Abstract
In this paper, the notion of hybrid structure is applied to the ideal theory in BCI-algebras. In fact, we introduce the notions of hybridp-ideal, hybrid h-ideal, and hybrid a-ideal in BCI-algebras and investigate their related properties. Furthermore, we show that every hybridp-ideal (or h-ideal or a-ideal) is a hybrid ideal in a BCI-algebra but converse need not be true in general and in support, and we exhibit counter examples for each case. Moreover, we consider characterizations of hybridp-ideal, hybrid h-ideal, and hybrid a-ideal in BCI-algebras.
Highlights
Imai and Iseki [1, 2] initiated the study of “BCK/BCI-algebras. In (BCK/BCI)-algebras” in 1966 as a generalization of the notions of settheoretical difference and propositional calculus
A great deal of literature has been developed on the theory of (BCK/BCI)-algebras since in particular, more focus has been placed on the “ideal theory” of BCK/BCI-algebras
Molodtsov [8] proposed the concept of a “soft set” as a new mathematical framework for dealing with uncertainties, free of the difficulties that have disrupted normal theoretical approaches
Summary
Imai and Iseki [1, 2] initiated the study of “BCK/BCI-algebras” in 1966 as a generalization of the notions of settheoretical difference and propositional calculus. Molodtsov applied soft set theory in a variety of ways, such as smoothness of functions, game theory, operational research, Riemann integration, Perron integration, probability, and measurement theory (see [8,9,10]). Algebraic structures such as (BCK/BCI)-algebra [11], d-algebras [12], group [13], semigroup [14], ring [15], semiring [16], and decisionmaking [17, 18] are theoretically applied by soft set theory. We provide conditions for a hybrid p-ideal (or hybrid h-ideal or hybrid a-ideal) to be a hybrid ideal
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