in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

This paper presents a multiobjective genetic algorithm which obtains fuzzy rules for subgroup discovery in disjunctive normal form. This kind of fuzzy rules lets us represent knowledge about patterns of interest in an explanatory and understandable form which can be used by the expert. The evolutionary algorithm follows a multiobjective approach in order to optimize in a suitable way the differ...

Let F be a family of subgroups of a group G = (G, ·) such that ⋃F = G. Then P = (F,≤) is a partially ordered set (with an order dual to ⊆) and let a mapping A: G −→ P be a P-(fuzzy) subgroup of a group G defined by (6). The theory of fuzzy-subgroups is known [2] but in this paper we will apply it to the theory of Riemann surfaces. Mbius transformations form a group M and we introduce a connecti...

Bijective transformations play an important role in generating fuzzy implications from fuzzy implications. In [Representations through a Monoid on the set of Fuzzy Implications, Fuzzy Sets and Systems, 247, 5167], Vemuri and Jayaram proposed a monoid structure on the set of fuzzy implications, which is denoted by I, and using the largest subgroup S of this monoid discussed some group actions on...

Murali and Makamba (2001) introduced an equivalence of fuzzy subgroups. Dudek Jun (2004) studied the defined by in ideals a BCI-algebra. In this paper, we obtained sequence BCI-algebra X from ideal on X. We will show that, if two are equivalent, then them equivalent. that there is relationship between with adjoint A, where A Abelian subgroup Autµ(X).

It is known that fuzzy systems have a universal approximation property. A natural question is: can this property be extended to a universal representation property? Somewhat surprisingly, the answer to this question depends on whether the following Continuum Hypothesis holds: every infinite subset of the real line has • either the same number of elements as the real line itself • or as many ele...

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradictio...