Interval-valued Pointwise Sustaining Degree Fuzzy Reasoning Algorithms And Its Applications In Multi-attribute Decision-making

Fuzzy reasoning is an important branch of fuzzy set theory.As the theoretical basis of fuzzy control,fuzzy reasoning has achieved many results.Compared with fuzzy sets,interval-valued fuzzy sets have more advantages in dealing with imprecise and uncertain information,and can effectively avoid information loss.As a consequence,this paper studies the interval-valued pointwise sustaining degree fuzzy reasoning algorithms based on left-continuous t-representable t-norm,and applies it to multiattribute decision-making.The specific research contents and innovations are as follows:(1)The left-continuous interval-valued t-representable t-norms and their induced interval-valued residuated implications and interval-valued biresiduum implications are given.Interval-value pointwise sustaining degree is proposed from the point of view,and interval-value pointwise sustaining degree full implication algorithm and representation of its solution are given.Then its robustness is studied based on Moore measure,and it is applied to multi-attribute decision-making.(2)By analyzing the counterintuitive situation of full implication algorithm,interval-value pointwise sustaining degree quintuple implication algorithm and representation of its solution are given and its robustness is studied based on Moore measure,and the two algorithms are comparing and analyzing in the multi-attribute decision-making problem.Combined with the example,it shows that the latter can overcome the counterintuitive situation of the former.(3)Through the data analysis of the unreasonable situation of quintuple implication algorithm,interval-value pointwise sustaining degree similarity measure algorithm and representation of its solution are given and its robustness is discussed based on similarity measure,and the multi-attribute decision-making algorithm is given and applied to practical problems.