In this paper, the concept of fuzzy Convex subgroup (resp. fuzzy Convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy Convex subgroup (resp. fuzzy Convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore, the Fundamental Homomorphism Theorem is established. Finally, it is proved that the class of all fuzzy Convex lattice-ordered subgroups of a lattice-ordered group G forms a complete Heyting sublattice of the lattice of fuzzy subgroups of G.

In this paper, we define the notions of fuzzy congruence relations and fuzzy Convex sub algebras on a commutative resituated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy Convex subalgcbras on a commutative residuatcd lattice. Then we study fuzzy Convex sub algebras of an integral commutative residuated lattice and will prove that fuzzy filters and fuzzy Convex suhalgebras of an integral commutative residuated lattice coincide.

In this paper, (L, M)-fuzzy domain finiteness and (L, M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L, M)-CS of (L, M)-fuzzy Convex spaces are obtained. Then, (L, M)-fuzzy stratified (resp. weakly induced, induced) Convex spaces are introduced. It is proved that both categories, the category (L, M)-SCS of (L, M)-fuzzy stratified Convex spaces and the category (L, M)-WICS of (L, M)-fuzzy weakly induced Convex spaces, are coreflective subcategories of (L, M)-CS. It is also proved that three isomorphic categories, namely, the category M-CS of M-fuzzifying Convex spaces, the category (L, M)-CGCS of (L, M)-fuzzy Convex spaces induced by M-fuzzifying Convex spaces and the category (L, M)-ICS of (L, M)-fuzzy induced Convex spaces, are coreflective subcategories of both (L, M)-SCS and (L, M)-WICS.

Application of the network equivalent concept for external system representation for power system transient analysis is well known. However, the challenge to utilize an equivalent network, approximated by a rational function, is to guarantee the passivity of the corresponding model. In this regard, special techniques are required to enforce the passivity of the equivalent model through a post processing approach that minimizes its impact on the original model characteristics. In this paper, the passivity is enforced by expressing the problem in terms of a Convex optimization problem that guarantees the global optimal solution. The Convex optimization problem is efficiently solved by recently developed numerical interior–point methods. This passivity enforcement is also global which indicates that the passivity enforcement in one region does not lead to passivity violation in other regions.

In this paper, a new inequality for generalized Convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

In this paper, we aim to  state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ Convex functions. This generalized class of Convex function contains other well-known Convex functions from literature, allowing us to derive Ostrowski-type inequalities as specific instances. Moreover, we present Ostrowski-type inequalities for which certain powers of absolute derivatives are $\phi-\lambda-$ Convex using various techniques, including Hölder's inequality and the power mean inequality. Consequently, various established results would be captured as special cases. Moreover, we provide applications in terms of special means, allowing us to derive many numerical inequalities related to special means from Ostrowski-type inequalities.

The linear systems are one of the most important tools for modeling real-world phenomena. Because the real-world phenomena are always associated with uncertainty, solving the fuzzy linear system have a great importance. One of the proposed methods to find the exact and approximate solutions of a fuzzy linear system is using the least squares method. In this method, by choosing an arbitrary meter and solving a quadratic programming, they provide an approximate (or exact) solution for the fuzzy linear system. In this paper, at first, we prove that under some conditions and not depending on the selected meter the quadratic programming is Convex. Therefore, by considering three different meters and solving several examples, we compare the obtained approximate solutions.

In this paper, fuzzy convergence theory in the framework of L-Convex spaces is introduced. Firstly, the concept of L-Convex remote-neighborhood spaces is introduced and it is shown that the resulting category is isomorphic to that of L-Convex spaces. Secondly, by means of L-Convex ideals, the notion of L-convergence spaces is introduced and it is proved that the category of L-Convex spaces can be embedded in that of L-convergence spaces as a reflective subcategory. Finally, the concepts of Convex and preConvex L-convergence spaces are introduced and it is shown that the resulting categories are isomorphic to the categories of L-Convex spaces and L-preConvex remote-neighborhood spaces, respectively