Walker et al. ([18], [19]) defined two families of binary operations on M (set of functions of [0,1] in [0,1]), and they determined that, under certain conditions, those operations are t-norms (triangular norm) or t-conorms on L (all the normal and convex functions of M). We define binary operations on M, more general than those given by Walker et al., and we study many properties of these gene...

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

and Applied Analysis 3 A finite subset of j consecutive positive integers starting with 1 is denoted by j : {1, 2, . . . , j}. The set R−h : −h, 0 ∪ R0 will be used to define the solution of functional differential equations on R0 including its initial condition in −h, 0 . C i R0 ,Rm0 is the set of m-vector real functions of class C i and definition domain R0 and PC i R0 ,Rm0 is the set of m-ve...

In this paper we use a comparison measure which can be adapted to various different applications and has many good properties for further analysis. This comparison measure is based on the adaptive aggregation of the t-norms and t-conorms. We test this measure in classification tasks, with Dombi and Yager type of t-norm and t-conorm operators. The classification results are compared to plain t-n...

In this contribution, we first introduce the concept of metrical T-norm-based similarity measure for hesitant fuzzy sets (HFSs) {by using the concept of T-norm-based distance measure}. Then,the relationship of the proposed {metrical T-norm-based} similarity {measures} with the {other kind of information measure, called the metrical T-norm-based} entropy measure {is} discussed. The main feature ...

A bounded linear operator T on a complex Hilbert space H is called complex symmetric if T = CT ∗C, where C is a conjugation (an isometric, antilinear involution of H). We prove that T = CJ |T |, where J is an auxiliary conjugation commuting with |T | = √ T ∗T . We consider numerous examples, including the Poincaré-Neumann singular integral (bounded) operator and the Jordan model operator (compr...

let h be an infinite--dimensional hilbert space and k(h) be the set of all compact operators on h. we will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher jordan derivation on k(h) associated with the following cauchy-jencen type functional equation 2f(frac{t+s}{2}+r)=f(t)+f(s)+2f(r) for all t,s,rin k(h).