This paper proves the approximate intermediate value theorem, constructively and from notably weak hypotheses: from pointwise rather than uniform continuity, without assuming that reals are presented with rational approximants, and without using countable choice. The theorem is that if a pointwise continuous function has both a negative and a positive value, then it has values arbitrarily close...

The familiar Intermediate Value Theorem of elementary calculus says that if a real valued function f is continuous on the interval [a, b] ⊆ R then it takes each value between f(a) and f(b). As our next result shows, the critical fact is that the domain of f , the interval [a, b], is a connected space, for the theorem generalizes to real-valued functions on any connected space. The Intermediate ...

The notation and terminology used here are introduced in the following papers: [21], [22], [23], [3], [4], [2], [12], [18], [6], [1], [20], [7], [5], [8], [16], [14], [13], [15], [11], [19], [17], [9], and [10]. The following propositions are true: (1) Let R be a non empty subset of R and r0 be a real number. If for every real number r such that r ∈ R holds r ¬ r0, then supR ¬ r0. (2) Let X be ...

 The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generate...

In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and som...

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m...

in this paper, we give some new definitions of m-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete m-fuzzy metric spaces.

in this paper, we shall introduce the fuzzyw-distance, then prove a common fixed point theorem with respectto fuzzy w-distance for two mappings under the condition ofweakly compatible in complete fuzzy metric spaces.

Based upon the upper expected value, lower expected value and expected value operators of a fuzzy variable, this paper first presents three types of multicriteria maximum expected value models. Then a theorem about the connection of Pareto solutions among the maximum expected value models is proved. In addition, the relationship between maximum and minimum expected value models is discussed. At...