A family of fuzzification schemes is proposed that can be used to transform cardinality-based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe. These schemes are based on the Frank t-norm family and preserve transitivity in the fuzzification process.

A generalization of bags is proposed and fundamental operations are described. That is, a real-valued bag is proposed which is a straightforward generalization of the traditional bags, but is necessary for complementation, and s-norm and t-norm operations. We mainly describe how complementation and s-norms are related. As a result a duality theorem between s-norm and t-norm is obtained. R-bag r...

This paper presents new image processing operations based on the Dubois and Prade proposal of a fuzzy triangular norm. This definition is recalled, and a computational efficient algorithm is derived for its fast computation. This procedure also gives a comprehensive model for reasoning about the qualitative effects of the Dubois and Prade fuzzy norm on data. The presented image processing opera...

We continue to develop a construction of an L-fuzzy valued measure by extending a measure defined on a σalgebra of crisp sets to an L-fuzzy valued measure defined on a TM-tribe in the case when operations with L-sets and L-fuzzy numbers are defined by using the minimum triangular norm TM . We introduce an L-fuzzy valued integral over an L-set with respect to an L-fuzzy valued measure, consider ...

We study the transitivity of fuzzy preference relations, often considered as a fundamental property providing coherence to a decision process. We consider the transitivity of fuzzy relations w.r.t. conjunctors, a general class of binary operations on the unit interval encompassing the class of triangular norms usually considered for this purpose. Having fixed the transitivity of a large prefere...

In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator...

We develope a construction of an L-fuzzy valued measure by extending a measure defined on a σ-algebra of crisp sets to an L-fuzzy valued TM-countably additive measure defined on a TMclan of L-fuzzy sets in the case when operations for L-fuzzy sets and L-fuzzy real numbers are based on the minimum t-norm TM. Keywords— L-fuzzy set, L-fuzzy real number, L-fuzzy valued measure.

This paper studies a renewal reward process with fuzzy random interarrival times and rewards under the >-independence associated with any continuous Archimedean t-norm >. The interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are >-independent fuzzy variables. Under these conditions, some limit theorems in mean...

In fuzzy logic in wider sense t norms got a prominent r ole in recent times In many valued logic the Lukasiewicz systems the G odel sytems and also the product logic are t norm based The present paper discusses the more general problem of the adequate axiomatizability for such t norm based logical systems in general survey ing results of the last years

Lipschitzian and kernel aggregation operators with respect to the natural T indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator w...