Madad Khan, Florentin Smarandache
This research work will give a new direction for applications of fuzzy set theory particularly in algebraic logics, non-classical logics, fuzzy finite state machines, fuzzy automata, fuzzy languages, cognitive modeling, multiagent decision analysis and mathematical morphology. Introducing (∈,∈ ∨q_k)-fuzzy ideals, (∈_γ,∈_γ ∨q_δ)-fuzzy ideals and (∈_γ,∈_γ ∨q_δ)-fuzzy soft ideals in a new non-associative algebraic structure called Abel-Grassmann’s groupoid, discuss several important features of a regular AG-groupoid, investigate some characterizations of regular and intra-regular AG-groupoids using the properties of classical ideals and these generalized fuzzy ideals.
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