Triangular Norm-Based Aggregation of Evidence Under Fuzziness

Several types of aggregation operators on fuzzy sets are discussed, all of them based on triangular norms and triangular conorms. The main stress is given to the operators allowing to compensate a low input value by another high input value, i. e., to the compensatory operators. We discuss only the pointwise aggregation and the crisp output can be obtained afterwards by any defuzzification procedure. The properties of exponential compensatory operators, convex-linear compensatory operators, convex non-linear compensatory operators, uni-norms and generated aggregative operators are investigated.

[1]  K. Menger.  Statistical Metrics. , 1942, Proceedings of the National Academy of Sciences of the United States of America.

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

[3]  H. Zimmermann,et al.  Latent connectives in human decision making , 1980 .

[4]  J. Dombi.  Basic concepts for a theory of evaluation: The aggregative operator , 1982 .

[5]  E. Klement.  Construction of Fuzzy σ-algebras using triangular norms , 1982 .

[6]  J. Dombi.  A general class of fuzzy operators, the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators , 1982 .

[7]  M. K. Luhandjula.  Compensatory operators in fuzzy linear programming with multiple objectives , 1982 .

[8]  I. Turksen.  Interval-valued fuzzy sets and “compensatory AND” , 1992 .

[9]  H. Zimmermann,et al.  Advanced fuzzy logic control of a model car in extreme situations , 1992 .

[10]  R. Yager.  Aggregation operators and fuzzy systems modeling , 1994 .

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

[12]  Ronald R. Yager,et al.  A note on the incompatibility of openness and associativity , 1997, Fuzzy Sets Syst..

[13]  Ronald R. Yager,et al.  On a Class of Weak Triangular Norm Operators , 1997, Inf. Sci..

[14]  Ronald R. Yager,et al.  Full reinforcement operators in aggregation techniques , 1998, IEEE Trans. Syst. Man Cybern. Part B.