In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...

The paper presents the comparison of fuzzy conclusions derived from the use of t-norms with the fuzzy conclusions derived from the use of H-norm. The idea was to examine the application of H-logical norm to fuzzy reasoning, which is not monotonious while it is known that t-norms used in fuzzy reasoning have the characteristic of monotonicity. The comparison of fuzzy conclusions was performed by...

 Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and suffi...

For theoretical fuzzy control it is a well known strategy to transform a system of control rules into a system of relation equations. Because these systems of relation equations are not always solvable, solvability criteria and approximate solutions have been discussed. We reconsider some of the results in this field and extend them using more recent results on t-norm based fuzzy logics and on ...

Two ways to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous archimedean t-norm are given. The first one aggregates the transitive closure R of R with a (maximal) T -transitive relation B contained in R. The second one modifies the values of R or B to better fit them with the ones of R.

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

In this paper the notion of idempotent fuzzy subquasigroups with respect to a s-norm is introduced and some related properties are investigated. Then properties of homomorphic image and inverse image of fuzzy subquasigroups respect to a s-norm are discussed. Next some properties of direct product of fuzzy subquasigroups with respect to a s-norm are presented. Finally abnormalization of fuzzy su...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

By the representation's theorem it is known that a fuzzy relation R is a preorder if and only if R = inf~ e so If, where -~ is the set of logical states of I~ In this paper it is shown how, in almost all cases, both for the t-norm Min and archimedean t-norms T, it is possible to consider that the fuzzy sets I~ are normalized. Furthermore a partial order between logical states, defined from the ...