101. A complete ranking of trapezoidal fuzzy numbers and its applications to multi-criteria decision making
- Author
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Dhanasekaran Ponnialagan, Jeevaraj Selvaraj, and Lakshmana Gomathi Nayagam Velu
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Fuzzy classification ,Fuzzy measure theory ,Fuzzy set ,02 engineering and technology ,Type-2 fuzzy sets and systems ,Defuzzification ,020901 industrial engineering & automation ,Artificial Intelligence ,0202 electrical engineering, electronic engineering, information engineering ,Fuzzy number ,Fuzzy set operations ,020201 artificial intelligence & image processing ,Algorithm ,Software ,Membership function ,Mathematics - Abstract
The problem (or scenario) involving qualitative or imprecise information is not solvable by classical set theory. To overcome the shortcoming of classical set theory, Zadeh (Inf Control 8(3):338–356, 26) introduced the concept of fuzzy sets that generalizes the concept of classical sets. Fuzzy set theory allows modelling and handling of imprecise information in an effective way. As a special class of fuzzy sets, fuzzy numbers (FN) which are very much important in decision making was introduced by Dubois and Prade (Int J Syst Sci 9:631–626, 12). The available methods for solving multi-criteria decision making problems (MCDM) are problem dependent in nature due to the partial ordering on the class of FN. Total ordering on the class of FN by countable number of real-valued parameters was achieved by Wang and Wang (Fuzzy Sets Syst 243:131–141, 21). A complete ranking on the class of trapezoidal fuzzy numbers (TrFNs) using finite number of score functions is achieved in this paper. In this paper, a new ranking procedure (complete) on the class of TrFNs using the concepts of mid-point, radius, left and right fuzziness of TrFN is proposed and further we introduce a method for solving fuzzy multi-criteria decision making (Fuzzy MCDM) problem. Finally, comparisons of our proposed method with familiar existing methods are listed.
- Published
- 2017