Abstract
In many decision situations, decision-makers face a kind of complex problems. In these decision-making problems, different types of fuzzy numbers are defined and, have multiple types of membership functions. So, we need a standard form to formulate uncertain numbers in the problem. Shadowed fuzzy numbers are considered granule numbers which approximate different types and different forms of fuzzy numbers. In this paper, a new ranking approach for shadowed fuzzy numbers is developed using value, ambiguity and fuzziness for shadowed fuzzy numbers. The new ranking method has been compared with other existing approaches through numerical examples. Also, the new method is applied to a hybrid multi-attribute decision making problem in which the evaluations of alternatives are expressed with different types of uncertain numbers. The comparative study for the results of different examples illustrates the reliability of the new method.
Highlights
Vague information is represented by many uncertain sets
Fuzzy set is determined by its membership function that represents vagueness and imprecision in linguistic term. fuzzy number is a special type of fuzzy set which is defined on real numbers scale
This paper is proposed a new approach to rank shadowed fuzzy numbers (SFNs)
Summary
Vague information is represented by many uncertain sets. Fuzzy set is one of the most important uncertain set which was proposed by Zadeh. Chutia discussed the concept of parametric form of fuzzy number and proposed a new ranking method using the value and the ambiguity of it at different decision levels [14]. A new method for ranking shadowed fuzzy numbers is proposed to order different types of fuzzy numbers and different membership functions. The new algorithm is proposed to solve a hybrid multi-attribute decision making problem that includes the new SFNs ranking approach This MADM problem has different data types include interval numbers, type-l fuzzy numbers with two different membership function types and intuitionistic fuzzy numbers. The reset of this paper is organized as follows: section 2 introduces the basic definitions of FNs, IFNs and SFNs. Section 3 defines the concepts of the value, the ambiguity and the fuzziness of SFNs. we introduce proposed steps for new ranking method of SFNs. Section 4, numerical examples are provided, and a comparative study is presented with previous methods.
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