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Concepts Valuation by Conjugate Möebius Function

Concepts Valuation by Conjugate Möebius Function. Background Context , Concept and Concept Lattice Diversity Function Conjugate Möebius Inverse Concept Lattice Valuation Diversity, Weight, CMI Dissimilarity, hierarchy Splitting into hierarchy Basic interpretation of numbers Conclusion

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Concepts Valuation by Conjugate Möebius Function

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  1. Concepts Valuation by Conjugate Möebius Function • Background • Context, Concept and Concept Lattice • Diversity Function • Conjugate Möebius Inverse • Concept Lattice Valuation • Diversity, Weight, CMI • Dissimilarity, hierarchy • Splitting into hierarchy • Basic interpretation of numbers • Conclusion • Next research • References

  2. Context, Concept and Concept Lattice • Context • Incidence matrix Description of objects and features in incidence matrix. C = cat q = quadrupped (four feet) M = monkey (chimpanzee) p = pilli D = dog i = intelligence F = fish (delphinus) w = live in water H = human h = hand W = whale Whales live in water

  3. Context, Conceptand Concept Lattice • Concept Sample of formal concept:({C,M,D},{p})

  4. Context, Concept and Concept Lattice • Concept lattice

  5. Concept Lattice Valuation • Diversity

  6. Concept Lattice Valuation • CMI

  7. Concept Lattice Valuation

  8. Concept Lattice Valuation • Weighting by CMI

  9. Concept Lattice Valuation • Dissimilarity There are two models in Theory of Diversity. Hierarchical a more generalline model. Concept lattice are hierarchical ordered. But, weighting of concepts is a difficult task. We can assign value to concepts only in small simly lattice because of next condition.

  10. Concept Lattice Valuation

  11. Concept Lattice Valuation • Splitting into hierarchies

  12. Splitting into hierarchies

  13. Basic interpretation of numbers • What represent the numbers (diversity, weight) • For example, we have a set of different people with different skills. We are looking for teams of people (concepts), which can cover most of required skills. • 1. We assign value to each attribute. Higher value represents more important attribute. • 2. We compute diversities of concepts = v(Ci). • 3. v(Ci) / v(Ctop) … upon normalization we get a number that represents measure of covering of skills according to their values. • We want to find „compact“ teams (concepts) whose members have general knowledge. Compact = most of skills of pleople in the team are shared. • 1. We assign value to each attribute. Higher value represents more important attribute • 2. We compute diversities and weights of concepts = v(Ci), (Ci) • 3. v(Ci) / v(Ctop) … upon normalization we get a number that represents measure of covering of skills according to their values. • 4. (Ci) / (v(Ci) / v(Ctop))

  14. Basic interpretation of numbers

  15. Basic interpretation of numbers

  16. Conclusion • Next research • Input • Output • Evaluated, reduced concept lattice Hierarchy of attributes Incidence matrix

  17. Conclusion

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