Z-number CCR using Trapezoidal Fuzzy Numbers
Irdayu Ibrahim1, Noraida Abdul Ghani2, Norazura Ahmad3, Nurulhuda Ramli4
1Irdayu Ibrahim, School of Distance Education, USM, Minden, Penang, Malaysia.
2Noraida Abdul Ghani, School of Distance Education, USM, Minden, Penang, Malaysia.
3Norazura Ahmad, School of Quantitative Sciences, College of Arts and Sciences, UUM, Sintok, Kedah, Malaysia.
4Nurulhuda Ramli, School of Distance Education, USM, Minden, Penang, Malaysia.
Manuscript received on 06 September 2019 | Revised Manuscript received on 15 September 2019 | Manuscript Published on 26 October 2019 | PP: 294-298 | Volume-8 Issue-11S2 September 2019 | Retrieval Number: K104609811S219/2019©BEIESP | DOI: 10.35940/ijitee.K1046.09811S219
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Data envelopment analysis (DEA) is a powerful tool for measuring efficiency of multiple inputs and outputs of a set of decision making units (DMUs). There are several models in DEA such as the Banker, Charnes and Cooper (BCC) model, Andersen and Peterson (AP) model and many more. The data used are normally crisps but in real life, data are usually vague or imprecise such as in real problems that are characterized by linguistic information given by experts. In such cases, the Z-number has been used as it takes into account expert’s reliability on the information given. Currently, the triangular membership function is used in the Z-number CCR model. However, in linguistic assessment the trapezoidal membership function is better suited to capture the vagueness of the assessment. The Z-number CCR model using the trapezoidal membership function for inputs and outputs of a set of DMUs is proposed in this paper. In the present study, the Z-number CCR using trapezoidal membership function is converted into a linear programming model and a crisp linear programming model is obtained by employing α-cut approach,. A numerical example on portfolio selection in Information Systems/Information Technology (IS/IT) is presented to demonstrate the proposed method and to find the best portfolio by ranking them according to their efficiency score.
Keywords: Z-number, Data Envelopment Analysis (DEA), Fuzzy Data Envelopment Analysis (FDEA), Reliability.
Scope of the Article: Fuzzy Logics