aspects of the fuzzy logic extension, one of which is OFN. It includes basic definitions of that discipline. It also compares fuzzy logic arithmetic with the arithmetic of ordered fuzzy numbers in L-R notation. Computational experiments were based on fuzzy observation of the impounding basin. The results of the study show that there is a connection between the order of OFN number and trend of changes in the environment. The experiment was carried out using computer software developed specially for that purpose. When comparing the arithmetic of fuzzy numbers in L-R notation with the arithmetic of ordered fuzzy numbers on the grounds of the experiment, it has been concluded that with fuzzy numbers it is possible to expand the scope of solutions in comparison to fuzzy numbers in classic form. The symbol of OFN flexibility is the possibility to determine the X number that always satisfies the equation A+X=C, regardless of the value of arguments. Operations performed on OFN are less complicated, as they are performed in the same way regardless the sign of the input data and their results are more accurate in the majority of cases. The promising feature of ordered fuzzy numbers is their lack of rapidly growing fuzziness. Authors expect to see implication of that fact in practice in the near future

Computing the Performance Parameters of the Markovian Queueing System FM/FM/1 In Transient State

In this chapter, we utilize L–R method to calculate the parameters of performance of fuzzy Markovian queueing system FM/FM/1 in transient regime. The technique of calculating used is the arithmetic of L–R fuzzy numbers restricted to secant approximations. The membership function has helped us to represent graphically the curves of fuzzy parameters of performance into the space in three dimensions in transient regime in fuzzy environment. An illustrative example is given in the medical field to show the relevance of this study in operational research and in particular in queueing systems

Genetic Algorithm for Fuzzy Neural Networks using Locally Crossover

Fuzzy feed-forward (FFNR) and fuzzy recurrent networks (FRNN) proved to be solutions for "real world problems". In the most cases, the learning algorithms are based on gradient techniques adapted for fuzzy logic with heuristic rules in the case of fuzzy numbers. In this paper we propose a learning mechanism based on genetic algorithms (GA) with locally crossover that can be applied to various topologies of fuzzy neural networks with fuzzy numbers. The mechanism is applied to FFNR and FRNN with L-R fuzzy numbers as inputs, outputs and weights and fuzzy arithmetic as forward signal propagation. The α-cuts and fuzzy biases are also taken into account. The effectiveness of the proposed method is proven in two applications: the mapping a vector of triangular fuzzy numbers into another vector of triangular fuzzy numbers for FFNR and the dynamic capture of fuzzy sinusoidal oscillations for FRNN

Economic-mathematical modeling of the total costs of innovative chemical enterprise methods of fuzzy set theory

© Medwell Journals, 2017. Three approaches is suggested to determining the total cost of innovative chemical enterprise in the face of uncertainty. This approach is based on the discrete fuzzy numbers gives more accurate results than approaches based on continuous fuzzy numbers solutions through a-sections and the number of L-R-type. Uncertainty intervals for all three solutions are the same

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. International Journal of Approximate Reasoning, 19(3-4), 391-417. doi:10.1016/s0888-613x(98)10017-8Medaglia, A. L., Fang, S.-C., Nuttle, H. L. W., & Wilson, J. R. (2002). An efficient and flexible mechanism for constructing membership functions. European Journal of Operational Research, 139(1), 84-95. doi:10.1016/s0377-2217(01)00157-6Mikhailov, L. (2003). Deriving priorities from fuzzy pairwise comparison judgements. Fuzzy Sets and Systems, 134(3), 365-385. doi:10.1016/s0165-0114(02)00383-4Appadoo, S. S. (2014). Possibilistic Fuzzy Net Present Value Model and Application. Mathematical Problems in Engineering, 2014, 1-11. doi:10.1155/2014/865968Mikhailov, L., & Tsvetinov, P. (2004). Evaluation of services using a fuzzy analytic hierarchy process. Applied Soft Computing, 5(1), 23-33. doi:10.1016/j.asoc.2004.04.001Hepu Deng. (1999). Multicriteria analysis with fuzzy pairwise comparison. FUZZ-IEEE’99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315). doi:10.1109/fuzzy.1999.793038Van Laarhoven, P. J. M., & Pedrycz, W. (1983). A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems, 11(1-3), 229-241. doi:10.1016/s0165-0114(83)80082-7Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 17(3), 233-247. doi:10.1016/0165-0114(85)90090-9Chang, D.-Y. (1996). Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95(3), 649-655. doi:10.1016/0377-2217(95)00300-2Enea, M., & Piazza, T. (2004). Project Selection by Constrained Fuzzy AHP. Fuzzy Optimization and Decision Making, 3(1), 39-62. doi:10.1023/b:fodm.0000013071.63614.3dKrejčí, J., Pavlačka, O., & Talašová, J. (2016). A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic. Fuzzy Optimization and Decision Making, 16(1), 89-110. doi:10.1007/s10700-016-9241-0Cakir, O., & Canbolat, M. S. (2008). A web-based decision support system for multi-criteria inventory classification using fuzzy AHP methodology. Expert Systems with Applications, 35(3), 1367-1378. doi:10.1016/j.eswa.2007.08.041Isaai, M. T., Kanani, A., Tootoonchi, M., & Afzali, H. R. (2011). Intelligent timetable evaluation using fuzzy AHP. Expert Systems with Applications, 38(4), 3718-3723. doi:10.1016/j.eswa.2010.09.030Büyüközkan, G., & Güleryüz, S. (2016). A new integrated intuitionistic fuzzy group decision making approach for product development partner selection. Computers & Industrial Engineering, 102, 383-395. doi:10.1016/j.cie.2016.05.038Zheng, G., Zhu, N., Tian, Z., Chen, Y., & Sun, B. (2012). Application of a trapezoidal fuzzy AHP method for work safety evaluation and early warning rating of hot and humid environments. Safety Science, 50(2), 228-239. doi:10.1016/j.ssci.2011.08.042Calabrese, A., Costa, R., & Menichini, T. (2013). Using Fuzzy AHP to manage Intellectual Capital assets: An application to the ICT service industry. Expert Systems with Applications, 40(9), 3747-3755. doi:10.1016/j.eswa.2012.12.081Ishizaka, A., & Nguyen, N. H. (2013). Calibrated fuzzy AHP for current bank account selection. Expert Systems with Applications, 40(9), 3775-3783. doi:10.1016/j.eswa.2012.12.089Somsuk, N., & Laosirihongthong, T. (2014). A fuzzy AHP to prioritize enabling factors for strategic management of university business incubators: Resource-based view. Technological Forecasting and Social Change, 85, 198-210. doi:10.1016/j.techfore.2013.08.007Chan, H. K., Wang, X., & Raffoni, A. (2014). An integrated approach for green design: Life-cycle, fuzzy AHP and environmental management accounting. The British Accounting Review, 46(4), 344-360. doi:10.1016/j.bar.2014.10.004Tan, R. R., Aviso, K. B., Huelgas, A. P., & Promentilla, M. A. B. (2014). 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. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 26(03), 475-491. doi:10.1142/s021848851850023xAkbar, M. A., Shameem, M., Mahmood, S., Alsanad, A., & Gumaei, A. (2020). Prioritization based Taxonomy of Cloud-based Outsource Software Development Challenges: Fuzzy AHP analysis. Applied Soft Computing, 95, 106557. doi:10.1016/j.asoc.2020.106557Jung, H. (2011). A fuzzy AHP–GP approach for integrated production-planning considering manufacturing partners. Expert Systems with Applications, 38(5), 5833-5840. doi:10.1016/j.eswa.2010.11.039Shaw, K., Shankar, R., Yadav, S. S., & Thakur, L. S. (2012). Supplier selection using fuzzy AHP and fuzzy multi-objective linear programming for developing low carbon supply chain. Expert Systems with Applications, 39(9), 8182-8192. doi:10.1016/j.eswa.2012.01.149Abdullah, L., & Zulkifli, N. (2015). Integration of fuzzy AHP and interval type-2 fuzzy DEMATEL: An application to human resource management. Expert Systems with Applications, 42(9), 4397-4409. doi:10.1016/j.eswa.2015.01.021Akkaya, G., Turanoğlu, B., & Öztaş, S. (2015). An integrated fuzzy AHP and fuzzy MOORA approach to the problem of industrial engineering sector choosing. Expert Systems with Applications, 42(24), 9565-9573. doi:10.1016/j.eswa.2015.07.061Kutlu, A. C., & Ekmekçioğlu, M. (2012). Fuzzy failure modes and effects analysis by using fuzzy TOPSIS-based fuzzy AHP. Expert Systems with Applications, 39(1), 61-67. doi:10.1016/j.eswa.2011.06.044Büyüközkan, G., & Çifçi, G. (2012). A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic service quality in healthcare industry. Expert Systems with Applications, 39(3), 2341-2354. doi:10.1016/j.eswa.2011.08.061Taylan, O., Bafail, A. O., Abdulaal, R. M. S., & Kabli, M. R. (2014). Construction projects selection and risk assessment by fuzzy AHP and fuzzy TOPSIS methodologies. Applied Soft Computing, 17, 105-116. doi:10.1016/j.asoc.2014.01.003Patil, S. K., & Kant, R. (2014). A fuzzy AHP-TOPSIS framework for ranking the solutions of Knowledge Management adoption in Supply Chain to overcome its barriers. Expert Systems with Applications, 41(2), 679-693. doi:10.1016/j.eswa.2013.07.093Sun, L., Ma, J., Zhang, Y., Dong, H., & Hussain, F. K. (2016). Cloud-FuSeR: Fuzzy ontology and MCDM based cloud service selection. Future Generation Computer Systems, 57, 42-55. doi:10.1016/j.future.2015.11.025Ar, I. M., Erol, I., Peker, I., Ozdemir, A. I., Medeni, T. D., & Medeni, I. T. (2020). Evaluating the feasibility of blockchain in logistics operations: A decision framework. Expert Systems with Applications, 158, 113543. doi:10.1016/j.eswa.2020.113543Yalcin, N., Bayrakdaroglu, A., & Kahraman, C. (2012). Application of fuzzy multi-criteria decision making methods for financial performance evaluation of Turkish manufacturing industries. Expert Systems with Applications, 39(1), 350-364. doi:10.1016/j.eswa.2011.07.024Chang, S.-C., Tsai, P.-H., & Chang, S.-C. (2015). A hybrid fuzzy model for selecting and evaluating the e-book business model: A case study on Taiwan e-book firms. Applied Soft Computing, 34, 194-204. doi:10.1016/j.asoc.2015.05.011Li, N., & Zhao, H. (2016). Performance evaluation of eco-industrial thermal power plants by using fuzzy GRA-VIKOR and combination weighting techniques. Journal of Cleaner Production, 135, 169-183. doi:10.1016/j.jclepro.2016.06.113Mandic, K., Delibasic, B., Knezevic, S., & Benkovic, S. (2014). Analysis of the financial parameters of Serbian banks through the application of the fuzzy AHP and TOPSIS methods. Economic Modelling, 43, 30-37. doi:10.1016/j.econmod.2014.07.036Li, Y., Liu, X., & Chen, Y. (2012). Supplier selection using axiomatic fuzzy set and TOPSIS methodology in supply chain management. Fuzzy Optimization and Decision Making, 11(2), 147-176. doi:10.1007/s10700-012-9117-xKaya, Ö., Alemdar, K. D., & Çodur, M. Y. (2020). A novel two stage approach for electric taxis charging station site selection. Sustainable Cities and Society, 62, 102396. doi:10.1016/j.scs.2020.102396Chen, J.-F., Hsieh, H.-N., & Do, Q. H. (2015). Evaluating teaching performance based on fuzzy AHP and comprehensive evaluation approach. Applied Soft Computing, 28, 100-108. doi:10.1016/j.asoc.2014.11.050Javanbarg, M. B., Scawthorn, C., Kiyono, J., & Shahbodaghkhan, B. (2012). Fuzzy AHP-based multicriteria decision making systems using particle swarm optimization. Expert Systems with Applications, 39(1), 960-966. doi:10.1016/j.eswa.2011.07.095Che, Z. H., Wang, H. S., & Chuang, C.-L. (2010). A fuzzy AHP and DEA approach for making bank loan decisions for small and medium enterprises in Taiwan. Expert Systems with Applications, 37(10), 7189-7199. doi:10.1016/j.eswa.2010.04.010Krejčí, J. (2015). Additively reciprocal fuzzy pairwise comparison matrices and multiplicative fuzzy priorities. Soft Computing, 21(12), 3177-3192. doi:10.1007/s00500-015-2000-2Xu, Z., & Liao, H. (2014). Intuitionistic Fuzzy Analytic Hierarchy Process. IEEE Transactions on Fuzzy Systems, 22(4), 749-761. doi:10.1109/tfuzz.2013.2272585Mikhailov, L. (2000). A fuzzy programming method for deriving priorities in the analytic hierarchy process. Journal of the Operational Research Society, 51(3), 341-349. doi:10.1057/palgrave.jors.260089

FLIP - Multiobjective Fuzzy Linear Programming Package

FLIP (Fuzzy LInear Programming) is a package designed to help in analysis of multiobjective linear programming (MOLP) problems in an uncertain environment. The uncertainty of data is modeled by L-R type fuzzy numbers. They can appear in the objective functions as well as on the both sides of the constraints. The input data to the FLIP package include the characteristics of the analyzed fuzzy MOLP problem, i.e., the number of criteria, constraints and decision variables, fuzzy cost coefficients for every objective and fuzzy coefficients of LHS and RHS for all constraints. The data loading is supported by a graphical presentation of fuzzy coefficients. The calculation is preceded by a transformation of the fuzzy MOLP problem into a multiobjective linear fractional program. It is then solved with an interactive method using a linear programming procedure as the only optimiser. In every iteration, one gets a series of solutions that are presented very clearly in a graphical and numerical form. In FLIP, interaction with the user takes place at two levels: first, when safety parameters have to be defined in the transformation phase, and second, when the associate deterministic problem is solved. The package is written in TURBO-Pascal and can be used on microcomputers compatible with IBM-PC XT/AT with hard disc and a graphic card

Some questions in fuzzy metric spaces

The George and Veeramani's fuzzy metric defined by $M^*(x,y,t)=\frac{min\{x,y\}+t}{max\{x,y\}+t}$ on $[0,\infty[$ (the set of non-negative real numbers) has shown some advantages in front of classical metrics in the process of filtering images. In this paper we study from the mathematical point of view this fuzzy metric and other fuzzy metrics related to it. As a consequence of this study we introduce, throughout the paper, some questions relative to fuzzy metrics. Also, as another practical application, we show that this fuzzy metric is useful for measuring perceptual colour differences between colour samples.The authors wish to thank both the associated editors coordinating this submission and the reviewers for their insightful suggestions and comments which have been useful to increase the scientific quality and presentation of the paper. Also, the authors thank Dr. M. Melgosa, Dr. R. Huertas and Dr. L. Gomez-Robledo from the Department of Optics of University of Granada, for providing data, information and invaluable comments and suggestions. Valentin Gregori and Samuel Morillas acknowledge the support of Spanish Ministry of Education and Science under Grant MTM 2009-12872-C02-01. Samuel Morillas acknowledges the support of Research Project FIS2010-19839, Ministerio de Educacion y Ciencia (Espana) with European Regional Development Funds (ERDFs).Gregori Gregori, V.; Miñana Prats, JJ.; Morillas Gómez, S. (2012). Some questions in fuzzy metric spaces. Fuzzy Sets and Systems. 204:71-85. https://doi.org/10.1016/j.fss.2011.12.008718520