Two Type-2Fuzzy Inventory Models With Decision-making Prefereces And Game Problems

Inventory problems are considered very important in the production andmanagement in recent years. With the deepening of the study, it wasdiscovered that human behavior factors play a great role on the operationsresearch theory. Currently, the research of inventory problems based onhuman behavioral factors and fuzzy environment is relatively small. Somedeficiencies of the ordinary fuzzy sets in the application are analyzed. Basedon a type-2fuzzy environment, that is, the model parameters withinterval-valued fuzzy numbers, the decision makers preferences andnon-cooperative game behavior are taken into account in the inventoryproblem. Then two types of type-2fuzzy inventory models with behavioralfactors are discussed. And the new inventory models are considered more inline with the objective requirements. This research is great significance notonly for the development of the inventory theory but also for the practicalapplication of the inventory theory. The main contents on this paper are asfollows:(1) The ordinary2fold numbers and double continuous operator aredefined. The decomposition theorem of the interval-valued fuzzy numbers is given. And the closed of the operation of the interval-valued fuzzy numbersin the double continuous operator is discussed. The arithmetic of theinterval-valued fuzzy numbers is given based on the fuzzy structuredelement method. And the weighted characteristic numbers and order relationof the interval-valued fuzzy numbers are given based on the fuzzy structuredelement method;(2) The decision makers preferences are converted into a single(mixed)preferences weighted function. Thus a class of type-2fuzzy inventory modelwith defective rate and decision-making preferences is constructed. And theweighted signed distance and weighted signed hybrid distance are definedbased on the fuzzy structured element method. Then a second signeddistance defuzzification method is proposed. The general solution method ofthe optimal economic lot of such model is given;(3) A class of supply chain two non-cooperative game type-2fuzzyinventory models is built. Then the two type-2fuzzy inventory models aredefuzzification based on the weighted characteristics numbers(order relation)of the interval-valued fuzzy numbers. The Nash equilibrium solutions of twotype-2fuzzy inventory models are given.