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In this paper, some properties of a BPFR were studied. Also, level sets of BPFRs were studied with their properties. Some results were given and, in some cases, examples and counter-examples were constructed. In particular, we have shown that if a BPFR Q is a subset of another BPFR ρ, (s, t)-level (or strong level) subsets of Q are classical subsets of the (s, t)-level (or strong level) subsets of ρ and that the strong level subsets of a BPFR is a subset of the ordinary level subset of the same among others. By these, we have improved on some of the results in the previous work and have laid the right foundation for further works on these concepts.

The issue of distributivity of aggregation operations is crucial for many different areas such as utility theory and integration theory. Of special interest are aggregation operations with annihilator. This paper is focused on the problem of distributivity for some so called associative, commutative aggregation operations with annihilator a, known as associative a-CAOA, and uninorms. The full characterization of distributive pairs for T-uninorms, S-uninorms and bi-uninorms is given. [ABSTRACT FROM AUTHOR]

A new generalized class of fuzzy implications, called ($h,f,g$)-implications, is introduced and discussed in this paper. The results show that the new fuzzy implications possess some good properties, such as the left neutrality property and the exchange principle. [ABSTRACT FROM AUTHOR]

In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product (or, more generally, from any strict Frank t-norm) all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess this property. We give a full solution to this problem (in the case of strict t-norms), together with convenient sufficient conditions. We list several families of strict t-norms having this property and provide also counterexamples (the Hamacher product is one of them). Finally, we discuss the consequences of these results for the characterization of tribes based on strict t-norms. [ABSTRACT FROM AUTHOR]

We characterizen-ary operationsFon the unit intervalIsuch thatholds for every increasing bijection f fromIontoIand for everyWe also describe invariant domains and apply these results to binary operations onI. [ABSTRACT FROM AUTHOR]