Decision-making under uncertainty processed by lattice-valued possibilistic measures

summary:The notion and theory of statistical decision functions are re-considered and modified to the case when the uncertainties in question are quantified and processed using lattice-valued possibilistic measures, so emphasizing rather the qualitative than the quantitative properties of the resulting possibilistic decision functions. Possibilistic variants of both the minimax (the worst-case) and the Bayesian optimization principles are introduced and analyzed

Possibilistic alternatives of elementary notions and relations of the theory of belief functions

summary:The elementary notions and relations of the so called Dempster–Shafer theory, introducing belief functions as the basic numerical characteristic of uncertainty, are modified to the case when probabilistic measures and basic probability assignments are substituted by possibilistic measures and basic possibilistic assignments. It is shown that there exists a high degree of formal similarity between the probabilistic and the possibilistic approaches including the role of the possibilistic Dempster combination rule and the relations concerning the possibilistic nonspecificity degrees

Partial Convergence and Continuity of Lattice-Valued Possibilistic Measures

The notion of continuity from above (upper continuity) for lattice-valued possibilistic measures as investigated in [7] has been proved to be a rather strong condition when imposed as demand on such a measure. Hence, our aim will be to introduce some versions of this upper continuity weakened in the sense that the conditions imposed in [7] to the whole definition domain of the possibilistic measure in question will be restricted just to certain subdomains. The resulting notion of partial upper convergence and continuity of lattice-valued possibilistic measures will be analyzed in more detail and some results will be introduced and proved

std-Convergence in fuzzy metric spaces

In this note we answer two recent questions posed by Morillas and Sapena [10] related to standard convergence in fuzzy metric spaces in the sense of George and Veeramani. The obtained results lead us to establish what conditions must satisfy a concept about sequential convergence to be considered compatible with a concept of Cauchyness.Juan Jose Minana acknowledges the support of Conselleria de Educacion, Formacion y Empleo (Programa Vali+d para investigadores en formacion) of Generalitat Valenciana, Spain, ACIF/2012/040, and the support of Universitat Politecnica de Valencia under Grant PAID-06-12 SP20120471.Gregori Gregori, V.; Miñana, JJ. (2015). std-Convergence in fuzzy metric spaces. Fuzzy Sets and Systems. 267:140-143. https://doi.org/10.1016/j.fss.2014.05.007S14014326

On Yager and Hamacher t-Norms and Fuzzy Metric Spaces

Recently, Gregori et al. have discussed (Fuzzy Sets Syst 2011;161:2193 2205) the so-called strong fuzzy metrics when looking for a class of completable fuzzy metric spaces in the sense of George and Veeramani and state the question of finding a non-strong fuzzy metric space for a continuous t-norm different from the minimum. Later on, Gutíerrez-García and Romaguera solved this question (Fuzzy Sets Syst 2011;162:91 93) by means of two examples for the product and the Lukasiewicz t-norm, respectively. In this direction, they posed to find further examples of nonstrong fuzzy metrics for continuous t-norms that are greater than the product but different from minimum. In this paper, we found an example of this kind. On the other hand, Tirado established (Fixed Point Theory 2012;13:273 283) a fixed-point theorem in fuzzy metric spaces, which was successfully used to prove the existence and uniqueness of solution for the recurrence equation associated with the probabilistic divide and conquer algorithms. Here, we generalize this result by using a class of continuous t-norms known as ω-Yager t-norms.The second author acknowledges the support of the Ministry of Economy and Competitiveness of Spain under grant MTM2012-37894-C02-01 and the support of Universitat Politecnica de Valencia under grant PAID-06-12-SP20120471.Castro Company, F.; Tirado Peláez, P. (2014). On Yager and Hamacher t-Norms and Fuzzy Metric Spaces. International Journal of Intelligent Systems. 29:1173-1180. https://doi.org/10.1002/int.21688S1173118029Sherwood, H. (1966). On the completion of probabilistic metric spaces. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 6(1), 62-64. doi:10.1007/bf00531809Gregori, V. (2002). On completion of fuzzy metric spaces. Fuzzy Sets and Systems, 130(3), 399-404. doi:10.1016/s0165-0114(02)00115-xGregori, V., Morillas, S., & Sapena, A. (2010). On a class of completable fuzzy metric spaces. Fuzzy Sets and Systems, 161(16), 2193-2205. doi:10.1016/j.fss.2010.03.013Gutiérrez García, J., & Romaguera, S. (2011). Examples of non-strong fuzzy metrics. Fuzzy Sets and Systems, 162(1), 91-93. doi:10.1016/j.fss.2010.09.017Yager, R. R. (1980). On a general class of fuzzy connectives. Fuzzy Sets and Systems, 4(3), 235-242. doi:10.1016/0165-0114(80)90013-5Castro-Company, F., & Tirado, P. (2012). Some classes of t-norms and fuzzy metric spaces. doi:10.1063/1.4756272George, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), 395-399. doi:10.1016/0165-0114(94)90162-7Hadžić, O., & Pap, E. (2001). Fixed Point Theory in Probabilistic Metric Spaces. doi:10.1007/978-94-017-1560-7Klement, E. P., Mesiar, R., & Pap, E. (2000). Triangular Norms. Trends in Logic. doi:10.1007/978-94-015-9540-