The Fuzzy System Constructed By Bernstein Polynomial And Group Decision Making Method Of The Intuitionistic Polygonal Fuzzy Set

The fuzzy system is composed of four partsifuzzy rule base,fuzzy inference engine,fuzzifier and defuzzifier.Its essence is a mapping from the input domain to the output domain.Generally,the rule antecedent of the fuzzy system is fuzzy,while the rule consequent is definite.For example,the output of the T-S fuzzy system is a linear combination of input variables.Normally,the T-S fuzzy system is better than Madamni fuzzy system in dealing with ambiguous information.The non mem-benship degree is increased at the same as the intuitionistic fuzzy set describes the membership degree of things.Thus the concept of hesitation has emerged.The intuitionistic fuzzy set not only broadens new ideas and methods for the processing of fuzzy information,but also describes the fuzzy information more comprehensively.The polygonal fuzzy set is an effective tool to express a class of fuzzy information with the help of finite ordered real numbers.lt can not only guarantee the closeness of arithmetic operation of the polygonal fuzzy sets,but also has good linearity and intu-itiveness.Therefore,it will be a new attempt in this paper to establish an n-intuitionistic polygonal fuzzy set based on the respective advantages of polygonal fuzzy set and intuitionistic fuzzy set.The first part:introduction,introduces the background of this paper and the research status of the fuzzy system and group decision.The second part:preparatory knowledge,including several expressions of n-Bernstein polyno-mial and the representation of the fuzzy system.In the third part,we construct a class of multiple input single output fuzzy system which are different from Mamdani and T-S fuzzy system by n-Bernstein polynomial as a rule s consequence.and the output algorithm of the fuzzy system is given by the Bernystein polynomial determined with some random subdivision numbers.Especially,the analytic formula of the fuzzy system is simplified under the premise that the membership function of the preceding fuzzy set chooses triangular two-phase wave.Then,It proves that the fuzzy system has approximation by lemma of Bernstein polynomial.An example is given to show the output value of the fuzzy system with Bernstein polynomial as its rule's consequence at the sample point and its calculation process.In the final part:based on the respective advantages of polygonal fuzzy set and intuitionistic fuzzy set,the n-intuitionistic polygonal fuzzy set and its ordered representation are established.And integration method of the multi attribute fuzzy information is given by new operational rules,then discuss the character of weighted arithmetic mean operator and weighted geometric mean opera-tor.On the other hand,the sorting rules of n-intuitionistic polygonal fuzzy are obtained by using the score function and the exact function.And a new group decision making method is proposed for urban residents to choose the livable city problem based on the multi attribute index informa-tion.Finally.the superiority and practicability of the method are verified by an example.