The commutator of Lie algebra is extended to a product of fuzzy Lie subspaces over fuzzy field. An action of fuzzy field is introduced as an extension of scalar multiplication in Lie algebra. The notion of derived series and descending central series of fuzzy Lie ∼ideal over fuzzy field and the concepts of ∼nilpotent and ∼solvable fuzzy Lie ∼ideals over fuzzy field are studied. Mathematics Subj...

Molodstov introduced soft sets to deal with uncertainties and not clear objects. Researchers developed the relationship between soft sets and information systems. Fuzzification of the notions of soft sets and soft topology have been discussed in the literature. In this paper, we define and establish the topological structures of fuzzy soft semi-open sets and fuzzy soft semi-closed sets. We intr...

In this paper, we apply the concepts of fuzzy subsets to coalgebras and define fuzzy subcoalgebras and fuzzy left (right) coideals. Considering the applications of fuzzy subcoalgebras and fuzzy left (right) coideals, we discuss their properties under homomorphisms of coalgebras and the relationship among them. A fuzzy subcoalgebra and its duality as well as a fuzzy subalgebra and its duality is...

We have presented trapezoidal intuitionistic fuzzy number. Arithmetic operations of trapezoidal intuitionistic fuzzy number is presented based on (α, β)-cuts. We have presented intuitionistic fuzzy fault tree analysis using trapezoidal intuitionistic fuzzy number. In application of intuitionistic fuzzy fault tree analysis, we have computed failure of fire protection system taking failure of eac...

In this paper the notions of bipolar valued fuzzy subsemigroup, bipolar valued fuzzy bi-ideal, bipolar valued fuzzy (1,2)ideal and bipolar valued fuzzy ideal in a Γ-semigroup have been introduced. Some important characterizations are also obtained. Mathematics Subject Classification: 20M12, 03F55, 03E72

Berstel and Pin have characterized local languages by introducing local automaton. In this paper fuzzy local language is introduced and the fuzzy local languages recognized by partial fuzzy local automata in max-min and min-max compositions are studied. Some closure properties of fuzzy local languages are provided. Mathematics Subject Classification: 68Q45

In this paper the notion of fuzzy BF -algebra and fuzzy topological BF -algebras are introduced. We stated and proved some theorem in fuzzy BF -algebras and level subalgebras. Finally the Foster’s results on homomorphic images and inverse images in fuzzy topological BF algebras are studied. Mathematics Subject Classification: 06F35, 03G25, 94D05

Metric on the space of fuzzy sets plays a very important role in decision making and some other fuzzy application systems. The purpose of this paper is to give a fuzzy metric on the space of fuzzy numbers and investigate some of its properties. Mathematics Subject Classification: 03E72, 54A40, 54E35

Multi-fuzzy set theory is an extension of fuzzy set theory, which deals with the multi dimensional fuzziness. In this paper we introduce the concepts of multi-fuzzy subgroups and normal multi-fuzzy subgroups. Mathematics Subject Classification: MSC: 20N25; 03E72; 08A72

Measures on clans of fuzzy sets are traditionally studied as certain functionals on collections of [0, 1]-valued functions. The goal of this paper is to make first steps towards establishing this part of fuzzy mathematics as a formal theory over a suitable predicate fuzzy logic. Two concepts of formal measure theory are sketched within Henkin-style ω-order fuzzy logic.