In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) characteristic function, and BCF point. Then, subgroup, normal conjugate, normalizer cosets, abelian factor group. Furthermore, present associated examples theorems, prove these theorems. After that, image pre-image of subgroups under homomorphism related

In this note, by using the concept of Bipolar-valued fuzzy set, the notion of bipolar-valued fuzzy BCK/BCI-algebra is introduced. Moreover, the notions of (strong) negative s-cut (strong) positive t-cut are introduced and the relationship between these notions and crisp subalgebras are studied.

This paper shows, by examples, that Lemma 2.1, Lemma 3.1, Corollary 3.1, Corollary 3.2, Theorem 3.1, Corollary 3.3, Theorem 3.3 and Lemma 4.1 in [Y. Luo, Resolution of fuzzy relation equation (I) based on Boolean-type implications, Comput. Math. Appl. 52 (2006) 421–428] about resolution of fuzzy relation equations based on Boolean-type implications, are false. We also point out that the solutio...

Systems of fuzzy relation equations and inequalities in which an unknown is on the one side equation or inequality are linear systems. They most studied ones, a vast literature systems focuses finding solutions solvability criteria for such The situation quite different with so-called weakly systems, both sides inequality. Precisely, scholars have only given characterization set exact to This p...