A General Framework for Upper and Lower Possibilities and Necessities

1998 ◽  
Vol 06 (01) ◽  
pp. 1-33 ◽  
Author(s):  
Elena Tsiporkova ◽  
Bernard de Baets
Keyword(s):  
Multivalued Mapping ◽  
General Framework ◽  
Multivalued Mappings ◽  
Possibility Measure ◽  
Confidence Measure ◽  
Triangular Norms ◽  
Necessity Measure ◽  
The Given ◽  
Equivalent Expressions ◽  
Fuzzy Subsets

We show that a (fuzzy) multivalued mapping carries a possibility and necessity measure defined over (fuzzy) subsets of a first universe into a system of upper and lower possibilities and necessities defined over (fuzzy) subsets of a second universe. Upper possibilities (resp. lower necessities) form again a possibility measure (resp. necessity measure), while lower possibilities and upper necessities both form a confidence measure. The approach presented is based on possibilistic conditioning, in particular on the definitions of conditional possibilities and necessities in a general framework based on triangular norms and conorms. In case of a multivalued mapping, upper and lower possibilities and necessities can be expressed equivalently in terms of conditional possibilities and necessities of lower and upper inverse images under the given multivalued mapping, or in terms of a basic possibility assignment and a basic necessity assignment. In case of a fuzzy multivalued mapping, such equivalent expressions cannot be established in general. Upper and lower possibilities and necessities can then be introduced in two alternative ways. For normalized fuzzy multivalued mappings or crisp multivalued mappings, interesting relationships are obtained.

EPQ Inventory Models under mλ-Measure

2016 ◽  
pp. 152-175
Author(s):  
Hardik N. Soni ◽  
Shivangi Suthar
Keyword(s):  
Real Life ◽  
Optimal Decision ◽  
Chance Constrained Programming ◽  
Possibility Measure ◽  
Setup Cost ◽  
Necessity Measure ◽  
Real Life Situation ◽  
Holding Cost ◽  
Epq Model ◽  
Constrained Programming

This chapter considers an EPQ model with and without shortages under linear combination of Possibility measure and Necessity measure. Based on the possibility measure and necessity measure, m? -measure is introduced and some important properties are discussed. To capture the real life situation, various EPQ model parameters for instance, demand, setup cost, holding cost and backorder cost are characterized as Trapezoidal Fuzzy Number. Two fuzzy chance-constrained programming models are constructed under m?-measure. The objective is to determine optimistic and pessimistic values of the fuzzy objective function with some predefined degree of m?-measure. Using fuzzy arithmetical operations under Function Principle, the fuzzy problem is first transferred to an equivalent crisp problem. An analytical approach is developed to resolve the reduced models. To investigate the characteristics of the proposed model and to obtain the optimal decision under different situations, numerical illustrations are presented along with a sensitivity analysis.

scholarly journals On one control problem with disturbance and vectograms depending linearly on given sets

2020 ◽  
Vol 30 (3) ◽  
pp. 429-443
Author(s):  
V.I. Ukhobotov ◽  
V.N. Ushakov
Keyword(s):  
Control Problem ◽  
Multivalued Mapping ◽  
Control Process ◽  
Multivalued Function ◽  
Convex Compact ◽  
Compact Sets ◽  
Stable Bridge ◽  
Multivalued Functions ◽  
The Given ◽  
Convex Compact Sets

A control problem with a given end time is considered, in which the control vectograms and disturbance depend linearly on the given convex compact sets. A multivalued mapping of the phase space of the control problem to the linear normed space E is given. The goal of constructing a control is that at the end of the control process the fixed vector of the space E belongs to the image of the multivalued mapping for any admissible realization of the disturbance. A stable bridge is defined in terms of multivalued functions. The presented procedure constructs, according to a given multivalued function which is a stable bridge, a control that solves the problem. Explicit formulas are obtained that determine a stable bridge in the considered control problem. Conditions are found under which the constructed stable bridge is maximal. Some problems of group pursuit can be reduced to the considered control problem with disturbance. The article provides such an example.

scholarly journals Common fixed point of g-approximative multivalued mapping in partially ordered metric space

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1173-1182 ◽  
Author(s):  
Mujahid Abbas ◽  
Ali Erduran
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Partially Ordered

In this paper, we introduce g-approximative multivalued mappings. Based on this definition, we gave some new definitions. Further, common fixed point results for g-approximative multivalued mappings satisfying generalized contractive conditions are obtained in the setup of ordered metric spaces. Our results generalize Theorems 2.6-2.9 given in ([1]).

The set of regularity of a multivalued mapping in a space with a vector-valued metric

2019 ◽  
pp. 39-46
Author(s):  
Tatiana Zhukovskaia ◽  
Elena Pluzhnikova
Keyword(s):  
Normed Space ◽  
Multivalued Mapping ◽  
Linear Normed Space ◽  
Multivalued Mappings ◽  
Vector Valued

We consider multivalued mappings acting in spaces with a vector-valued metric. A vector-valued metric is understood as a mapping satisfying the axioms “of an ordinary metric” with values in the cone of a linear normed space. The concept of the regularity set of a multivalued mapping is defined. A set of regularity is used in the study of inclusions in spaces with a vector-valued metric.

scholarly journals Rendering Spaces for Architectural Environments

1995 ◽  
Vol 4 (3) ◽  
pp. 286-296 ◽  
Author(s):  
Jeffry S. Nimeroff ◽  
Eero Simoncelli ◽  
Norman I. Badler ◽  
Julie Dorsey
Keyword(s):  
Virtual Environments ◽  
General Framework ◽  
Geometric Model ◽  
Natural Light ◽  
Artificial Light ◽  
Light Sources ◽  
Scene Description ◽  
The Given ◽  
New Framework

We present a new framework for rendering virtual environments. This framework is proposed as a complete scene description, which embodies the space of all possible renderings, under all possible lighting scenarios of the given scene. In effect, this hypothetical rendering space includes all possible light sources as part of the geometric model. While it would be impractical to implement the general framework, this approach does allow us to look at the rendering problem in a new way. Thus, we propose new representations that are subspaces of the entire rendering space. Some of these subspaces are computationally tractable and may be carefully chosen to serve a particular application. The approach is useful both for real and virtual scenes. The framework includes methods for rendering environments which are illuminated by artificial light, natural light, or a combination of the two models.

scholarly journals Image Reconstruction Based on Novel Sets of Generalized Orthogonal Moments

2020 ◽  
Vol 6 (6) ◽  
pp. 54
Author(s):  
R. M. Farouk
Keyword(s):  
Fractional Order ◽  
General Framework ◽  
Recurrence Relations ◽  
Global Features ◽  
Orthogonal Moments ◽  
Recurrence Formulas ◽  
Intensity Images ◽  
Generalized Orthogonal ◽  
The Given ◽  
Comprehensive Study

In this work, we have presented a general framework for reconstruction of intensity images based on new sets of Generalized Fractional order of Chebyshev orthogonal Moments (GFCMs), a novel set of Fractional order orthogonal Laguerre Moments (FLMs) and Generalized Fractional order orthogonal Laguerre Moments (GFLMs). The fractional and generalized recurrence relations of fractional order Chebyshev functions are defined. The fractional and generalized fractional order Laguerre recurrence formulas are given. The new presented generalized fractional order moments are tested with the existing orthogonal moments classical Chebyshev moments, Laguerre moments, and Fractional order Chebyshev Moments (FCMs). The numerical results show that the importance of our general framework which gives a very comprehensive study on intensity image representation based GFCMs, FLMs, and GFLMs. In addition, the fractional parameters give a flexibility of studying global features of images at different positions and scales of the given moments.

scholarly journals Fixed points of asymptotically regular multivalued mappings

1992 ◽  
Vol 53 (3) ◽  
pp. 313-326 ◽  
Author(s):  
Ismat Beg ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Coincidence Points ◽  
Asymptotically Regular

AbstractSome results on fixed point of asymptotically regular multivalued mapping are obtained in metric spaces. The structure of common fixed points and coincidence points of a pair of compatible multivalued mappings is also discussed. Our work generalizes known results of Aubin and Siegel, Dube, Dube and Singh, Hardy and Rogers, Hu, Iseki, Jungck, Kaneko, Nadler, Ray and Shiau, Tan and Wong.

scholarly journals Analysis and optimization of tendinous actuation for biomorphically designed robotic systems

Robotica ◽  
2000 ◽  
Vol 18 (1) ◽  
pp. 23-31 ◽  
Author(s):  
Antonio Bicchi ◽  
Domenico Prattichizzo
Keyword(s):  
General Framework ◽  
Rigid Bodies ◽  
Robotic Manipulation ◽  
Robotic Systems ◽  
Force Distribution ◽  
Unilateral Constraints ◽  
Internal Forces ◽  
The Given ◽  
Proper Operation ◽  
Virtual Springs

We present a general framework for modeling a class of mechanical systems for robotic manipulation, consisting of articulated limbs with redundant tendinous actuation and unilateral constraints. Such systems, that include biomorphically designed devices, are regarded as a collection of rigid bodies, inter-acting through connections that model both joints and contacts with virtual springs. Methods previously developed for the analysis of force distribution in multiple whole-limb manipulation are generalized to this broader class of mechanisms, and are shown to provide a basis for the control of co-contraction and internal forces that guarantee proper operation of the system. In particular, in the presence of constraints such as those due to limited friction between surfaces or object fragility, the choice of tendon tensions is crucial to the success of manipulation. An algorithm is described that allows to evaluate efficiently set-points for the control of tendon actuators that “optimally” (in a sense to be described) comply with the given constraints.

scholarly journals Linear connections with and without torsion, making parallel an integrable endomorphism on a manifold

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 2943-2949
Author(s):  
Cornelia-Livia Bejan ◽  
Ana Velimirovic
Keyword(s):  
Tensor Field ◽  
General Framework ◽  
Linear Connections ◽  
The Given

Our study is developed in a general framework, namely a manifold M endowed with a (1,1)- tensor field ?, which is integrable. The present paper solves the following two problems: how many linear connections with torsion and without torsion exist, having the property of being parallel with respect to ?. To count all these connections with the given properties, certain algebraic techniques and results are used throughout the paper.

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