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Authors: Park, Choonkil | Rehman, Noor | Ali, Abbas

Article Type: Research Article

Abstract: The q -rung orthopair fuzzy sets accommodate more uncertainties than the Pythagorean fuzzy sets and hence their applications are much extensive. Under the q -rung orthopair fuzzy set, the objective of this paper is to develop new types of q -rung orthopair fuzzy lower and upper approximations by applying the tolerance degree on the similarity between two objects. After employing tolerance degree based q -rung orthopair fuzzy rough set approach to it any times, we can get only the six different sets at most. That is to say, every rough set in a universe can be approximated by only six …sets, where the lower and upper approximations of each set in the six sets are still lying among these six sets. The relationships among these six sets are established. Furthermore, we propose tolerance degree based multi granulation optimistic/pessimistic q -rung orthopair fuzzy rough sets and investigate some of their properties. Another main contribution of this paper is to disclose the ideas of different kinds of approximations called approximate precision, rough degree, approximate quality and their mutual relationship. Finally a technique is devloped to rank the alternatives in a q -rung orthopair fuzzy information system based on similarity relation. We find that the proposed method/technique is more efficient when compared with other existing techniques. Show more

Keywords: q-rung orthopair fuzzy set, fuzzy rough set, similarity relation, tolerance classes, multigranulation q-rung orthopair fuzzy rough sets

DOI: 10.3233/JIFS-221249

Citation: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 3, pp. 4301-4321, 2023

Authors: Park, Choonkil | Rehman, Noor | Ali, Abbas | Alahmadi, Reham A. | Khalaf, Mohammed M. | Hila, Kostaq

Article Type: Research Article

Abstract: In clasical logic, it is possible to combine the uniary negation operator ¬ with any other binary operator in order to generate the other binary operators. In this paper, we introduce the concept of (N ∗ , O , N , G )-implication derived from non associative structures, overlap function O , grouping function G and two different fuzzy negations N ∗ and N are used for the generalization of the implication p  → q  ≡ ¬ [p  ∧ ¬ (¬ p  ∨ q )] . We show that (N ∗ , O , N , G )-implication are fuzzy implication without any restricted conditions. Further, we also …study that some properties of (N ∗ , O , N , G )-implication that are necessary for the development of this paper. The key contribution of this paper is to introduced the concept of circledcircG ,N -compositions on (N ∗ , O , N , G )-implications. If ( N 1 ∗ , O ( 1 ) , N 1 , G ( 1 ) ) - or ( N 2 ∗ , O ( 2 ) , N 2 , G ( 2 ) ) -implications constructed from the tuples ( N 1 ∗ , O ( 1 ) , N 1 , G ( 1 ) ) or ( N 2 ∗ , O ( 2 ) , N 2 , G ( 2 ) ) satisfy a certain property P , we now investigate whether circledcircG ,N -composition of ( N 1 ∗ , O ( 1 ) , N 1 , G ( 1 ) ) - and ( N 2 ∗ , O ( 2 ) , N 2 , G ( 2 ) ) -implications satisfies the same property or not. If not, then we attempt to characterise those implications ( N 1 ∗ , O ( 1 ) , N 1 , G ( 1 ) ) -, ( N 2 ∗ , O ( 2 ) , N 2 , G ( 2 ) ) -implications satisfying the property P such that circledcircG ,N -composition of ( M 1 ∗ , O ( 1 ) , M 1 , G ( 1 ) ) - and ( M 2 ∗ , O ( 2 ) , M 2 , G ( 2 ) ) -implications also satisfies the same property. Further, we introduced sup-circledcircO -composition of (N ∗ , O , N , G )-implications constructed from tuples (N ∗ , O , N , G ) . Subsequently, we show that under which condition sup-circledcircO -composition of (N ∗ , O , N , G )-implications are fuzzy implication. We also study the intersections between families of fuzzy implications, including R O -implications (residual implication), (G , N )-implications, QL -implications, D -implications and (N ∗ , O , N , G )-implications. Show more

Keywords: Overlape function, grouping function, fuzzy implication, fuzzy negation

DOI: 10.3233/JIFS-222878

Citation: Journal of Intelligent & Fuzzy Systems, vol. 45, no. 3, pp. 4949-4977, 2023