Several Types Of Soft And Fuzzy Filter Filters MTL- Algebra

MIL-algebra is a basic algebra system, it is meaningful to research logic algebras of n-value. In this paper, using soft sets and fuzzy sets as the main tools, we study some types of filters in ML-algebra, such as intersectional soft ML-filters theory and fuzzy n-fold filters theory. The main contents that we study in the following aspects:1. We introduce the concept of λ-intersectional soft filter and then we give several important characterizations and relevant properties of λ-intersectional soft filter in MIL-algebra. Meanwhile, the properties of image and preimage of λ-intersectional soft MIL-filters under a homomorphism are discussed.2. We also discuss intersectional soft MIL-filter which is the special case of λ-intersectional soft MIL-filter if λ is a global set. Further, we define some special intersectional soft filters of MIL-algebra such as intersectional soft implicative filter, intersectional soft positive implicative filter, intersectional soft fantastic filter, intersectional soft EIMIL-filter, intersectional soft1MIL-filter and prove that they are intersectional soft MIL-filters. Then the relationships among them are studied.3. Using fuzzification method as the main method, we define the fuzzy n-fold EIMIL-filter and fuzzy n-fold IMIL-filter respectively and give several important characterizations of them. Using the level cut set as the bridge, we prove that a fuzzy filter of MIL-algebra is a fuzzy n-fold EIMIL-filter if and only if its level cut is a n-fold EIMIL-filter.We spread the concepts of some special fuzzy n-fold filters of BL-algebra such as fuzzy n-fold fantastic filter, fuzzy n-fold normal filter, fuzzy n-fold implicative filter, fuzzy n-fold positive implicative filter into MIL-algebra in order to discuss the relations among fuzzy n-fold EIMIL-filter, fuzzy n-fold IMIL-filter and the filters that are spread from BL-algebra into MIL-algebra. Finally, we prove that quotient algebras induced by fuzzy n-fold EIMIL-filter and fuzzy n-fold IMIL-filter are corresponding n-fold EIMIL-algebra and IMIL-algebra.