In this paper, we shall generalize the definition of (φ− k) −B contraction to multi-valued mappings which was presented before in single valued case by Mihet. Then we shall prove two fixed point theorems for multi-valued (φ− k) − B contraction mappings in probabilistic metric space.

In this paper we review the development & advantages of multi valued logic. The multi valued logic has been object of research over last few decades. Since 1971 there have been annual symposiums on multi valued logic. The use of non binary logic or discrete-analog signal processing is not out of the question if the multiple-valued hardware algorithms are developed for fast parallel operations. ...

Multi-valued partial CFL functions are computed by one-way nondeterministic pushdown automata equipped with write-only output tapes. We give an answer to a fundamental question, raised by Konstantinidis, Santean, and Yu [Act. Inform. 43 (2007) 395–417], of whether all multi-valued partial CFL functions can be refined by single-valued partial CFL functions. We negatively solve this question by p...

This paper describes our multi-valued symbolic modelchecker χChek. χChek is a generalization of an existing symbolic model-checking algorithm for a multi-valued extension of the temporal logic CTL. Multi-valued modelchecking supports reasoning with values other than just TRUE and FALSE. Multi-valued logics are useful in software engineering because they support explicit modeling of uncertainty,...

In this work, we use a notion of convexificator [25] together with the support function [3, 4, 15, 16, 41] to establish necessary optimality conditions for set valued bilevel optimization problems. Fortunately, the Lipschitz property of a set-valued mapping is conserved for its support function. An intermediate set-valued optimization problem is introduced to help us in our investigation.

Abstract In low-resource domains, it is challenging to achieve good performance using existing machine learning methods due a lack of training data and mixed types (numeric categorical). particular, categorical variables with high cardinality pose challenge tasks such as classification regression because requires sufficiently many points for the possible values each variable. Since interpolatio...

We consider a variational inequality problem, where the cost mapping is the sum of a single-valued mapping and the subdifferential mapping of a convex function. For this problem we introduce a new class of equivalent optimization formulations; based on them, we also provide the first convergence analysis of descent algorithms for the problem. The optimization formulations constitute generalizat...

Single valued neutrosophic hesitant fuzzy set has three independent parts, namely the truth membership hesitancy function, indeterminacy membership hesitancy function, and falsity membership hesitancy function, which are in the form of sets that assume values in the unit interval [0, 1]. Single valued neutrosophic hesitant fuzzy set is considered as a powerful tool to express uncertain, incompl...