MI-groups: New Approach
The notion of MI-group introduced in ,  and later on elaborated in  is redefined and its structure analysed. In our approach, the role of the “Many Identities” set is replaced by an involutive anti-automorphism. Every finite MI-group coincides with some classical group, whilst infinite MI-groups comprise two parts: a group part and a semigroup part.
Keywordsmany identities group algebraic structures fuzzy numbers involutive anti-automorphism
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- 1.Holčapek, M., Štěpnička, M.: Arithmetics of extensional fuzzy numbers – part I: Introduction. In: Proc. IEEE Int. Conf. on Fuzzy Systems, Brisbane, pp. 1517–1524 (2012)Google Scholar
- 2.Holčapek, M., Štěpnička, M.: Arithmetics of extensional fuzzy numbers – part II: Algebraic framework. In: Proc. IEEE Int. Conf. on Fuzzy Systems, Brisbane, pp. 1525–1532 (2012)Google Scholar
- 3.Holčapek, M., Štěpnička, M.: MI-algebras: A new framework for arithmetics of (extensional) fuzzy numbers. Fuzzy Sets and Systems (2014), http://dx.doi.org/10.1016/j.fss.2014.02.016
- 4.Hage, J., Harju, T.: On Involutive Anti-Automorphisms of Finite Abelian Groups. Technical UU WINFI Informatica en Informatiekunde (2007)Google Scholar
- 6.Dummit, D.S., Foote, R.M.: Abstract Algebra. Wiley (2003)Google Scholar