The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated 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 subalgebras on a commutative residuated lattice. then we study fuzzy...

For a set P of n points in the unit ball b ⊆ Rd, consider the problem of finding a small subset T ⊆ P such that its convex-hull ε-approximates the convex-hull of the original set. Specifically, the Hausdorff distance between the convex hull of T and the convex hull of P should be at most ε. We present an efficient algorithm to compute such an ε′-approximation of size kalg, where ε′ is a functio...

We present an extension of convex-hull non-negative matrix factorization (CH-NMF) which was recently proposed as a large scale variant of convex non-negative matrix factorization or Archetypal Analysis. CH-NMF factorizes a non-negative data matrix V into two nonnegative matrix factors V ≈ WH such that the columns of W are convex combinations of certain data points so that they are readily inter...

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.

In the present article, we extend our study of Kantorovich type exponential sampling operators introduced in [4]. We derive Voronovskaya theorem and its quantitative estimates for these terms an appropriate K-functional. Further, improve order approximation by using convex linear combinations operators. Finally, provide few examples kernels along with graphical representations.

in this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.when the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. additionally for linear feasibil...

Fitting the parameters of a discrete nite mixture distribution to a set of data using the EM algorithm can be extremely diicult when the likelihood surface has many local maxima, the form of the components is unknown, and the number of components is unknown. The exponential explosion in the number of diierent models and diierent starting points for EM which must be tested can be reduced by ndin...

The notion of valuation on convex sets can be considered as a generalization of the notion of measure, which is defined only on the class of convex compact sets. It is well-known that there are important and interesting examples of valuations on convex sets, which are not measures in the usual sense as, for example, the mixed volumes. Basic definitions and some classical examples are discussed ...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...