INTERVAL-VALUED NEUTROSOPHIC AHP WITH POSSIBILITY DEGREE METHOD
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Abstract
The Analytic Hierarchy Process (AHP) is one of the most widely used methods in multi criteria decision making (MCDM) in many areas. The method has been extended with hesitant fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, and type -2 fuzzy sets etc. These extended methods can consider the vagueness in decision making problems through different definitions of membership functions. Each of them tries to increase the effectiveness of AHP under uncertainty. Decision makers can fully express their judgments through neutrosophic sets (NS) since NS are based on three independent parameters, truthiness (T), indeterminancy (I) and falsity (F), providing a distinction between a ‘relative truth’ and an ‘absolute truth’. In this paper, we employ the possibility degree method for ranking interval numbers in our neutrosophic AHP approach by utilizing NS’ representation power. Besides, we employ interval-valued NS since a larger domain for the definition of T, I, and F is provided. Pairwise comparison matrices can be filled in by using linguistic terms such as weakly more important, moderately more important or extremely important. Then, we obtain the relative importance degrees of criteria by using the possibility degree method. In order to show the effectiveness of our method, a MCDM application is given in energy planning. Comparative and sensitivity analyses are also presented in the paper.
How to Cite
Downloads
##plugins.themes.bootstrap3.article.details##
multi criteria decision making, energy, interval-valued neutrosophic sets, possibility degree method, AHP
Abdel-Basset, M., Mohamed, M., & Smarandache, F. (2018a). An extension of neutrosophic AHP-SWOT analysis for strategic planning and decision-making. Symmetry, 10(4.) Doi:10.3390/sym10040116.
Abdel-Basset, M., Manogaran, G., & Mohamed, M. (2018b). Internet of things (IoT) and its impact on supply chain: A framework for building smart, secure and efficient systems. Future Generation Computer Systems, 86, 614-628. Doi:10.1016/j.future.2018.04.051
Abdel-Basset, M., Mohamed, M., Zhou, Y., & Hezam, I. (2017b). Multi-criteria group decision making based on neutrosophic analytic hierarchy process. Journal of Intelligent and Fuzzy Systems, 33(6), 4055-4066. Doi:10.3233/JIFS-17981.
Abdullah L, Najib L (2016). Integration of interval Type-2 fuzzy sets and analytic hierarchy process: Implication to computational procedures. AIP Conference Proceedings 1750(1), 020019 Doi: 10.1063/1.4954532.
Atanassov KT (1983) Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia.
Biswas P, Pramanik S, Giri BC (2014). A new methodology for neutrosophic multi-attribute decision making with unknown weight information. Neutrosophic Sets and Systems, 3, 42-50.
Bolturk, E., Kahraman, C. (2018) A novel interval-valued neutrosophic AHP with cosine similarity measure. Soft Computing, 22(15), 4941-4958. Doi: https://doi.org/10.1007/s00500-018-3140-y
Buckley, J.J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 34, 187-195.
Buyukozkan G, Feyzioglu O, Gocer F (2016). Evaluation of hospital web services using intuitionistic fuzzy AHP and intuitionistic fuzzy VIKOR. IEEE International Conference on Industrial Engineering and Engineering Management 2016, 607-611. Doi: 10.1109/IEEM.2016.7797947
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
Deepika M, Kannan ASK (2016). Global supplier selection using intuitionistic fuzzy Analytic Hierarchy Process. International Conference on Electrical, Electronics, and Optimization Techniques, ICEEOT 2016, 2390. Doi: 10.1109/ICEEOT.2016.7755122
Erdogan M, Kaya I (2016) Evaluating alternative-fuel busses for public transportation in Istanbul using interval type-2 fuzzy AHP and TOPSIS. Journal of Multiple-Valued Logic and Soft Computing, 26(6), 625-642.
Ilbahar, E., Kara?an, A., Cebi, S., & Kahraman, C. (2018). A novel approach to risk assessment for occupational health and safety using pythagorean fuzzy AHP & fuzzy inference system. Safety Science, 103, 124-136. Doi:10.1016/j.ssci.2017.10.025.
Kahraman C, Bolturk E, Onar SC, Oztaysi B, Goztepe K (2016). Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP. International Journal of the Analytic Hierarchy Process, 8(2), 271-298. Doi: https://doi.org/10.13033/ijahp.v8i2.387
Kahraman, C., Öztay?i, B., Sar?, ?.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
Lee, H-C., Chang, C-T. (2018). Comparative analysis of MCDM methods for ranking renewable energy sources in Taiwan,. Renewable and Sustainable Energy Reviews, 92, 883-896. Doi: https://doi.org/10.1016/j.rser.2018.05.007
Li Y, Wang Y, Liu P (2016). Multiple attribute group decision-making methods based on trapezoidal fuzzy two-dimension linguistic power generalized aggregation operators. Soft Computing, 20(7), 2689-2704. Doi: https://doi.org/10.1007/s00500-015-1668-7
Oztaysi B, Onar SC, Bolturk E, Kahraman C (2015). Hesitant fuzzy analytic hierarchy process. IEEE International Conference on Fuzzy Systems,1-7. Doi: https://doi.org/10.1109/FUZZ-IEEE.2015.7337948
Radwan NM, Senousy MB, Riad AEDM (2016). Neutrosophic AHP Multi Criteria Decision Making Method applied on the selection of learning management system.
International Journal of Advancements in Computing Technology (IJACT), 8(5), 95-105. Doi: https://doi.org/10.1111/exsy.12170
Rivieccio U., (2008). Neutrosophic logics: prospects and problems. Fuzzy Sets Systems 159(14), 1860–1868. Doi: https://doi.org/10.1016/j.fss.2007.11.011
Senvar OA (2018). Systematic customer oriented approach based on hesitant fuzzy AHP for performance assessments of service departments. Advances in Intelligent Systems and Computing, 643,289-300. Doi: https://doi.org/10.1007/978-3-319-66827-7_26
Smarandache F (1998) Neutrosophy neutrosophic probability. set, and logic. Rehoboth: American Research Press.
Smarandache, F. (1995). Neutrosophic logic and set, mss., http://fs.gallup.unm.edu/neutrosophy.htm
Torra V (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems 25,529–539. Doi: https://doi.org/10.1002/int.20418
Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010). Single valued neutrosophic sets. Multispace Multistruct, 4, 410–413.
Wu, J., Huang. H., & Cao, Q. (2013). Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems. Applied Mathematical Modelling. 37(24), 9898-9906. Doi: https://doi.org/10.1016/j.apm.2013.05.035
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
Zeng, J., An, M., & Smith, N. J. (2007). Application of a fuzzy based decision making methodology to construction project risk assessment. International Journal of Project Management, 25(6), 589-600. Doi: https://doi.org/10.1016/j.ijproman.2007.02.006
Zhang HY, Wang JQ, Chen, XH (2014). Interval neutrosophic sets and their application in multicriteria decision-making problems. The Scientific World Journal, 2014, 15. Doi: http://dx.doi.org/10.1155/2014/645953
Zhu B, Xu Z, Zhang R, Hong M (2016). Hesitant analytic hierarchy process. European Journal of Operational Research, 250(2),602-614. Doi: https://doi.org/10.1016/j.ejor.2015.09.063
Copyright of all articles published in IJAHP is transferred to Creative Decisions Foundation (CDF). However, the author(s) reserve the following:
- All proprietary rights other than copyright, such as patent rights.
- The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In case of whole articles, such third parties must obtain permission from CDF as well. However, CDF may grant rights with respect to journal issues as a whole.
- The right to use all or parts of this article in future works of their own, such as lectures, press releases, reviews, textbooks, or reprint books.
- The authors affirm that the article has been neither copyrighted nor published, that it is not being submitted for publication elsewhere, and that if the work is officially sponsored, it has been released for open publication.
The only exception to the statements in the paragraph above is the following: If an article published in IJAHP contains copyrighted material, such as a teaching case, as an appendix, then the copyright (and all commercial rights) of such material remains with the original copyright holder.
CDF will receive permission for publication of copyrighted material in IJAHP. This permission is not transferable to third parties. Permission to make electronic and paper copies of part or all of the articles, including all computer files that are linked to the articles, for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage.
This permission does not apply to previously copyrighted material, such as teaching cases. In paper copies of the article, the copyright notice and the title of the publication and its date should be visible. To copy otherwise is permitted provided that a per-copy fee is paid.
To republish, to post on servers, or redistribute to lists requires that you post a link to the IJAHP article, which is available in open access delivery mode. Do not upload the article itself.
Authors are permitted to present a talk, based on a paper submitted to or accepted by IJAHP, at a conference where the paper would not be published in a copyrighted publication either before or after the conference and where the author did not assign copyright to the conference or related publisher.