In this paper, we focuse on different important properties in fuzzy (set-valued) measure theory, such as, non-atomicity, diffusion, regularity, order continuity, exhaustivity, countable subadditivity, increasing/decreasing convergence, semi-convexity, Darboux property for different types of set multifunctions defined on a ring of subsets of an abstract, nonvoid space and taking values in the fa...

The aim of this paper is to define the productoperation on a family of interval valued events and the notion ofjoint interval valued observable. We show the connection betweenproduct operations for interval valued events and intuitionisticfuzzy events, too. We display the relation between joint intervalvalued observable and joint intuitionistic fuzzy observable. We...

It is argued that the ‘inner’ negation ∼ familiar from 3-valued logic can be interpreted as a form of ‘conditional’ negation: ∼A is read “A is false if it has a truth value”. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language ...

Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional log...

For set-valued information systems, there are many original dot-based approximation models based on tolerance relations and other developed relations. Because of the lack efficient algorithms, they not to accommodate bigger table. Therefore, it is a real challenge how efficiently calculate high-quality set in systems. To address challenge, we propose reliable operators semi-monolayer covering f...

This paper deals with approximate solutions of a nonsmooth semi-infinite programming multiple interval-valued objective functions. We first introduce four types quasi Pareto the considered problem by considering lower-upper interval order relation and then apply some advanced tools variational analysis generalized differentiation to establish necessary optimality conditions for these solutions....

While the purpose of conventional proof calculi is to axiomatise the set of valid sentences of a logic, refutation systems axiomatise the invalid sentences. Such systems are relevant not only for proof-theoretic reasons but also for realising deductive systems for nonmonotonic logics. We introduce Gentzen-type refutation systems for two basic three-valued logics and we discuss an application of...

This paper deals with semi-infifinite programming multiple fuzzy-valued objective functions. Firstly, some types of effificient solutions are proposed and illustrated in examples. Then, necessary suffificient Karush-Kuhn-Tucker optimality conditions for functions established.