Abstract
Intuitionistic trapezoidal fuzzy multi-numbers (ITFM-numbers) are a special intuitionistic fuzzy multiset on a real number set, which are very useful for decision makers to depict their intuitionistic fuzzy multi-preference information. In the ITFM-numbers, the occurrences are more than one with the possibility of the same or the different membership and non-membership functions. In this paper, we define ITFM-numbers based on multiple criteria decision-making problems in which the ratings of alternatives are expressed with ITFM-numbers. Firstly, some operational laws using t-norm and t-conorm are proposed. Then, some aggregation operators on ITFM-numbers are developed. Also, the ranking order of alternative is given according to the similarity of the alternative with respect to the positive ideal solution. Finally, a numerical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Highlights
In 1986, the theory of intuitionistic fuzzy set was first presented by Atanassov [1] to deal with uncertainty of imperfect information
Since the intuitionistic fuzzy set theory was proposed by Atanassov [1], many researches treating imprecision and uncertainty have been developed and studied: for example, trapezoidal fuzzy multi-number [2], intuitionistic fuzzy sets [3,4,5,6,7,8,9,10,11], methodology for ranking triangular intuitionistic fuzzy numbers [12,13,14,15,16,17,18,19,20,21,22,23], intuitionistic trapezoidal fuzzy aggregation operator [21,24,25,26,27,28,29], interval-valued trapezoidal fuzzy numbers aggregation operator [30,31,32,33], interval-valued generalized intuitionistic fuzzy
The ITFM-numbers are a generalization of trapezoidal fuzzy numbers and intuitionistic trapezoidal fuzzy numbers which are commonly used in real decision problems, because the lack of information or imprecision of the available information in real situations is more serious
Summary
In 1986, the theory of intuitionistic fuzzy set was first presented by Atanassov [1] to deal with uncertainty of imperfect information. Since the intuitionistic fuzzy set theory was proposed by Atanassov [1], many researches treating imprecision and uncertainty have been developed and studied: for example, trapezoidal fuzzy multi-number [2], intuitionistic fuzzy sets [3,4,5,6,7,8,9,10,11], methodology for ranking triangular intuitionistic fuzzy numbers [12,13,14,15,16,17,18,19,20,21,22,23], intuitionistic trapezoidal fuzzy aggregation operator [21,24,25,26,27,28,29], interval-valued trapezoidal fuzzy numbers aggregation operator [30,31,32,33], interval-valued generalized intuitionistic fuzzy
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