On pseudo-homogeneity of t-subnorms

Triangular subnorms, in short t-subnorm, are generalizations of t-norms introduced by Sándor Jenei in 1999. From then several works on this class of operator have been made. In this paper, we introduce the concept of pseudo-homogeneous t-subnorms and study their properties and characteristics. We illustrated our results with an application in a multi-expert decision making problem.

[1]  Humberto Bustince,et al.  An interval extension of homogeneous and pseudo-homogeneous t-norms and t-conorms , 2016, Inf. Sci..

[2]  Radko Mesiar,et al.  Triangular Norms , 2000, Trends in Logic.

[3]  Witold Pedrycz,et al.  A motion compression/reconstruction method based on max t-norm composite fuzzy relational equations , 2006, Inf. Sci..

[4]  Benjamín R. C. Bedregal,et al.  On interval fuzzy negations , 2010, Fuzzy Sets Syst..

[5]  A. Mesiarová,et al.  Continuous triangular subnorms , 2004 .

[6]  Andrea Mesiarová-Zemánková,et al.  Cancellativity properties for t-norms and t-subnorms , 2009, Inf. Sci..

[7]  Benjamín R. C. Bedregal,et al.  Interval representations, Łukasiewicz implicators and Smets-Magrez axioms , 2013, Inf. Sci..

[8]  Francisco Herrera,et al.  Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations , 1998, Fuzzy Sets Syst..

[9]  S. Ovchinnikov,et al.  On strict preference relations , 1991 .

[10]  Humberto Bustince,et al.  New results on overlap and grouping functions , 2013, Inf. Sci..

[11]  Benjamín R. C. Bedregal,et al.  Archimedean overlap functions: The ordinal sum and the cancellation, idempotency and limiting properties , 2014, Fuzzy Sets Syst..

[12]  Balasubramaniam Jayaram.  T-subnorms with strong associated negation: Some properties , 2017, Fuzzy Sets Syst..

[13]  Cheng-Shang Chang.  Calculus , 2020, Bicycle or Unicycle?.

[14]  M. J. Frank,et al.  Associative Functions: Triangular Norms And Copulas , 2006 .

[15]  Benjamín R. C. Bedregal,et al.  Interval Valued Versions of T-Conorms, Fuzzy Negations and Fuzzy Implications , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[16]  Humberto Bustince,et al.  On additive generators of overlap functions , 2016, Fuzzy Sets Syst..

[17]  Michal K. Urbanski,et al.  Fuzzy Arithmetic Based On Boundary Weak T-Norms , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[18]  Bao Qing Hu,et al.  On homogeneous, quasi-homogeneous and pseudo-homogeneous overlap and grouping functions , 2019, Fuzzy Sets Syst..

[19]  Sándor Jenei,et al.  Fibred triangular norms , 1999, Fuzzy Sets Syst..

[20]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[21]  Berthold Schweizer,et al.  Probabilistic Metric Spaces , 2011 .

[22]  Bernard De Baets,et al.  Fuzzy preference structures without incomparability , 1995, Fuzzy Sets Syst..

[23]  Francisco Herrera,et al.  A Historical Account of Types of Fuzzy Sets and Their Relationships , 2016, IEEE Transactions on Fuzzy Systems.

[24]  Benjamín R. C. Bedregal,et al.  Interval Valued QL-Implications , 2007, WoLLIC.

[25]  Sándor Jenei,et al.  Structure of left-continuous triangular norms with strong induced negations (I) Rotation construction , 2000, J. Appl. Non Class. Logics.

[26]  Eyke Hüllermeier,et al.  Grouping, Overlap, and Generalized Bientropic Functions for Fuzzy Modeling of Pairwise Comparisons , 2012, IEEE Transactions on Fuzzy Systems.

[27]  Lazaros S. Iliadis,et al.  Application of fuzzy T-norms towards a new Artificial Neural Networks' evaluation framework: A case from wood industry , 2008, Inf. Sci..

[28]  Sándor Jenei,et al.  Continuity of left-continuous triangular norms with strong induced negations and their boundary condition , 2001, Fuzzy Sets Syst..

[29]  Mourad Oussalah,et al.  On the use of Hamacher's t-norms family for information aggregation , 2003, Inf. Sci..

[30]  Francisco Herrera,et al.  Managing non-homogeneous information in group decision making , 2005, Eur. J. Oper. Res..

[31]  R. Mesiar,et al.  Aggregation Functions: Aggregation on ordinal scales , 2009 .

[32]  Yong Su,et al.  On pseudo-homogeneous triangular norms, triangular conorms and proper uninorms , 2016, Fuzzy Sets Syst..

[33]  Bernard De Baets,et al.  Rotation-invariant t-norms: Where triple rotation and rotation-annihilation meet , 2009, Fuzzy Sets Syst..

[34]  Gabriele Steidl,et al.  Homogeneous Penalizers and Constraints in Convex Image Restoration , 2013, Journal of Mathematical Imaging and Vision.