scholarly journals Conditional operations on fuzzy numbers

2013 ◽  
Vol 5 (1) ◽  
pp. 110-113
Author(s):  
Kh.O. Nykyforchyn
Keyword(s):  
Fuzzy Numbers ◽  
Fuzzy Variable ◽  
Fuzzy Relations ◽  
Possibility Distribution ◽  
Possibility Distributions

An estimate of a joint possibility distribution of two fuzzy numbers, based on fuzzy relations with a third fuzzy variable, is suggested. This leads to the operations of conditional addition and conditional multiplication, of interactive fuzzy numbers for which joint possibility distributions with a fuzzy variable are known.

Characterization of a Class of Possibility Distributions

2015 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 91-94
Author(s):  
Dan Ralescu ◽  
Anca Ralescu
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Variable ◽  
Possibility Distribution ◽  
Possibility Distributions

This note presents the characterization of a fuzzy variable whose possibility distribution is a convex fuzzy set.

Possibilistic Uncertainty Quantification in 1-D Consolidation Problems

2021 ◽  
Author(s):  
Djamalddine Boumezerane
Keyword(s):  
Uncertainty Quantification ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Possibility Distribution ◽  
Coefficient Of Consolidation ◽  
Consolidation Process ◽  
Possibility Distributions ◽  
Coverage Function ◽  
The One ◽  
Measure Of Uncertainty

Abstract In this study, we use possibility distribution as a basis for parameter uncertainty quantification in one-dimensional consolidation problems. A Possibility distribution is the one-point coverage function of a random set and viewed as containing both partial ignorance and uncertainty. Vagueness and scarcity of information needed for characterizing the coefficient of consolidation in clay can be handled using possibility distributions. Possibility distributions can be constructed from existing data, or based on transformation of probability distributions. An attempt is made to set a systematic approach for estimating uncertainty propagation during the consolidation process. The measure of uncertainty is based on Klir's definition (1995). We make comparisons with results obtained from other approaches (probabilistic…) and discuss the importance of using possibility distributions in this type of problems.

scholarly journals Enhanced Two-Step Method via Relaxed Order ofα-Satisfactory Degrees for Fuzzy Multiobjective Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Na Wang ◽  
Chaofang Hu ◽  
Wuxi Shi ◽  
Chunbo Xiu ◽  
Yimei Chen
Keyword(s):  
Multiobjective Optimization ◽  
Set Theory ◽  
Optimization Problem ◽  
Fuzzy Numbers ◽  
Fuzzy Relations ◽  
Preemptive Priority ◽  
Step Method ◽  
Satisfactory Solution ◽  
Order Constraint ◽  
Fuzzy Parameters

An enhanced two-step method via relaxed order of satisfactory degrees for fuzzy multiobjective optimization is proposed in this paper. By introducing the concept of fuzzy numbers andα-level set theory, fuzzy parameters are taken as variables, and all the objectives are transformed into fuzzy goals involving three fuzzy relations. The order ofα-satisfactory degrees which means the objectives with higher priority achieving higher satisfactory degree is applied to model preemptive priority requirement. This strict order constraint is relaxed by priority variable to find the preferred solution satisfying optimization and priority. The original optimization problem is divided into two steps to be solved iteratively. The M-α-Pareto optimality of the solution is ensured, and the satisfactory solution can be acquired by regulating the slack parameterΔδor changingα. The numerical examples demonstrate the power of the proposed method.

scholarly journals ESTIMATIONS OF EXPECTEDNESS AND POTENTIAL SURPRISE IN POSSIBILITY THEORY

1994 ◽  
Vol 02 (04) ◽  
pp. 417-428 ◽  
Author(s):  
HENRI PRADE ◽  
RONALD R. YAGER
Keyword(s):  
Possibility Theory ◽  
Point Of View ◽  
Possibility Distribution ◽  
Owa Operators ◽  
Set Functions ◽  
Basic Set ◽  
Potential Applications ◽  
Possibility Distributions

This note investigates how various ideas of "expectedness" can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying "I would not be surprised that…" before an event takes place, or by saying "I knew it" after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of possibility of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined.

A procedure for ranking fuzzy numbers using fuzzy relations

1988 ◽  
Vol 26 (1) ◽  
pp. 49-62 ◽  
Author(s):  
M. Delgado ◽  
J.L. Verdegay ◽  
M.A. Vila
Keyword(s):  
Fuzzy Numbers ◽  
Fuzzy Relations

POSSIBILISTIC NORMALISATION AND REASONING UNDER PARTIAL INCONSISTENCY

2001 ◽  
Vol 09 (04) ◽  
pp. 413-436 ◽  
Author(s):  
JONATHAN LAWRY
Keyword(s):  
Fuzzy Sets ◽  
Possibility Distribution ◽  
Interval Approach ◽  
Possibility Distributions ◽  
Inconsistent Knowledge ◽  
Definition Of

The problem of normalisation of non-normalised fuzzy sets/possibility distributions is considered. A definition of a valid normalised possibility distribution is given at the mass assignment level and a characterisation of this definition at the distribution level is proposed. A number of possible normalisations are considered these being related to certain epistemic principles. Finally an interval approach to reasoning with partially inconsistent knowledge is introduced.

Transportation Chance Constrained Model with Fuzzy Parameters

2011 ◽  
Vol 135-136 ◽  
pp. 1193-1200
Author(s):  
Guo Qiang Yuan ◽  
Ming Qiang Meng ◽  
Chun Ping Li
Keyword(s):  
Fuzzy Variable ◽  
Optimization Method ◽  
Variable Coefficients ◽  
Credibility Theory ◽  
Infinite Dimensional ◽  
Fuzzy Environment ◽  
Ga Algorithm ◽  
Possibility Distributions ◽  
Constrained Model ◽  
Conventional Optimization

This paper presents how credibility theory and chance constrained optimization method can be efficiently applied for modelling and solving transportation problem in fuzzy environment. Since the proposed transportation model includes fuzzy variable coefficients defined through possibility distributions with infinite supports, it is infinite-dimensional optimization problem. Therefore, we can not solve directly it by conventional optimization algorithms. To overcome this difficulty, we will discuss the approximation of the fuzzy transportation chance constrained problem in this paper, and design a heuristic algorithm, which combines approximation method (AM), neural network (NN) and genetic algorithm (GA) algorithm to solve this transportation chance constrained model. Finally, we present one numerical example to show the feasibility and effectiveness of the proposed method.

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