On topological structures of fuzzy parametrized soft sets

In this paper, we introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated basic properties of it. We study the closure, interior, base, continuity and compactness and properties of these concepts in fuzzy parametrized soft topological space

Fuzzy inequational logic

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermore, we present a logic for reasoning about graded if-then rules which is obtained as particular case of the general result

Tangential Extremal Principles for Finite and Infinite Systems of Sets, I: Basic Theory

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. The first part of the paper concerns the basic theory of tangential extremal principles while the second part presents applications to problems of semi-infinite programming and multiobjective optimization

Capital budgeting problems with fuzzy cash flows

We consider the internal rate of return (IRR) decision rule in capital budgeting problems with fuzzy cash flows. The possibility distribution of the IRR at any r � 0, is defined to be the degree of possibility that the (fuzzy) net present value of the project with discount factor requals to zero. Generalizing our earlier results on fuzzy capital budegeting problems [5] we show that the possibility distribution of the IRR is a highly nonlinear function which is getting more and more unbalanced by increasing imprecision in the future cash flow. However, it is stable under small changes in the membership functions of fuzzy numbers representing the lingusitic values of future cash flows