Keywords:Membership function, Measure, Conditional distribution, Bi-conditional distribution, Elementary event, Bayes rule.
In this paper, a new kind of infinite logic will be introduced. The elements of this logic are truth function that assigns truth value belongs to the range [0,1] to any statement representing degree of truth and probability function that assigns a value ranging [0,1] to any random event representing degree of likelihood (both truth and probability are measures satisfying the classical axioms of probability theory). New axioms and definitions will be added to the axioms and definitions of probability theory to represent intersection, union, implication and double implication between truth statements, probabilistic events and truth statements and probabilistic events. By this, we can evaluate degree of truth and degree of likelihood and the interaction between them.
Goguen J.A, "L-fuzzy sets". Journal of Mathematical Analysis and Applications 18: 145â€“174, 1967.
Fazlalipor Miyandoab, M., Arzideh, K., Farbod, D,.Fuzzy Hypothesis Testing With Fuzzy Data by Using Fuzzy P-value, Acta Universitatis Apulensis, pp. 293-307, 2012.
Zimmermann, H. J. Fuzzy Set Theory and its Applications, Kluwer-Nijho publishing, 1984.
Doob, J. L, "The Development of Rigor in Mathematical Probability", Amer. Math. Monthly 103, 586-595, 1996.
Shiryaev. A. N., Probability (Graduate Text in Mathematics), Springer-Verlag, 1995.
George Casella and Roger L. Berger, "Statistical Inference", Duxbury Press, ISBN 0-534-11958-1 (p. 18 et seq), 1990.
How to Cite
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.