Research On Approaches To Multiple Attribute Decision Making Based On Linguistic Interval2-tuple Power Aggregation Operators

In the wake of the rapid development of production practice, science and technology, theapplication of decision making theory in many fields has become more and more popular,such as economy, management, engineering and military. Multiple attribute decision makingis an important part of decision making theory, aiming at choose the most desirablealternative from several alternatives according to multiple evaluation information provided bya number of decision makers. In many multiple attribute decision making problems, thanks tothe complexity, uncertainty of objective things and the ambiguity of human thinking, peoplehave difficulty in quantitatively describing decision objects by specific numerical values,qualitatively evaluating decision objects by linguistic terms more conforms to the practicalsituation and human thinking. Consequently, the research on linguistic multiple attributedecision making is of great significance in theory and practice and has a good applicationprospect.The main research achievements of this paper are as follows:（ⅰ）We summarize2-tuple linguistic representation model and introduce severalrelated aggregation operators, such as OWA operator, PA operator and POWA operator;（ⅱ）We develop the linguistic interval2-tuple representation model and the method tocompare with two linguistic interval2-tuple. We also present some linguistic interval2-tupleaggregation operators, i.e., linguistic interval2-tuple power average (LI2TPA) operator,linguistic interval2-tuple weighted power average (LI2TWPA) operator and linguisticinterval2-tuple power ordered weighted average (LI2TPOWA) operator. Furthermore, wediscuss and demonstrate several properties of these new operators;（ⅲ）We present the extended hesitant fuzzy linguistic term set and some basicoperations for extended hesitant fuzzy linguistic term sets. Two aggregation operators forextended hesitant fuzzy linguistic term sets are developed, i.e., hesitant fuzzy linguistic termset weighted average (HFLTSWA) operator and hesitant fuzzy linguistic term set orderedweighted average (HFLTSOWA) operator. We also present a extension principle for extendedhesitant fuzzy linguistic term sets.（ⅳ）Due to the complexity of the objects and the vagueness of inherent subjectivenature of human thinking, there are many multiple attribute decision making problems inwhich the linguistic evaluation information provided decision makers may take the form ofinterval. In terms of these multiple attribute decision making problems, we develop twolinguistic multiple attribute decision making methods based on the presented linguisticinterval2-tuple power aggregation operators. Moreover, a numerical example is provided toshow the practicality of our new method.