PRIORITIZATION OF ALTERNATIVES BASED ON ANALYTIC HIERARCHY PROCESS USING INTERVAL TYPE-2 FUZZY SETS AND PROBABILITY-THEORETICAL INTERVAL COMPARISON

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Published Dec 6, 2018
Konstantin Yury Degtiarev Mikhail Yury Borisov

Abstract

The Analytic Hierarchy Process (AHP) enables decision-makers to prioritize alternatives. However, when an expert expresses judgments using natural language statements (e.g. words or phrases) inherent vagueness of language constructs can cause the interpretation to be imprecise. The fuzzy Analytic Hierarchy Process (FAHP) can be viewed in the context of the classical AHP expansion. While performing pairwise comparisons domain experts are accustomed to operating with verbal terms in their judgments. Most existing FAHP approaches do not consider a human’s confidence in the estimates provided. This paper presents a model that gives weight to the constraints on domains of expert assessments as they are almost always supplied with certain degrees of confidence. Interval type-2 membership functions (IT2MF) along with the probability-theoretical procedure for comparison of intervals can be applied here as suitable modeling options. Empirical comparison of FAHP that makes use of triangular fuzzy numbers and IT2MF-based FAHP is also presented.   

How to Cite

Degtiarev, K. Y., & Borisov, M. Y. (2018). PRIORITIZATION OF ALTERNATIVES BASED ON ANALYTIC HIERARCHY PROCESS USING INTERVAL TYPE-2 FUZZY SETS AND PROBABILITY-THEORETICAL INTERVAL COMPARISON. International Journal of the Analytic Hierarchy Process, 10(3). https://doi.org/10.13033/ijahp.v10i3.586

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Keywords

Analytic Hierarchy Process, expert assessment, degree of confidence, fuzzy logic, linguistic label, type-1 membership function, interval type-2 membership function, Fuzzy Synthetic Extents, interval calculations, threshold values, prioritizing alternatives

References
Abdullah, L., & Najib, L. (2014). A new type-2 fuzzy set of linguistic variables for the Fuzzy Analytic Hierarchy Process. Expert Systems with Applications, 41(7), 3297 – 3305. Doi: https://doi.org/10.1016/j.eswa.2013.11.028

Ahmed, F., & K?l?ç, K. (2015). Modification to fuzzy extent analysis method and its performance analysis. Proceedings of the 6th International Conference on Industrial Engineering and Systems Management (IESM), 435 – 438. Doi: https://doi.org/10.1109/IESM.2015.7380193

Ahmed, F., & K?l?ç, K. (2018). Fuzzy Analytic Hierarchy Process: A performance analysis of different algorithms. Fuzzy Sets and Systems, Doi: https://doi.org/10.1016/j.fss.2018.08.009.

Azadeh, A., Saberi, M., Atashbar, N.Z., Chang, E., & Pazhoheshfar, P. (2013). Z-AHP: A z-number extension of Fuzzy Analytical Hierarchy Process. Proceedings of the 7th IEEE International Conference on Digital Ecosystems and Technologies, 141–147. Doi: https://doi.org/10.1109/DEST.2013.6611344

Bellman, R., & Zadeh, L.A. (1970). Decision-making in fuzzy environment. Management Science, 17(4), B141 – B164. Doi: https://doi.org/10.1287/mnsc.17.4.B141

Buckley, J.J. (1985). Fuzzy hierarchical analysis, Fuzzy Sets and Systems, 17, 233 – 247. Doi: https://doi.org/10.1016/0165-0114(85)90090-9

Bustince, H., Fernandez, J., Hagras, H., Herrera, F., Pagola, M., & Barrenechea, E. (2015). Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: Towards a wider view on their relationship. IEEE Trans. on Fuzzy Systems, 23(5), 1876 – 1882. Doi: https://doi.org/10.1109/TFUZZ.2014.2362149

Chang, D.Y. (1992). Extent analysis and synthetic decision. Optimization Techn. and Applications, 1, 352 – 355.

Chang, D.Y. (1996). Applications of the Extent Analysis Method on fuzzy AHP. European Journal of Operational Research, 95(3), 649 – 655. Doi: https://doi.org/10.1016/0377-2217(95)00300-2

Chen, S.M., & Lee, L.-W. (2010). Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Systems with Applications, 37, 824 – 833. Doi: https://doi.org/10.1016/j.eswa.2009.06.094

Chen, S.-M., Yang, M.-W., Lee, L.-W., & Yang, S.-W. (2012). Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets. Expert Systems with Applications, 39, 5295 – 5308. Doi: https://doi.org/10.1016/j.eswa.2011.11.008

Chiao, K.-P. (2016). The multi-criteria group decision making methodology using type-2 fuzzy linguistic judgments. Applied Soft Computing, 49, 189 – 211. Doi: https://doi.org/10.1016/j.asoc.2016.07.050

Fine, K. (1975). Vagueness, truth and logic. Synthese, 30(3-4), 265 – 300. Doi: https://doi.org/10.1007/BF00485047

Gimaletdinova, A.R., & Degtiarev, K.Y. (2017). Type-2 fuzzy rule-based model of urban metro positioning service. Proceedings of the Institute for System Programming (ISP RAS), 29(4), 87 – 106. Doi: 10.15514/ISPRAS-2017-29(4)-6

de Graan, J.G. (1980). Extensions of the multiple criteria analysis method of T. L. Saaty. Tech. Report 80-3. Leidschendam, the Netherlands : National Institute for Water Supply,.

Kabir, G., & Hasin, M.A.A. (2011). Comparative analysis of AHP and fuzzy AHP models for multicriteria inventory classification. International Journal of Fuzzy Logic Systems (IJFLS), 1(1), 1 – 16.

Kahneman, D. (2013). Thinking, fast and slow. New York: Farrar, Straus and Giroux.

Kahraman, C., Öztay?i, B., Sar?, I.U., & Turano?lu, 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

Kang, B., Deng Y., & Sadiq R. (2018). Total utility of z-number. Applied Intelligence, 48(3), 703 – 729. Doi: https://doi.org/10.1007/s10489-017-1001-5

Kang, B., Wei, D., Li, Y., & Deng, Y. (2012). A method of converting z-number to classical fuzzy number. Journal of Information and Computational Science, 9(3), 703 – 709.

Keefe, R. (2007). Theories of vagueness. Cambridge, UK: Cambridge University Press.

Klir, G.J., & Yuan, B. (1995). Fuzzy sets and fuzzy logic: Theory and applications. Upper Saddle River, New Jersey: Prentice Hall. Doi: https://doi.org/10.1080/03081079708945184

Krohling, R., Pacheco A.G.C., & Dos Santos, G.A. (2017). TODIM and TOPSIS with z-numbers. In Pan, Y. Lu, X. (Eds). Frontiers of Information Technology & Electronic Engineering. Zhejiang University Press & Springer.

van 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: https://doi.org/10.1016/S0165-0114(83)80082-7

Lootsma, F.A. (1980). Saaty’s priority theory and the nomination of a senior professor in operations research. European Journal of Operational Research, 4(6), 380 – 388. Doi: https://doi.org/10.1016/0377-2217(80)90189-7

Mendel, J.M. (2017). Uncertain rule-based fuzzy systems: Introduction and new directions, 2nd ed. Springer International Publishing. Doi: https://doi.org/10.1007/978-3-319-51370-6_1

Mendel, J.M., & John, R.I. (2002). Type-2 fuzzy sets made simple, IEEE Transactions on Fuzzy Systems, 10(2), 117 – 127. Doi: https://doi.org/10.1109/91.995115

Mendel, J.M., John, R.I. & Liu, F. (2006). Interval type-2 fuzzy logic systems made simple. IEEE Transactions on Fuzzy Systems, 14(6), 808 – 821. Doi: https://doi.org/10.1109/TFUZZ.2006.879986

Mendel, J.M., Hagras, H., Bustince, H., & Herrera, F. (2016). Comments on “Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: Towards a wide view on their relationship”. IEEE Transactions on Fuzzy Systems, 24(1), 249 – 250. Doi: https://doi.org/10.1109/TFUZZ.2015.2446508

Mendel, J.M., Hagras, H., & John, R.I. (n.d.). Standard background material about interval type-2 fuzzy logic systems that can be used by all authors. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.125.4195&rep=rep1&type=pdf

Mendel, J.M., & Wu, H. (2006). Type-2 fuzzistics for symmetric interval
type-2 fuzzy sets: Part 1, forward problems. IEEE Transactions on Fuzzy Systems,
14(6), 781 – 792. Doi: https://doi.org/10.1109/TFUZZ.2006.881441

Nie, M., & Tan, W.W. (2008). Towards an efficient type-reduction method for interval type-2 fuzzy logic systems. Proceedings of IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 1425 – 1432. Doi: https://doi.org/10.1109/FUZZY.2008.4630559

Runkler, T., Chen, C., & John, R. (2018). Type reduction operators for interval type-2 defuzzification. Information Sciences, 467, 464 – 476. Doi: https://doi.org/10.1016/j.ins.2018.08.023

Runkler, T., Coupland, S., & John, R. (2017). Interval type-2 fuzzy decision making. International Journal of Approximate Reasoning, 80, 217 – 224. Doi: https://doi.org/10.1016/j.ijar.2016.09.007

Saaty, R.W. (1987). The Analytic Hierarchy Process – What it is and how it is used. Mathematical Modelling, 9(3-5), 161 – 176. Doi: https://doi.org/10.1016/0270-0255(87)90473-8

Saaty, T.L. (1980). The Analytic Hierarchy Process: Planning, priority setting, resource allocation (Decision-Making Series). McGraw-Hill Publ. (Russian translation: ????? ?. (1993). ???????? ???????. ????? ??????? ????????. ?.: ????? ? ?????).

Saaty, T.L. (1994a). Fundamentals of decision making and priority theory with the Analytic Hierarchy Process, 1st ed. Pittsburgh, PA: RWS Publications.

Saaty, T.L. (1994b). Highlights and critical points in the theory and application of the Analytic Hierarchy Process. European Journal of Operational Research, 74(3), 426 – 447. Doi: https://doi.org/10.1016/0377-2217(94)90222-4

Saaty, T.L., & Tran, L.T. (2007). On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process. Mathematical and Computer Modeling, 46(7-8), 962 – 975. Doi: https://doi.org/10.1016/j.mcm.2007.03.022

Sevastianov, P. (2007). Numerical methods for interval and fuzzy number comparison based on probabilistic approach and Dempster-Shafer theory. Information Sciences, 177, 4645 – 4661. Doi: https://doi.org/10.1016/j.ins.2007.05.001

Sevastyanov, P.V., Rog, P., & Venberg A.V. (2002). A constructive numerical method for the comparison of intervals. Proceedings of the 4th International Conference on Parallel Processing and Applied Mathematics (LNCS, 2328, eds, Wyrzykowski, R., et al.), 756 – 761. Doi: https://doi.org/10.1007/3-540-48086-2_84

Shapiro, A.F., & Koissi, M.-C. (2017). Fuzzy logic modifications of the Analytic Hierarchy Process. Insurance: Mathematics and Economics, 75, 189 – 202. Doi: https://doi.org/10.1016/j.insmatheco.2017.05.003

Wang, Y.-M., Luo, Y., & Hua, Z. (2008). On the extent analysis method for fuzzy AHP and its applications. European Journal of Operational Research, 186, 735 – 747. Doi: https://doi.org/10.1016/j.ejor.2007.01.050

Wierman, M.J. (1997). Central values of fuzzy numbers – defuzzification. Information Sciences, 100 (1-4), 207 – 215. Doi: https://doi.org/10.1016/S0020-0255(96)00278-2

Wu, D., & Mendel, J.M. (2007a). Uncertainty measures for interval type-2 fzzy sets. Information Sciences, 177, 5378 – 5393. Doi: https://doi.org/10.1016/j.ins.2007.07.012

Yaakob, A.M., & Gegov, A. (2016). Interactive TOPSIS based group decision making methodology using Z-Numbers. International Journal of Computational Intelligence Systems, 9(2), 311 – 324. Doi: http://dx.doi.org/10.1080/18756891.2016.1150003

Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338 – 353. Doi: https://doi.org/10.1016/S0019-9958(65)90241-X

Zadeh, L.A. (2011). A note on z-numbers. Information Sciences, 181(14), 2923 – 2932. Doi: https://doi.org/10.1016/j.ins.2011.02.022

Zhü, K. (2014). Fuzzy Analytic Hierarchy Process: Fallacy of the popular methods. European Journal of Operational Research, 236, 209 – 217. Doi: https://doi.org/10.1016/j.ejor.2013.10.034
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