###### On ps-ro semiopen fuzzy set and ps-ro fuzzy semicontinuous, semiopen functions

## Abstract

The aim of this paper is to introduce and characterize ps-ro semiopen (semiclosed) fuzzy sets, which are totally independent of the existing notion of fuzzy open (closed) sets and semiopen (semiclosed) fuzzy sets. Also, in term of these fuzzy sets and operators ps-scl and ps-sint, a class of functions named as ps-ro fuzzy semicontinuous and ps-ro fuzzy semiopen (closed) functions are defined and their various properties are studied. ps-ro fuzzy semicontinuity is indeed totally different from both the existing concepts of fuzzy continuity and fuzzy semicontinuity. Similarly, ps-ro fuzzy open (closed) and well known concept of fuzzy semiopen (closed) functions do not imply each other. These concepts are used as new tools to study different characterizations of the given fuzzy topological space, giving a new dimension in the study of fuzzy topological spaces.

###### Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system

## Abstract

Modeling the motion and propagation characteristics of waves have importance in coastal, ocean and maritime engineering. Especially, waves are the major source of environmental actions on beaches or on man-made fixed or floating structures in most geographical areas. So Maccari system has great application in mentioned areas. The modified KdV is ion acoustic perturbations evolution model in a plasma with two negative ion components which have different temperatures. As for the KdV equation, the modified ZK (mZK) equation arises naturally as weakly two-dimensional variations of the mKdV equation. In this paper authors used functional variable method(FVM) for the first time to obtain exact travelling wave and soliton solutions of conformable fractional modified KdV-Zakharov-Kuznetsov(mKdv-ZK) equation and Maccari system. As a consequence, new solutions are obtained and it is seen that FVM is an valuable and efficient tool for solving nonlinear equations and systems where the derivatives defined by means of conformable fractional derivative.

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The Method of Infinite Ascent Applied on *2*
^{
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*A*
^{6} + *B*
^{3} = *C*
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###### A simple model of production and trade in an oligopolistic market: back to basics

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