On Bipolar Fuzzy Gradation of Openness

Abstract

The concept of bipolar fuzziness is of relatively recent origin where in addition to the presence of a property, which is done in fuzzy theory, the presence of its counter-property is also taken into consideration. This seems to be much natural and realistic. In this paper, an attempt has been made to incorporate this bipolar fuzziness in topological perspective. This is done by introducing a notion of bipolar gradation of openness and to redefine the bipolar fuzzy topology. Furthermore, a notion of bipolar gradation preserving map is given. A concept of bipolar fuzzy closure operator is also introduced and its characteristic properties are studied. A decomposition theorem involving our bipolar gradation of openness and Chang type bipolar fuzzy topology is established. Finally, some categorical results of bipolar fuzzy topology (both Chang type and in our sense) are proved.

Fuzzy Set and Soft Set Theories as Tools for Vocal Risk Diagnosis

“…Recently, fuzzy techniques have been used to design a sustainable development model for the agricultural sector for the critical circumstances of the COVID-19 pandemic [4], to assess the strength of competition among competitors in the feld of competitive network system [5], to present a novel rule-based approach using picture fuzzy sets to enable intelligent clinical decision support system [6], to propose a complete system for managing and extracting information in health systems using big data architecture [7], to present a new algorithm for making decisions for the assessment of the biological impact of nonionizing radiation [8], and to develop the rough D-TOPSIS method which provides a more comprehensive and rational framework for evaluation of crops farming without any assumptions or predetermined membership functions and which is applied in agricultural farming for increasing crop production in a specifc region with certain soil characteristics and water requirements and investment analysis in organic and inorganic farming systems [9] and to propose a novel model called dual 2-tuple linguistic rough number (D2tLRN) clouds or dual 2-tuple linguistic rough integrated (D2tLRN) clouds which is integrated with the TOPSIS method for the selection of medical disposal technologies [10]. Also, using the concepts of fuzzy set theory, some extensions have been proposed, such as an innovative concept of extended fuzzy set, in which the S-norm function of membership and nonmembership grades is less than or equal to one [11], a defnition of bipolar gradation of openness of bipolar fuzzy subsets and give a new defnition of bipolar fuzzy topological spaces [12], a new type of generalized fuzzy sets called CR-fuzzy sets [13], a novel concept called a linguistic complex fuzzy set [14], a new linguistic evaluation model they called the fuzzy integrated clouds (RFIC), to handle uncertain information by integrating approximate fuzzy numbers with cloud model theory [15], among others that have recently appeared.…”