We introduce and study fuzzy (co-)inner product and fuzzy (co)norm of hyperspaces. In this regard by considering the notion of hyperspaces, as a generalization of vector spaces, first we will introduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions of fuzzy (co-)norm and fuzzy (co-)orthogonality in hyperspaces. In particular, we will prove that ...

In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...

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 ...

in this paper, we introduce the concepts of norm and inner prod- uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...

In this paper, we introduce the concepts of norm and inner prod- uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.

Extensions of monoidal t-norm logic MTL and related fuzzy logics with truth stresser modalities such as globalization and “very true” are presented here both algebraically in the framework of residuated lattices and proof-theoretically as hypersequent calculi. Completeness with respect to standard algebras based on t-norms, embeddings between logics, decidability, and the finite embedding prope...

Finding strongly standard complete axiomatizations for t-norm based fuzzy logics (i.e. complete for deductions with infinite sets of premises w.r.t. semantics on the real unit interval [0, 1]) is still an open problem in general, even though results are already available for some particular cases like some infinitary logics based on a continuous t-norm or certain expansions of Monoidal t-norm b...