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...

Fuzzy valued measure ([7], [10], [3], [5]) is a natural generalization of a set valued measure ([6]). Infinite addition is defined ([12]) as a Zadeh’s extension principle of continuity. In [9], using an additive fuzzy valued measure, an integral of single valued function is defined and some basic properties are given. In this paper we proceed to investigate specific properties of integrals in f...

The unavoidable imprecision of measurements of continuous physical quantities can be modelled by using the concept of fuzzy numbers and fuzzy vectors. Concerning a quantitative usage of such data the classical concept of relative frequencies for real data has to be extended to so-called fuzzy relative frequencies for fuzzy data, whereby the fuzzy relative frequency of a set is a fuzzy number. A...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

in this paper, the picard method is proposed to solve the bernoulli equation with fuzzy initial condition under generalized h-differentiability. the existence and uniqueness of the solution and convergence of the proposed method are proved in details. finally an example shows the accuracy of this method.

The aim of this paper is investigate the notion of a generalized interval valued intuitionistic fuzzy number (GIVIFN), which extends the interval valuedintuitionistic fuzzy number. Firstly, the concept of GIVIFNBs is introduced.Arithmetic operations and cut sets over GIVIFNBBs are investigated. Then the values and ambiguities of the membership degree and the non-membership degree and the value ...

This article studies the determination of the rate of convergence to the unit of each of three newly introduced here multivariate fuzzy perturbed normalized neural network operators of one hidden layer. These are given through the multivariate fuzzy modulus of continuity of the involved multivariate fuzzy number valued function or its high order fuzzy partial derivatives and that appears in the...

Interval-valued intuitionistic fuzzy number uses membership degree and non-member ship degree to express a decision-maker’s hesitation, which make decision-maker express his/her opinion in uncertainty decision-making environment easily. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation. In application such as weak consistency...

The paper presents a form of rendering classical mathematical notions by formal theories over suitable t-norm fuzzy logics in such a way that references to real numbers are eliminated from definitions and theorems, being removed to the standard semantics of fuzzy logic. Several examples demonstrate how this move conceptually simplifies the theory in exchange for non-classical reasoning, facilit...

Direct Cover (DC) based techniques for synthesis of multiple-valued logic (MVL) functions have been reported in the literature. In this paper, we propose Fuzzy-based DC algorithm for synthesis of MVL functions. The proposed algorithm uses the principles of Fuzzy Logic in selecting the set of minterms and the appropriate set of implicants needed to synthesize a given MVL function. The proposed F...