In the paper we study a method extending fuzzy measures on the set N = {1, . . . , n} to n-ary aggregation functions on the interval [0, 1]. The method is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. This approach generalizes the wellknown Lovász and Owen extensions of fuzzy measures. We focus our attention on the special class o...

Abstract. The interval-valued prime fuzzy ideals (in brevity, the iv. prime fuzzy ideals) of a semigroup have been recently studied by Kar, Sarkar and Shum [18]. As a continued study of i-v fuzzy ideals, we are going to investigate the properties of i-v fuzzy quasi-ideal and i-v fuzzy bi-ideal of a semiring and then we characterize the regularity and intra-regularity of a semiring in terms of t...

In this paper we have generalized the concepts of   q   , -fuzzy ideals,   q   , -fuzzy quasi-ideals and   q   , -fuzzy bi-ideals by introducing the concepts of   k q   , -fuzzy ideals,   k q   , -fuzzy quasiideals and   k q   , -fuzzy bi-ideals in ternary semigroups and several related properties are investigated. Different characterizations of regular and weakly ...

In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a generalization of fuzzy ideals in ternary semigroups. We investigate the related properties of ternary semigroups. The lower and upper parts of fuzzy subsets of a ternary semigroup are defined. Characterizations of regular ternary semigroups by the properties of the lower part of (∈,∈∨q)-fuzzy left ...

olds ( α̃, β̃ ) and interval valued fuzzy generalized bi-ideals with thresholds ( α̃, β̃ ) , which are generalization of interval valued fuzzy ideals, interval valued fuzzy interior ideals, interval valued fuzzy quasi ideals and interval valued fuzzy generalized bi-ideals, in a semigroup are introduced, and related properties are investigated. Characterizations of regular semigroups by the properti...

In this paper, we study the existence of coupled coincidence andcoupled common fixed points for single-valued and fuzzy mappingsunder a contractive condition in metric space. Presented theoremsextend and improve the main results of Abbas and$acute{C}$iri$acute{c}$ {itshape et al.} [M. Abbas, L.$acute{C}$iri$acute{c}$, {itshape et al.}, Coupled coincidenceand common fixed point theorems for hybr...

Using the concept of a mixed g-monotone mapping, we prove some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete quasi-metric spaces with a Q-function q. The presented theorems are generalizations of the recent coupled fixed point theorems due to Bhaskar and Lakshmikantham 2006 , Lakshmikantham and Ćirić 2009 and many ot...

We introduce the concept of (γ, δ)-bifuzzy Lie subalgebra, where γ, δ are any two of {∈, q, ∈∨q, ∈∧q} with γ ≠ ∈∧q, by using belongs to relation (∈) and quasi-coincidence with relation (q) between bifuzzy points and bifuzzy sets and discuss some of its properties. Then we introduce bifuzzy soft Lie subalgebras and investigate some of their properties.

This paper proves that validity and satisfiability of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic with universal and existential quantifiers (which are non-interdefinable) is decidable when we only consider quasi-witnessed interpretations. We prove that this restriction is neither necessary for the validity problem (i.e., the validity of assertions in the Fu...

Abstract. In this paper, by using a continuation theorem of coincidence degree theory and a differential inequality, we establish some sufficient conditions ensuring the existence and global exponential stability of anti-periodic solutions for a class of fuzzy Cohen–Grossberg neural networks with time-varying and distributed delays. In addition, we present an illustrative example to show the fe...