感性工程Kansei EngineeringDay 2: Kansei ModelingNovember21,2017YoshiteruNAKAMORl,ProfessorEmeritusJapanAdvanced Institute of ScienceandTechnology
Kansei Engineering Day 2: Kansei Modeling November 21, 2017 Yoshiteru NAKAMORI, Professor Emeritus Japan Advanced Institute of Science and Technology 感性工程
Today's Contents1.FuzzySetTheory模糊集理论2.Exercise2:FuzzyReasoning模糊推理3.PossibilityModels可能性模型4.KanseiEvaluationExperiment感性评价实验:Report:Personal ModelsCheerful快乐愁绪Melancholy1234567Possibilitymodels可能性模型Rating scale
1. Fuzzy Set Theory 2. Exercise 2: Fuzzy Reasoning 3. Possibility Models 4. Kansei Evaluation Experiment 感性评价实验 • Report: Personal Models Today’s Contents Melancholy Cheerful 1 2 3 4 5 6 7 Rating scale 愁绪 快乐 2 Possibility models 可能性模型 模糊集理论 可能性模型 模糊推理
暖味模糊1. Fuzzy Set Theory·Afuzzyset=Asetwiththeindefiniteboundary·Amembershipfunction=Afunction indicatingthedegreeofmembershiptoa setThepossibilitythatanelementbelongstoafuzzyset.Thepossibilitythat6belongsto(Example)Afuzzyset"About5"1"About5"is0.781Membershipfunction5Y29123456897Thisseemstobesimilartotheprobabilitydensityfunction,butthisis regardedas apossibilitydistributionfunctionAbout5isalsocalledafuzzynumber3
• A fuzzy set = A set with the indefinite boundary • A membership function = A function indicating the degree of membership to a set 1. Fuzzy Set Theory 曖昧 模糊 3 The possibility that an element belongs to a fuzzy set. (Example) A fuzzy set “About 5” 5 1 2 3 4 6 7 8 9 1 2 3 4 5 6 7 8 9 The possibility that 6 belongs to 1 “About 5” is 0.7 This seems to be similar to the probability density function, but this is regarded as a possibility distribution function. Membership function About 5 is also called a fuzzy number
Sets (in traditional mathematics)X:The setofpositive integersX: The entire set[1,2,3,4,5,6, ..?(theframeworkofconsideration)A:ThesetofpositiveevennumbersYAcXA: A subset of X2,4,6,...7 C 1.2,3,4,5,6, ...aA2EAaisamemberofA2 is a member of A3± AaisnotamemberofAα±A3 is not a member of AThe boundary is crisp.The characteristic function (binary)Thecharacteristicfunction(binary)if aeA1f.(a)f,(3)= 0f,(2)=1;if aA0
X : The entire set (the framework of consideration) A : A subset of X a is a member of A a is not a member of A The characteristic function (binary) Sets (in traditional mathematics) 4 A ⊂ X a∈ A a∉ A ∉ ∈ = a A a A f A a 0, if 1, if ( ) X : The set of positive integers 1, 2, 3, 4, 5, 6, ⋯ A : The set of positive even numbers 2, 4, 6, ⋯ ⊂ 1, 2, 3, 4, 5, 6, ⋯ 2 is a member of A 3 is not a member of A The characteristic function (binary) 2∈ A 3∉ A f A (2) =1; f A (3) = 0 The boundary is crisp. A X a
A set whose boundaryis not clearAsetinmathematicshasacrispboundarythatis,anymemberiseitherinoroutofthe set.Therefore,the characteristicfunction takes the valueof o or 1.However,inthesociety,therearemanysetswhereboundariesarenot clear.A = Furniture set = (chair, table, closet, piano, refrigerator, bathtub)Introduceamembershipfunctionbyexpandingthecharacteristicfunction:μ,(x):ThedegreethatxbelongstoA.μA(table )=μA(chair) =μA (closet) =μ(piano) =从 (refrigerator) =μ(bathtub)
• A set in mathematics has a crisp boundary, that is, any member is either in or out of the set. Therefore, the characteristic function takes the value of 0 or 1. • However, in the society, there are many sets where boundaries are not clear. A set whose boundary is not clear 5 A = Furniture set = {chair, table, closet, piano, refrigerator, bathtub} Introduce a membership function by expanding the characteristic function: (x) µ A : The degree that x belongs to A. µ A ( chair ) = µ A ( table ) = µ A (closet ) = µ A ( piano) = µ A (refrigerator ) = µ A ( bathtub) = 0.8 0.7 1.0 0.3 0.2 0.1