The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

We investigate the distribution functions and the moments of the so-called Choquet integral, also known as the Lovász extension, when regarded as a real function of a random sample drawn from a continuous population. Since the Choquet integral includes weighted arithmetic means, ordered weighted averaging operators, and lattice polynomials as particular cases, our results encompass the correspo...

The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

The soft set theory is a newly mathematical tool to deal with uncertain problems. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, we introduce the average function and propose the interval-valued intuitionistic hesitant fuzzy soft sets (IVIHFSSs) which are a combination of the interval-valued intuitionistic hesitant fuzzy sets and...

Bipolar fuzzy set theory has been successfully applied in some areas, but there are situations real life which can’t be represented by bipolar sets. However, all the existing approaches unsuitable to describe positive and negative membership degree an element uncertain linguistic label have interval value, can reflect decision maker’s confidence level when they making evaluation. In order overc...

The primary aim of this article is to extend the bipolar fuzzy N -soft sets with concern pursuing periodicity involved real-world problems and introduce a new multiskilled hybrid model, namely, complex id="M2"> sets. novel model possesses parametric characteristics versatile id="M3"> set enjoys distinguished attributes h...

Active Learning Method (ALM) is a soft computing method which is used for modeling and control, based on fuzzy logic. Although ALM has shown that it acts well in dynamic environments, its operators cannot support it very well in complex situations due to losing data. Thus ALM can find better membership functions if more appropriate operators be chosen for it. This paper substituted two new oper...

This paper studies the nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set of the problems is non-convex, in a general case. Therefore, conventional nonlinear optimization methods cannot be ideal for resolution of such problems. Hence, a Genetic Algorithm (GA) is proposed to find their optimal solution. This algorithm uses th...

Data fusion is a long term of research in image processing that is becoming more and more relevant owing to the complementary developments of computer and sensory technologies. Although operator research related to soft-computing, specially in the eld of fuzzy systems, has evolved considerably during this last two decades, implemented frameworks of data fusion for image processing take seldom i...

On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine...