Abstract
In this paper we introduce the notion of anti Q-fuzzy subgroups of G with respect to t‑conorm C and study their important properties. Next we define the union, normal and direct product of two anti Q-fuzzy subgroups of G with respect to t-conorm C and we show that the union, normal and direct product of them is again an anti Q-fuzzy subgroup of G with respect to t-conorm C. It is also shown that the homomorphic image and pre image of anti Q-fuzzy subgroup of G with respect to t-conorm C is again an anti Q-fuzzy subgroup of G with respect to t-conorm C.
Highlights
The notion of fuzzy set theory initiated by Zadeh [31] in 1965 in a seminal paper, plays the central role for further development
The notion of a fuzzy set is completely non-statistical in nature and the concept of fuzzy set provides a natural way of dealing with problems in which the source of imprecision is the absence of sharply defined criteria of class membership rather than the presence of random variables
Yuan and Lee [30] defined the fuzzy subgroup and fuzzy subring based on the theory of falling shadows
Summary
The notion of fuzzy set theory initiated by Zadeh [31] in 1965 in a seminal paper, plays the central role for further development. This notion tries to show that an object corresponds more or less to the particular category we want to assimilate it to; that was how the idea of defining the membership of an element to a set not on the Aristotelian pair {0, 1} any more but on the continuous interval [0, 1] was born. Solairaju and Nagarajan [29] introduced the notion of Q-fuzzy groups.
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