On a new class of uninorms on bounded lattices

We study and propose some new construction methods to obtain uninorms on bounded lattices. Considering an arbitrary bounded lattice L, we show the existence of idempotent uninorms on L for any element e ź L\{0, 1} playing the role of a neutral element. By our construction method, we obtain the smallest idempotent uninorm and the greatest idempotent uninorm with the neutral element e ź L\{0, 1}. We see that the obtained uninorms are conjunctive and disjunctive uninorms, respectively. On the other hand, if L is not a chain, we also provide an example of an idempotent uninorm which is neither conjunctive nor disjunctive.

[1]  Bernard De Baets,et al.  Uninorms: The known classes , 1998 .

[2]  B. Schweizer,et al.  Statistical metric spaces. , 1960 .

[3]  Ronald R. Yager.  Responses to Elkan (Ronald R. Yager) , 1994, IEEE Expert.

[4]  Pawel Drygas,et al.  On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums , 2010, Fuzzy Sets Syst..

[5]  Martin Kalina,et al.  Construction of uninorms on bounded lattices , 2014, 2014 IEEE 12th International Symposium on Intelligent Systems and Informatics (SISY).

[6]  Ronald R. Yager,et al.  Structure of Uninorms , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[7]  Ronald R. Yager,et al.  Uninorm aggregation operators , 1996, Fuzzy Sets Syst..

[8]  Andrea Mesiarová-Zemánková,et al.  Multi-polar t-conorms and uninorms , 2015, Inf. Sci..

[9]  Joan Torrens,et al.  On locally internal monotonic operations , 2003, Fuzzy Sets Syst..

[10]  Radko Mesiar,et al.  Different interpretations of triangular norms and related operations , 1998, Fuzzy Sets Syst..

[11]  Funda Karaçal,et al.  On the direct decomposability of strong negations and S-implication operators on product lattices , 2006, Inf. Sci..

[12]  Radko Mesiar,et al.  Order-equivalent triangular norms , 2015, Fuzzy Sets Syst..

[13]  Radko Mesiar,et al.  On the Relationship of Associative Compensatory operators to triangular Norms and Conorms , 1996, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Glad Deschrijver,et al.  Uninorms which are neither conjunctive nor disjunctive in interval-valued fuzzy set theory , 2013, Inf. Sci..

[15]  Radko Mesiar,et al.  Uninorms on bounded lattices , 2015, Fuzzy Sets Syst..

[16]  Joan Torrens,et al.  A characterization of a class of uninorms with continuous underlying operators , 2016, Fuzzy Sets Syst..

[17]  Pawel Drygas,et al.  Some Class of Uninorms in Interval Valued Fuzzy Set Theory , 2014, IEEE Conf. on Intelligent Systems.