A Decision Making Problem on FAHP with Z-Numbers
Sahaya Sudha2018, International Journal of Mathematics Trends and Technology
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Abstract
This paper deals with the study of the model based on FAHP with Z-number and the evaluation of the alternatives with respect to each criterion and is described using z number where the Z-number contains both uncertain variable and its reliability (i.e) the two components constitutes the triangular fuzzy number. In this paper a classical triangular fuzzy number has been transformed into a crisp value and a decision analysis has been proposed using AHP. Finally a practical example with risk assessment factor has been analysed and evaluated using this technique.
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A state of the art survey & testbed of fuzzy AHP (FAHP) applications
A state-of the-art survey & testbed of Fuzzy AHP (FAHP) applications
As a practical popular methodology for dealing with fuzziness and uncertainty in Multiple Criteria Decision-Making (MCDM), Fuzzy AHP (FAHP) has been applied to a wide range of applications. As of the time of writing there is no state of the art survey of FAHP, we carry out a literature review of 190 application papers (i.e., applied research papers), published between 2004 and 2016, by classifying them on the basis of the area of application, the identified theme, the year of publication, and so forth. The identified themes and application areas have been chosen based upon the latest state-of-the-art survey of AHP conducted by [Vaidya, O., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of operational research, 169(1), 1–29.]. To help readers extract quick and meaningful information, the reviewed papers are summarized in various tabular formats and charts. Unlike previous literature surveys , results and findings are made available through an online (and free) testbed, which can serve as a ready reference for those who wish to apply, modify or extend FAHP in various applications areas. This online testbed makes also available one or more fuzzy pairwise comparison matrices (FPCMs) from all the reviewed papers (255 matrices in total). In terms of results and findings, this survey shows that: (i) FAHP is used primarily in the Manufacturing, Industry and Government sectors; (ii) Asia is the torchbearer in this field, where FAHP is mostly applied in the theme areas of Selection and Evaluation; (iii) a significant amount of research papers (43% of the reviewed literature) combine FAHP with other tools, particularly with TOPSIS, QFD and ANP (AHP's variant); (iv) Chang's extent analysis method, which is used for FPCMs'weight derivation in FAHP, is still the most popular method in spite of a number of criticisms in recent years (considered in 57% of the reviewed literature).
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