MULTI-CRITERIONAL CHOICE OF AN ALTERNATIVE UNDER THE RULES OF FUZZY PRODUCTS WITH SOME RELIABILITY DEGREE
Abstract
One of the main problems of decision-making tasks is the need to take into account subjective expert assessments, the complete consistency of which is rare, and the choice of the best alternative. The complexity of the connections between the many-sided aspects of the decision-making situation and the lack of an accurate forecast of the consequences leads to the fact that when assessing and choosing alternatives, it is possible, and often necessary, to use and process qualitatively fuzzy estimates. In decision-making situations, when at least one of the elements (outcomes, criteria, preferences, expert opinions, etc.) is described qualitatively, indistinctly, there are problems of multi-criteria decision-making with fuzzy initial information.
Let’s consider the solution to the problem of multi-criteria choice based on the rules of fuzzy conditional inference, which have the form of fuzzy statements, the conditions and conclusions of which, along with expert assessments of the criteria, are presented in the form of interval fuzzy numbers of the second type (IT2FN). The convolution of private implications in each statement is made according to Lukasiewicz's rule. To reduce the type and defuzzify the resulting IT2FN, the Karrnik-Mendel algorithm was used to construct the minimum and maximum centroids of nested fuzzy sets of the first type, which give an estimate of the utility interval for each alternative. To refine the obtained utility estimates, under conditions of incomplete definiteness of statements, using the generalized Bayesian inference mechanism, adjusted estimates of the utility intervals of alternatives are constructed. By comparing these intervals, a larger interval is determined and the corresponding alternative is taken as a solution to the problem under consideration.
The application of the proposed approach to solving the problem of multicriteria selection of the most corroded section of a gas pipeline with ambiguous expert opinions is shown. To date, specific practical and theoretical results have been obtained for decision-making problems with fuzzy initial information
Downloads
References
Borisov, A. N., Alekseev, A. V., Merkur'eva, G. V. (1989). Obrabotka nechetkoy informatsii v sistemah prinyatiya resheniy. Moscow: Radio i svyaz', 304.
Borisov, A. I., Krumberg, O. A., Fedorov, I. P. (1990). Prinyatie resheniy na osnove nechetkih modeley. Primery ispol'zovaniya. Riga: Zinatne, 184.
Yager, R. R. (1977). Multiple objective decision-making using fuzzy sets. International Journal of Man-Machine Studies, 9 (4), 375–382. doi: https://doi.org/10.1016/s0020-7373(77)80008-4
Yager, R. R. (1984). General multiple-objective decision functions and linguistically quantified statements. International Journal of Man-Machine Studies, 21 (5), 389–400. doi: https://doi.org/10.1016/s0020-7373(84)80066-8
Loktyuhin, V. N., Mal'chenko, S. I., Cherepnin, A. A. (2009). Osnovy matematicheskogo obespecheniya podderzhki diagnosticheskih resheniy v biotekhnicheskih sistemah s ispol'zovaniem nechetkoy logiki. Ryazan': RGRTU, 64.
Gabibov, I. A., Dyshin, O. A., Agammedova, S. A. (2015). Kompleksnaya otsenka skorosti korrozionnyh protsessov v gazoprovode na osnove tekhnologii nechetkoy logiki. Gazovaya promyshlennost', 724, 99–104.
Dyshin, O. A., Yahyaeva, A. N. (2016). Selection based best alternative fuzzy inference interval of fuzzy sets of the second type. Herald of the Azerbaijan Engineering Academy, 8 (2), 87–95.
Veliyev, R. G., Dyshin, O. A. (2016). Linguistic model of decision making process for education system based on interval fuzzy sets II. Herald of the Azerbaijan Engineering Academy, 8 (4), 68–82.
Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning-III. Information Sciences, 9 (1), 43–80. doi: https://doi.org/10.1016/0020-0255(75)90017-1
Liang, Q., Mendel, J. M. (2000). Interval type-2 fuzzy logic systems: theory and design. IEEE Transactions on Fuzzy Systems, 8 (5), 535–550. doi: https://doi.org/10.1109/91.873577
Castillo, O., Melin, P. (2007). 12 Design of Fuzzy Inference Systems with the Interval Type-2 Fuzzy Logic Toolbox. Studies in Fuzziness and Soft Computing, 145–154. doi: https://doi.org/10.1007/978-3-540-76284-3_12
Castro, J. R., Castillo, O., Martinez, L. G. (2007). Interval Type-2 Fuzzy Logic Toolbox. Engineering Letters, 15 (1). Available at: http://www.engineeringletters.com/issues_v15/issue_1/EL_15_1_14.pdf
Liu, Z.-Q., Liu, Y.-K. (2010). Type-2 fuzzy variables and their arithmetic. Soft Computing, 14 (7), 729–747. doi: https://doi.org/10.1007/s00500-009-0461-x
Kahraman, C., Öztayşi, B., Uçal Sarı, İ., Turanoğlu, E. (2014). Fuzzy analytic hierarchy process with interval type-2 fuzzy sets. Knowledge-Based Systems, 59, 48–57. doi: https://doi.org/10.1016/j.knosys.2014.02.001
Mendel, J. M. (2017). Uncertain Rule-Based Fuzzy Systems. Introduction and New Directions. Springer. doi: https://doi.org/10.1007/978-3-319-51370-6
Chen, T.-Y., Tsao, C.-Y. (2008). The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets and Systems, 159 (11), 1410–1428. doi: https://doi.org/10.1016/j.fss.2007.11.004
Zhang, X., Xu, Z. (2014). Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets. International Journal of Intelligent Systems, 29 (12), 1061–1078. doi: https://doi.org/10.1002/int.21676
Yaakob, A. M., Gegov, A., Abdul Rahman, S. F. (2018). Selection of alternatives using fuzzy networks with rule base aggregation. Fuzzy Sets and Systems, 341, 123–144. doi: https://doi.org/10.1016/j.fss.2017.05.027
Karnik, N. N., Mendel, J. M. (2001). Centroid of a type-2 fuzzy set. Information Sciences, 132 (1-4), 195–220. doi: https://doi.org/10.1016/s0020-0255(01)00069-x
Verevka, O. V., Zalozhenkova, I. A., Parasyuk, I. N. (2000). Interval'nye bayesovskie mekhanizmy vyvoda i ih prilozheniya. Problemy programmirovaniya, 1-2, 467–470.
Verevka, O. V., Zalozhenkova, I. A., Parasyuk, I. N. (1998). Obobshchenie interval'nyh bayesovskih mekhanizmov vyvoda i perspektivy ih ispol'zovaniya. Kibernetika i sistemniy analiz, 6, 3–13.
Levin, V. I. (2016). Analysis of Interval Functions by Methods of Interval Differential Calculus. Systems of Control, Communication and Security, 1, 335–350.
Copyright (c) 2021 Ibrahim Abulfaz Habibov, Oleg Dyshin, Sevda Alipasha Аghаmmadova, Irada Sabir Hasanzade
This work is licensed under a Creative Commons Attribution 4.0 International License.
Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.
