Abstract
We introduce a new type of relations called complex multi-fuzzy relation (CMFR). The novelty of CMFR lies in the ability of complex multi- membership functions to achieve more range of values while handling uncertainty of data that is periodic in nature. The application of complex multi-fuzzy sets is then discussed in determining: the influence of modern methods of education on student performance, and the time required for the former to affect the latter. A comparison between different existing relations and CMFR to show the ascendancy of our proposed CMFR is provided. Thereafter, a few related concepts such as complement, union, intersection and inverse along with several propositions are discussed, followed by the composition of CMFR along with some related theorems. Finally, the notions of symmetric, transitive, reflexive, and equivalence complex multi-fuzzy relations are established in our work.
Highlights
The concept of fuzzy set (FS) was introduced for the first time by Zadeh [1] to handle uncertainty in many fields of everyday life
We introduce a new type of relations called complex multi-fuzzy relation (CMFR)
The novelty of CMFR lies in the ability of complex multi- membership functions to achieve more range of values while handling uncertainty of data that is periodic in nature
Summary
The concept of fuzzy set (FS) was introduced for the first time by Zadeh [1] to handle uncertainty in many fields of everyday life. There are many problems like complete colour characterization of colour images, taste recognition of food items and decision making problems with multi aspects which cannot be characterized by a single membership function of Zadeh’s fuzzy sets To overcome this problem, Sabu and Ramakrishnan [10]-[11] proposed the concept of the multifuzzy sets theory as a mathematical tool to deal life problems that have multi dimensional characterization properties. Thereafter, Thomas and John [26] introduced the concept of multi- fuzzy rough sets by combining the multi-fuzzy set and rough set models They defined a multi-fuzzy rough relation and studied its properties and operations. We will first extend the discussion on multi-fuzzy relation further by proposing a new concept of complex multi-fuzzy. Decision making is no longer limited to deterministic forms of linear programing [36]-[40] and data envelopment analysis [41]-[43]
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