Search Results (5)

In practical applications, the basic fuzzy set is used via symmetric uncertainty variables. In the research field, it is comparatively rare to discuss two-fold uncertainty due to its complication. To deal with the multi-polar uncertainty in real life problems, $m$-polar (multi-polar) fuzzy ($m$-PF) sets are put forward. The main objective of this paper is to explore the idea of $m$-PF sets, which is a generalization of bipolar fuzzy (BPF) sets, in ternary semirings. The major aspects and novel distinctions of this work are that it builds any multi-person, multi-period, multi-criteria, and complex hierarchical problems. The main focus of this study is to confine generalization of some important results of BPF sets to the results of $m$-PF sets. In this research, the notions of $m$-polar fuzzy ternary subsemiring ($m$-PFSS), $m$-polar fuzzy ideal ($m$-PFI), $m$-polar fuzzy generalized bi-ideal ($m$-PFGBI), $m$-polar fuzzy bi-ideal ($m$-PFBI), and $m$-polar fuzzy quasi-ideal ($m$-PFQI) in ternary semirings are introduced. Moreover, this paper deals with several important properties of $m$-PFIs and characterizes regular and intra-regular ternary semiring in terms of these ideals. Full article

The central objective of the proposed work in this research is to introduce the innovative concept of an m-polar fuzzy set (m-PFS) in semigroups, that is, the expansion of bipolar fuzzy set (BFS). Our main focus in this study is the generalization of some important results of BFSs to the results of m-PFSs. This paper provides some important results related to m-polar fuzzy subsemigroups (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs), m-polar fuzzy quasi-ideals (m-PFQIs) and m-polar fuzzy interior ideals (m-PFIIs) in semigroups. This research paper shows that every m-PFBI of semigroups is the m-PFGBI of semigroups, but the converse may not be true. Furthermore this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semigroups by the properties of m-PFIs and m-PFBIs. Full article

Research on the protein folding problem differentiates the protein folding process with respect to the duration of this process. The current structure encoded in sequence dogma seems to be clearly justified, especially in the case of proteins referred to as fast-folding, ultra-fast-folding or downhill. In the present work, an attempt to determine the characteristics of this group of proteins using fuzzy oil drop model is undertaken. According to the fuzzy oil drop model, a protein is a specific micelle composed of bi-polar molecules such as amino acids. Protein folding is regarded as a spherical micelle formation process. The presence of covalent peptide bonds between amino acids eliminates the possibility of free mutual arrangement of neighbors. An example would be the construction of co-micelles composed of more than one type of bipolar molecules. In the case of fast folding proteins, the amino acid sequence represents the optimal bipolarity system to generate a spherical micelle. In order to achieve the native form, it is enough to have an external force field provided by the water environment which directs the folding process towards the generation of a centric hydrophobic core. The influence of the external field can be expressed using the 3D Gaussian function which is a mathematical model of the folding process orientation towards the concentration of hydrophobic residues in the center with polar residues exposed on the surface. The set of proteins under study reveals a hydrophobicity distribution compatible with a 3D Gaussian distribution, taken as representing an idealized micelle-like distribution. The structure of the present hydrophobic core is also discussed in relation to the distribution of hydrophobic residues in a partially unfolded form. Full article

Our main objective is to introduce the innovative concept of $(\alpha ,\beta )$ -bipolar fuzzy ideals and $\left(\alpha ,\beta \right)$ -bipolar fuzzy generalized bi-ideals in ordered ternary semigroups by using the idea of belongingness and quasi-coincidence of an ordered bipolar fuzzy point with a bipolar fuzzy set. In this research, we have proved that if a bipolar fuzzy set $h=(S;h_n,h_p)$ in an ordered ternary semigroup $S$ is the $(\in ,\in \vee q)$ -bipolar fuzzy generalized bi-ideal of $S$ , it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the $(\in ,\in \vee q)$ -bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the $(\in ,\in \vee q)$ -bipolar fuzzy generalized bi-ideals. Full article

In this paper, we introduce a generalization of a bipolar fuzzy (BF) subsemigroup, namely, a $({\alpha }_1,{\alpha }_2;{\beta }_1,{\beta }_2)$ -BF subsemigroup. The notions of $({\alpha }_1,{\alpha }_2;{\beta }_1,{\beta }_2)$ -BF quasi(generalized bi-, bi-) ideals are discussed. Some inequalities of $({\alpha }_1,{\alpha }_2;{\beta }_1,{\beta }_2)$ -BF quasi(generalized bi-, bi-) ideals are obtained. Furthermore, any regular semigroup is characterized in terms of generalized BF semigroups. Full article