We sketch a development of constructive analysis in Bishop’s style, with special emphasis on low type-level witnesses (using separability of the reals). The goal is to set up things in such a way that realistically executable programs can be extracted from proofs. This is carried out for (1) the Intermediate Value Theorem and (2) the existence of a continuous inverse to a monotonically increasi...

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

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.

In this paper we consider the random fuzzy differential equations and show their application by an example. Under suitable conditions the Peano type theorem on existence of solutions is proved. For our purposes, a notion of ε-solution is exploited.

Considering current situation of production scheduling with uncertainties in modern manufacturing enviroments, flow shop production scheduling model is established based on the theory of fuzzy programming, in which fuzzy processing time is considered and the duration time of intermediate is unlimited. The maximum membership function of mean value has been applied to solve the non-linear fuzzy s...

the starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...

What is fuzzy logic? Fuzzy logic is an extension of Boolean logic which allows intermediate values between True and False. As in Boolean logic, a true statement is expressed by the value “1” and a false statement by the value “0”. However, unlike in probability theory, the value must not be interpreted as a confidence level but rather as a Membership Function (MF). Therefore, every statement is...

we prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of aliouche, et al. [2], rao et al. [14] and [15].