Fuzzy Stopping Research Articles

A Fuzzy Stopping Problem with the Concept

Stimulated by Zadeh's paper (Journal of Statistical Planning and Inference,2002, 105, 233--264), we will try to consider a perceptive analysis of the optimal stopping problem. In this paper, the fuzzy perception value of the expectation of the optimal stopped reward is characterized and calculated by a new recursive equation. Also, a numerical example described by triangular fuzzy numbers is given.

A multiobjective fuzzy stopping in a stochastic and fuzzy environment

In a stochastic and fuzzy environment, a multiobjective fuzzy stopping problem is discussed. The randomness and fuzziness are evaluated by probabilistic expectations and linear ranking functions, respectively. Pareto optimal fuzzy stopping times are given under the assumption of regularity for stopping rules, by using γ-optimal stopping times.

Fuzzy stopping problems in continuous-time fuzzy stochastic systems

In a continuous-time fuzzy stochastic system, a stopping model with fuzzy stopping times is presented. The optimal fuzzy stopping times are given under an assumption of regularity for stopping rules. Also, the optimal fuzzy reward is characterized as a unique solution of an optimality equation under a differentiability condition. An example in the Markov models is discussed.

Optimal stopping models in a stochastic and fuzzy environment

Optimal stopping models are discussed in a stochastic and fuzzy environment. The randomness and fuzziness are evaluated by expectations and scalarization functions, respectively. The optimal fuzzy stopping times and e-optimal fuzzy stopping times are given under the regularity assumption for stopping rules.

The set-indexed bandit problem

Motivated by spatial problems of allocations, we give a proof of the existence of an optimal solution to a set-indexed formulation of the bandit problem. The proof is based on a compactization of collections of fuzzy stopping sets and fuzzy optional increasing paths, and a construction of set-indexed integrals.

Fuzzy stopping in continuous-time dynamic fuzzy systems

In a continuous-time dynamic fuzzy system, a stopping problem regarding fuzzy rewards is discussed using fuzzy stopping times. The fuzzy rewards are evaluated by an expectation generated from a linear ranking function. The optimality equations for the optimal fuzzy rewards are given by variational inequalities, and an optimal fuzzy stopping time is constructed under assumptions of monotonicity and regularity for stopping rules. A numerical example is given to discuss that fuzzy stopping times are better than non-fuzzy ones in comparison between the fuzzy stopping models and the non-fuzzy ones.

An approach to stopping problems of a dynamic fuzzy system

We formulate a stopping problem for dynamic fuzzy systems concerning with fuzzy decision environment. It could be regarded as a natural fuzzification of non-fuzzy stopping problem with a deterministic dynamic system. The validity of the approach by α-cuts of fuzzy sets will be discussed in constructing One-step Look Ahead policy of an optimal fuzzy stopping time. A numerical example is given to illustrate the theoretical results and to show a merit to use fuzzy stopping times in dynamic fuzzy systems.

Optimal Stopping Problems in a Stochastic and Fuzzy System

In a stochastic and fuzzy environment, two kinds of stopping models are discussed and compared. The optimal fuzzy stopping times are given under the assumptions of monotonicity and regularity for stopping rules. Also, we find that fuzzy stopping times are favored in a comparison between fuzzy and classical stopping models.