Non-additive measure is a generalization of additive probability measure. Integral inequalities p... more Non-additive measure is a generalization of additive probability measure. Integral inequalities play important roles in classical probability and measure theory. Some well-known inequalities such as the Minkowski inequality and the Hölder inequality play important roles not only in the theoretical area but also in application. Non-additive integrals are useful tools in several theoretical and applied statistics which have been built on non-additive measure. For instance, in decision theory and applied statistics, the use of the non-additive integrals can be envisaged from two points of view: decision under uncertainty and multi-criteria decision-making. In fact, the non-additive integrals provide useful tools in many problems in engineering and social choice where the aggregation of data is required. In this paper, Hölder and Minkowski type inequalities for semi(co)normed non-additive integrals are discussed. The main results of this paper generalize some previous results obtained by the authors.
We consider discrete (finite) probability distributions where some of the probability values are ... more We consider discrete (finite) probability distributions where some of the probability values are uncertain. We model these uncertainties using fuzzy numbers. Then, employing restricted fuzzy arithmetic, we derive the basic laws of fuzzy (uncertain) probability theory. Applications are to the binomial probability distribution and queuing theory.
We consider probability density functions where some of the parameters are uncertain. We model th... more We consider probability density functions where some of the parameters are uncertain. We model these uncertainties using fuzzy numbers producing fuzzy probability density functions. In particular, we look at the fuzzy normal, fuzzy uniform, and the fuzzy negative exponential and show how to use them to compute fuzzy probabilities. We also use the fuzzy normal to approximate the fuzzy binomial. Our application is to inventory control (the economic order quantity model) where demand is given by a fuzzy normal probability density.
In this paper, we show how a neural net can be used to solve A¯X¯=C¯, for X¯, even though for som... more In this paper, we show how a neural net can be used to solve A¯X¯=C¯, for X¯, even though for some values of A¯ and C¯ there is no fuzzy arithmetic solution for X¯. The neural net solution is identified with our new solution (Buckley and Qu, Fuzzy Sets & Systems, vol. 39, pp. 291-301, 1991) to fuzzy equations
Pricing of options, forwards or futures often requires using uncertain values of parameters in th... more Pricing of options, forwards or futures often requires using uncertain values of parameters in the model. For example future interest rates are usually uncertain. We will use fuzzy numbers for these uncertain parameters to account for this uncertainty. When some of the parameters in the model are fuzzy the price then also becomes fuzzy. We first discuss options: (1) the discrete binomial method; and then (2) the Black-Scholes model. Then we look at pricing futures and forwards.
We consider joint probability density functions where some of the parameters are uncertain. We mo... more We consider joint probability density functions where some of the parameters are uncertain. We model these uncertainties using fuzzy numbers producing fuzzy joint probability density functions. Then we study the fuzzy marginal densities, the fuzzy conditional densities and fuzzy correlation. We look at one particular fuzzy joint density: the fuzzy bivariate normal. An application in fuzzy reliability theory is presented.
In this paper we consider fuzzy subsets of a universe as L-fuzzy subsets instead of [ 0, 1 ]-valu... more In this paper we consider fuzzy subsets of a universe as L-fuzzy subsets instead of [ 0, 1 ]-valued, where L is a complete lattice. We enrich the lattice L by adding some suitable operations to make it into a pseudo-BL algebra. Since BL algebras are main frameworks of fuzzy logic, we propose to consider the non-commutative BL-algebras which are more natural for modeling the fuzzy notions. Based on reasoning with in non-commutative fuzzy logic we model the linguistic modifiers such as very and more or less and give an appropriate membership function for each one by taking into account the context of the given fuzzy notion by means of resemblance L-fuzzy relations.
In this paper we first analyze some state of the art methods for text summarization. We discuss w... more In this paper we first analyze some state of the art methods for text summarization. We discuss what the main disadvantages of these methods are and then propose a new method using fuzzy logic. Comparisons of results show that our method beats most methods which use machine learning as their core.
In this paper we first analyze some state of the art methods for text summarization. We discuss w... more In this paper we first analyze some state of the art methods for text summarization. We discuss what the main disadvantages of these methods are and then propose a new method using fuzzy logic. Comparisons of results show that our method beats most methods which use machine learning as their core.
In this paper we introduce some types of filters in a BL algebra A, and we state and prove some t... more In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters.
Non-additive measure is a generalization of additive probability measure. Integral inequalities p... more Non-additive measure is a generalization of additive probability measure. Integral inequalities play important roles in classical probability and measure theory. Some well-known inequalities such as the Minkowski inequality and the Hölder inequality play important roles not only in the theoretical area but also in application. Non-additive integrals are useful tools in several theoretical and applied statistics which have been built on non-additive measure. For instance, in decision theory and applied statistics, the use of the non-additive integrals can be envisaged from two points of view: decision under uncertainty and multi-criteria decision-making. In fact, the non-additive integrals provide useful tools in many problems in engineering and social choice where the aggregation of data is required. In this paper, Hölder and Minkowski type inequalities for semi(co)normed non-additive integrals are discussed. The main results of this paper generalize some previous results obtained by the authors.
We consider discrete (finite) probability distributions where some of the probability values are ... more We consider discrete (finite) probability distributions where some of the probability values are uncertain. We model these uncertainties using fuzzy numbers. Then, employing restricted fuzzy arithmetic, we derive the basic laws of fuzzy (uncertain) probability theory. Applications are to the binomial probability distribution and queuing theory.
We consider probability density functions where some of the parameters are uncertain. We model th... more We consider probability density functions where some of the parameters are uncertain. We model these uncertainties using fuzzy numbers producing fuzzy probability density functions. In particular, we look at the fuzzy normal, fuzzy uniform, and the fuzzy negative exponential and show how to use them to compute fuzzy probabilities. We also use the fuzzy normal to approximate the fuzzy binomial. Our application is to inventory control (the economic order quantity model) where demand is given by a fuzzy normal probability density.
In this paper, we show how a neural net can be used to solve A¯X¯=C¯, for X¯, even though for som... more In this paper, we show how a neural net can be used to solve A¯X¯=C¯, for X¯, even though for some values of A¯ and C¯ there is no fuzzy arithmetic solution for X¯. The neural net solution is identified with our new solution (Buckley and Qu, Fuzzy Sets & Systems, vol. 39, pp. 291-301, 1991) to fuzzy equations
Pricing of options, forwards or futures often requires using uncertain values of parameters in th... more Pricing of options, forwards or futures often requires using uncertain values of parameters in the model. For example future interest rates are usually uncertain. We will use fuzzy numbers for these uncertain parameters to account for this uncertainty. When some of the parameters in the model are fuzzy the price then also becomes fuzzy. We first discuss options: (1) the discrete binomial method; and then (2) the Black-Scholes model. Then we look at pricing futures and forwards.
We consider joint probability density functions where some of the parameters are uncertain. We mo... more We consider joint probability density functions where some of the parameters are uncertain. We model these uncertainties using fuzzy numbers producing fuzzy joint probability density functions. Then we study the fuzzy marginal densities, the fuzzy conditional densities and fuzzy correlation. We look at one particular fuzzy joint density: the fuzzy bivariate normal. An application in fuzzy reliability theory is presented.
In this paper we consider fuzzy subsets of a universe as L-fuzzy subsets instead of [ 0, 1 ]-valu... more In this paper we consider fuzzy subsets of a universe as L-fuzzy subsets instead of [ 0, 1 ]-valued, where L is a complete lattice. We enrich the lattice L by adding some suitable operations to make it into a pseudo-BL algebra. Since BL algebras are main frameworks of fuzzy logic, we propose to consider the non-commutative BL-algebras which are more natural for modeling the fuzzy notions. Based on reasoning with in non-commutative fuzzy logic we model the linguistic modifiers such as very and more or less and give an appropriate membership function for each one by taking into account the context of the given fuzzy notion by means of resemblance L-fuzzy relations.
In this paper we first analyze some state of the art methods for text summarization. We discuss w... more In this paper we first analyze some state of the art methods for text summarization. We discuss what the main disadvantages of these methods are and then propose a new method using fuzzy logic. Comparisons of results show that our method beats most methods which use machine learning as their core.
In this paper we first analyze some state of the art methods for text summarization. We discuss w... more In this paper we first analyze some state of the art methods for text summarization. We discuss what the main disadvantages of these methods are and then propose a new method using fuzzy logic. Comparisons of results show that our method beats most methods which use machine learning as their core.
In this paper we introduce some types of filters in a BL algebra A, and we state and prove some t... more In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters.
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