Derivatives and differentials for multiplicative intuitionistic fuzzy information  

作　　者：YU Shan XU Ze-shui LIU Shou-sheng 

机构地区：[1]School of Sciences,PLA University of Science and Technology [2]Business School,Sichuan University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2017年第4期443-461,共19页高校应用数学学报（英文版）（B辑）

基　　金：supported in part by the National Natural Science Foundation of China(71571123,71771155)

摘　　要：By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty’s 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty's 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.

关 键 词：multiplicative intuitionistic fuzzy set multiplicative intuitionistic fuzzy number multiplicative intuitionistic fuzzy function DERIVATIVE DIFFERENTIAL 

分 类 号：O159[理学—数学] O172[理学—基础数学]