scholarly journals Matrix Games with Interval-Valued 2-Tuple Linguistic Information

Games ◽  
2018 ◽  
Vol 9 (3) ◽  
pp. 62 ◽  
Author(s):  
Anjali Singh ◽  
Anjana Gupta
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Real World ◽  
Upper Bound ◽  
Duality Theorem ◽  
Matrix Game ◽  
Matrix Games ◽  
Linguistic Information ◽  
The Real ◽  
Interval Valued

In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs.

A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers

2016 ◽  
Vol 33 (06) ◽  
pp. 1650047 ◽  
Author(s):  
Sanjiv Kumar ◽  
Ritika Chopra ◽  
Ratnesh R. Saxena
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Linear Programming ◽  
Matrix Game ◽  
Matrix Games ◽  
Trapezoidal Fuzzy Numbers ◽  
Fast Approach ◽  
The Matrix

The aim of this paper is to develop an effective method for solving matrix game with payoffs of trapezoidal fuzzy numbers (TrFNs). The method always assures that players’ gain-floor and loss-ceiling have a common TrFN-type fuzzy value and hereby any matrix game with payoffs of TrFNs has a TrFN-type fuzzy value. The matrix game is first converted to a fuzzy linear programming problem, which is converted to three different optimization problems, which are then solved to get the optimum value of the game. The proposed method has an edge over other method as this focuses only on matrix games with payoff element as symmetric trapezoidal fuzzy number, which might not always be the case. A numerical example is given to illustrate the method.

Monofunctional and polyfunctional information tools with an operative function

2018 ◽  
Vol 33 (1) ◽  
pp. 361-390 ◽  
Author(s):  
Heidi Agerbo
Keyword(s):  
21St Century ◽  
Real World ◽  
Information Needs ◽  
Future Research ◽  
Linguistic Information ◽  
The Real ◽  
Vast Amount ◽  
Information Tools ◽  
Types Of Information

AbstractThough a vast amount of dictionary analyses have been produced over the years, hardly any of these have mentioned the operative function, which has been overlooked in most lexicographical literature. With short analyses of 12 existing dictionaries ranging from the 18th century to the 21st century, this article shows that many dictionaries have indeed been produced to satisfy operative needs. Based on this result, it is clear that the operative function deserves a place in lexicographical theory. An interesting finding that came out of these analyses was that especially dictionaries from the 18th to the early 20th centuries (the old dictionaries) were written to accommodate several types of information needs that their users would come across in the real world, including operative needs, whereas the focus of most contemporary dictionaries is to satisfy linguistic information needs. This is an interesting change in focus, which this article criticises. Based on the above mentioned analyses, a number of questions are raised to guide future research into the operative function.

LOWER BOUNDS FOR STREETS AND GENERALIZED STREETS

2001 ◽  
Vol 11 (04) ◽  
pp. 401-421 ◽  
Author(s):  
ALEJANDRO LÓPEZ-ORTIZ ◽  
SVEN SCHUIERER
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real Line ◽  
Upper Bound ◽  
Competitive Ratio ◽  
Search Strategy ◽  
The Real ◽  
Simple Polygons ◽  
On Line ◽  
Special Classes

We present lower bounds for on-line searching problems in two special classes of simple polygons called streets and generalized streets. In streets we assume that the location of the target is known to the robot in advance and prove a lower bound of [Formula: see text] on the competitive ratio of any deterministic search strategy—which can be shown to be tight. For generalized streets we show that if the location of the target is not known, then there is a class of orthogonal generalized streets for which the competitive ratio of any search strategy is at least [Formula: see text] in the L2-metric—again matching the competitive ratio of the best known algorithm. We also show that if the location of the target is known, then the competitive ratio for searching in generalized streets in the L1-metric is at least 9 which is tight as well. The former result is based on a lower bound on the average competitive ratio of searching on the real line if an upper bound of D to the target is given. We show that in this case the average competitive ratio is at least 9-O(1/ log D).

LEXICOGRAPHIC METHOD FOR MATRIX GAMES WITH PAYOFFS OF TRIANGULAR FUZZY NUMBERS

2008 ◽  
Vol 16 (03) ◽  
pp. 371-389 ◽  
Author(s):  
DENG-FENG LI
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Order Relation ◽  
Programming Models ◽  
Matrix Game ◽  
Triangular Fuzzy Numbers ◽  
Matrix Games ◽  
Lexicographic Method

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fuzzy optimization problems are established for two players. Then, based on the order relation of triangular fuzzy numbers the fuzzy optimization problems for players are decomposed into three-objective linear programming models. Finally, using the lexicographic method maximin and minimax strategies for players and the fuzzy value of the matrix game with payoffs of triangular fuzzy numbers can be obtained through solving two corresponding auxiliary linear programming problems, which are easily computed using the existing Simplex method for the linear programming problem. It has been shown that the models proposed in this paper extend the classical matrix game models. A numerical example is provided to illustrate the methodology.

scholarly journals Optimization of the Real-Time Response to Roadside Incidents through Heuristic and Linear Programming

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1982
Author(s):  
Roman Buil ◽  
Jesica de Armas ◽  
Daniel Riera ◽  
Sandra Orozco
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Open Source ◽  
Real Time ◽  
Real World ◽  
Time Response ◽  
Innovative Approach ◽  
Large Set ◽  
The Real ◽  
Operational Costs

This paper presents a solution for a real-world roadside assistance problem. Roadside incidents can happen at any time. Depending on the type of incident, a specific resource from the roadside assistance company can be sent on site. The problem of allocating resources to these road-side incidents can be stated as a multi-objective function and a large set of constraints, including priorities and preferences, resource capacities and skills, calendars, and extra hours. The request from the client is to a have real-time response and to attempt to use only open source tools. The optimization objectives to consider are the minimization of the operational costs and the minimization of the time to arrive to each incident. In this work, an innovative approach to near-optimally solving this problem in real-time is proposed, combining a heuristic approach and linear programming. The results show the great potential of this approach: operational costs were reduced by 19%, the use of external providers was reduced to half, and the productivity of the resources owned by the client was significantly increased.

scholarly journals On Euclidean Designs and Potential Energy

10.37236/8 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Tsuyoshi Miezaki ◽  
Makoto Tagami
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Euclidean Space ◽  
Potential Energy ◽  
Harmonic Analysis ◽  
Upper Bound ◽  
Type Inequality ◽  
Linear Programming Bound ◽  
Concentric Spheres ◽  
Finite Set

We study Euclidean designs from the viewpoint of the potential energy. For a finite set in Euclidean space, we formulate a linear programming bound for the potential energy by applying harmonic analysis on a sphere. We also introduce the concept of strong Euclidean designs from the viewpoint of the linear programming bound, and we give a Fisher type inequality for strong Euclidean designs. A finite set on Euclidean space is called a Euclidean $a$-code if any distinct two points in the set are separated at least by $a$. As a corollary of the linear programming bound, we give a method to determine an upper bound on the cardinalities of Euclidean $a$-codes on concentric spheres of given radii. Similarly we also give a method to determine a lower bound on the cardinalities of Euclidean $t$-designs as an analogue of the linear programming bound.

NOTES ON "LINEAR PROGRAMMING TECHNIQUE TO SOLVE TWO-PERSON MATRIX GAMES WITH INTERVAL PAY-OFFS"

2011 ◽  
Vol 28 (06) ◽  
pp. 705-737 ◽  
Author(s):  
DENG-FENG LI
Keyword(s):  
Linear Programming ◽  
Inequality Constraints ◽  
Asia Pacific ◽  
Programming Models ◽  
Matrix Game ◽  
Programming Technique ◽  
Matrix Games ◽  
Lexicographic Method ◽  
Generic Matrix ◽  
Linear Programming Technique

The aim of this note is to point out and correct some vital mistakes in the paper by P K Nayak and M Pal, "Linear programming technique to solve two person matrix (games with interval pay-offs). Asia-Pacific Journal of Operational Research, 26(2), 285–305". Lots of serious mistakes on the definitions, conclusions, models, methods, proofs and computing results have been corrected and modified in this note. We also indicate inappropriate formulations regarding their proposed linear programming models for solving generic matrix games with interval pay-offs and suggest a pair of linear programming models with any minimal acceptance degree of the interval inequality constraints which may be allowed to violate. The lexicographic method is suggested so that a rational and credible solution of the generic matrix game with interval pay-offs can be achieved.

scholarly journals Representing prefix and border tables: results on enumeration

2015 ◽  
Vol 27 (2) ◽  
pp. 257-276
Author(s):  
JULIEN CLÉMENT ◽  
LAURA GIAMBRUNO
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Complexity Analysis ◽  
Minimal Size ◽  
Golden Mean ◽  
The Real ◽  
Maximal Size ◽  
Linear Algorithms

For some text algorithms, the real measure for the complexity analysis is not the string itself but its structure stored in its prefix table or equivalently border table. In this paper, we define the combinatorial class of prefix lists, namely a sequence of integers together with their size, and an injection ψ from the class of prefix tables to the class of prefix lists. We call a valid prefix list the image by ψ of a prefix table. In particular, we describe algorithms converting a prefix/border table to a prefix list and inverse linear algorithms from computing from a prefix list L = ψ(P) two words respectively in a minimal size alphabet and on a maximal size alphabet with P as prefix table. We then give a new upper bound on the number of prefix tables for strings of length n (on any alphabet) which is of order (1 + ϕ)n (with $\varphi=\frac{1+\sqrt{5}}{2}$ the golden mean) and also present a corresponding lower bound.

Sign in / Sign up

Export Citation Format

Share Document