Three-way Decision Based On Computing With Words

As a decision-making tool that is more in line with human thinking,threeway decision reduces the loss caused in the decision-making process by introducing accept,reject,and delay decision.Due to the complexity of practical problems and the ambiguity of information,it is difficult for decision makers to give quantitative evaluations directly,but to use language to give qualitative evaluations.In order to better express linguistic information,linguistic term sets are extended to hesitant fuzzy linguistic term sets,double hierarchy linguistic term sets,probabilistic linguistic term sets and so on.Three-way decisions based on these linguistic term sets are also being studied.However,it is not easy to directly give linguistic evaluations in the form of these linguistic term sets,and decision makers may directly use the words that are suitable for evaluation.Words can be represented as fuzzy sets over a basic set whose semantics can be represented by membership functions.The use of words means that they are used for computation.When decision makers use words to evaluate directly,the three-way decision model based on linguistic term sets cannot process these linguistic information.So we propose a three-way decision method based on computing with words.The main contents of this paper are given as follows:(1)First,based on the idea of computing with words,we propose an algorithm that converts words into the linguistic distribution assessments over a given linguistic term sets.We use treat the linguistic term set as a collection of special words,and propose a transformation algorithm based on computing with words.The algorithm converts words into linguistic distribution assessments over a given linguistic term set,that is,words are described by the distribution of some existing linguistic terms.With one transformation,we can process more linguistic information.(2)Secondly,combined with the advantages of decision-theoretic rough fuzzy sets,we propose a three-way decision based on decision-theoretic rough fuzzy sets in the environment of words.Considering that the weights of each attribute may be different,and the evaluation of each attribute by decision makers may also be evaluated by words,so we propose an attribute weight acquisition method based on analytic hierarchy process.Then,we generalize the values of attributes and the values of loss functions to the context of words,and use the proposed transformation algorithm to process the linguistic information,and also give the calculation methods of conditional probability and thresholds.Compared with the traditional three-way decision model based on linguistic term sets,our model processes a wider range of linguistic information,and the decision maker is more flexible in expressing linguistic information.In addition,interval type-2 fuzzy sets,as an extension of type-1 fuzzy sets,are superior to type-1 fuzzy sets in expressing uncertain information,but the calculation will be more complicated.In order to improve the ability of the model to deal with uncertain information,on the basis of type-1 fuzzy sets,we also study the multi-attribute three-way decision based on interval type-2 fuzzy sets.