Although simple additive weighting method (SAW) is the most popular approach for classical multiple attribute decision making (MADM), it is not practical any more if information is fuzzy. The existing methods of Fuzzy Simple Additive Weighting method (FSAW) apply defuzzification which distorts fuzzy numbers. Furthermore, most of the methods usually require lengthy and laborious manipulations. I...

In Dempster Shafer (DS) Theory, basic probability assignment plays a key role. All other measures can be defined in the terms of BPA. This assignment, as originally defined, can take only one value in the interval [0,1]. However in actual practice the BPA is usually provided by experts subjectivity. Experts cannot precisely give the value. We have to assign a number on their linguistic expressi...

The vague sum (product) of a finite number of real numbers and the vague integral multiples (powers) of real numbers based on a perfect vague addition (multiplication) operation are introduced, and some of their fundamental properties are pointed out. Furthermore, some examples are designed to show how they can be practically implemented. Keyword: Fuzzy arithmetic, Vague arithmetic, Vague arith...

We consider a generalized model of neural network with a fuzziness and chaos. The origin of the fuzzy signals lies in complex biochemical and electrical processes of the synapse and dendrite membrane excitation and the inhibition mechanism. The mathematical operations included into fuzzy neural network modeling are: the scalar product between inputs of layers and synaptic weights is replaced by...

in this paper, some results of the chebyshev type integral inequality for the pseudo-integral are proven. the obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. finally, we applied our results  to the case of comonotone functions.

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

We define some operations over Atanassov’s intuitionistic fuzzy sets (AIFSs), such as Einstein intersection, Einstein product, Einstein scalar multiplication and Einstein exponentiation, etc., and then define new concentration and dilation of AIFSs. These definitions will be useful while dealing with various linguistic hedges like “very”, “more or less”, “highly”, “very very” etc., involved in ...

Multiplicative operations for fuzzy numbers raise several problems both from the theoretical and practical point of view in fuzzy arithmetic. The multiplication based on Zadeh's extension principle and its triangular and trapezoidal approximation is used in several recent works in applications in geology. Recently, new product-type operation are introduced and studied, as e.g. the cross product...

This paper provides an algebraic formalization of mathematical structures formed by fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom has been given by G. Schmidt and T. Strohlein. Unlike Boolean relation algebras, fuzzy relation algebras are not Boolean but equipped with semi-scalar multipl...