The continuous evolution of information technology underscores the growing emphasis on data security. In the realm of medical imaging, various diagnostic images represent the privacy of individuals, and the potential repercussions of their unauthorized disclosure are substantial. Therefore, this study introduces a novel chaotic system (TLCMCML) and employs it to propose a multi-image medical image encryption algorithm. To simultaneously augment security and optimize encryption efficiency, we undertake a dual-pronged approach. Firstly, we identify the regions of interest (ROIs) within individual medical images, subsequently applying an independent scrambling technique based on an odd-even interleaving configuration. Secondly, we integrate all medical images through horizontal concatenation, forming a comprehensive large-scale image, upon which we implement a synchronized bit-level permutation-diffusion encryption mechanism. Following extensive testing, enhancements were verified across various metrics including information entropy analysis, adjacent pixel correlation examination, differential attack simulations, and robustness assessments, thereby attesting to the exceptional encryption efficacy of the proposed algorithm.

We introduce and study some types of fuzzy prefilters (filters) inEQ-algebras. First, we present several characterizations of fuzzy positive implicative prefilters (filters), fuzzy implicative prefilters (filters), and fuzzy fantastic prefilters (filters). Next, using their characterizations, we mainly consider the relationships among these special fuzzy filters. Particularly, we find some conditions under which a fuzzy implicative prefilter (filter) is equivalent to a fuzzy positive implicative prefilter (filter). As applications, we obtain some new results about classical filters inEQ-algebras and some related results about fuzzy filters in residuated lattices.

This paper introduces the implicative derivations and gives some of their characterizations on MTL-algebras. Furthermore, we provide some representation of MTL-algebras by implicative derivations and obtain some representation of Boolean algebra via the algebra of all implicative derivations. Finally, we explore the relationship between implicative derivation and other operators on MTL-algebras and show that there exists a bijection between the sets of multiplier and implicative derivations on IMTL-algebras. The results of this paper can provide the common properties of implicative derivations in the t-norm-based fuzzy logical algebras.