On fuzzy reasoning schemes

In this work we provide a short survey of the most frequently used fuzzy reasoning schemes. The paper is organized as follows: in the first section we introduce the basic notations and definitions needed for fuzzy inference systems; in the second section we explain how the GMP works under Mamdani, Larsen and G¨odel implications, furthermore we discuss the properties of compositional rule of inference with several fuzzy implications; and in the third section we describe Tsukamoto’s, Sugeno’s and the simplified fuzzy inference mechanisms in multi-input-single-output fuzzy systems

Multiple fuzzy reasoning approach to fuzzy mathematical programming problems

We suggest solving fuzzy mathematical programming problems via the use of multiple fuzzy reasoning techniques. We show that our approach gives Buckley’s solution [1] to possibilistic mathematical programs when the inequality relations are understood in possibilistic sense

The compositional rule of inference with several relations

The compositional rule of inference with several relations, which is the mainly used inference rule in approximate reasoning, is considered in this paper. Stability results are given and exact computational formulae are provided

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

A short survey of normative properties of possibility distributions

In 2001 Carlsson and Full´er [1] introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2003 Full´er and Majlender [4] introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. In 2003 Carlsson, Full´er and Majlender [2] proved the possibilisticCauc hy-Schwartz inequality. Drawing heavily on [1, 2, 3, 4, 5] we will summarize some normative properties of possibility distributions

A pure probabilistic interpretation of possibilistic expected value, variance, covariance and correlation

In this work we shall give a pure probabilistic interpretation of possibilistic expected value, variance, covariance and correlation

Optimization under fuzzy rule constraints

Suppose we are given a mathematical programming problem in which the functional relationship between the decision variables and the objective function is not completely known. Our knowledge-base consists of a block of fuzzy if-then rules, where the antecedent part of the rules contains some linguistic values of the decision variables, and the consequence part is a linear combination of the crisp values of the decision variables. We suggest the use of Takagi and Sugeno fuzzy reasoning method to determine the crisp functional relationship between the objective function and the decision variables, and solve the resulting (usually nonlinear) programming problem to find a fair optimal solution to the original fuzzy problem

Fuzzy linear programs with optimal tolerance levels

It is usually supposed that tolerance levels are determined by the decision maker a priori in a fuzzy linear program (FLP). In this paper we shall suppose that the decision maker does not care about the particular values of tolerance levels, but he wishes to minimize their weighted sum. This is a new statement of FLP, because here the tolerance levels are also treated as variables

On additions of interactive fuzzy numbers

In this paper we will summarize some properties of the extended addition operator on fuzzy numbers, where the interactivity relation between fuzzy numbers is given by their joint possibility distributio