Fuzzy Numbers and Fractional Programming in Making Decisions

This study surveys the use of fuzzy numbers in classic optimization models, and its effects on making decisions. In a wide sense, mathematical programming is a collection of tools used in mathematical optimization to make good decisions. There are many sectors of economy that employ it. Finance and government, logistics and manufacturing, the distribution of the electrical power are worth to be first mentioned. When real life problems are modeled mathematically, there is always a trade-off between model’s accuracy and complexity. By this survey, we aim to present in a concise form some mathematical models from the literature together with the methods to solve them. We will focus mainly on fuzzy fractional programming problems. We will also refer to but not describe in detail the multi-criteria decision-making problems involving fuzzy numbers and linear fractional programming models.

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Application of linear fractional programming problem with fuzzy nature in industry sector

Filomat ◽

10.2298/fil2015073d ◽

2020 ◽

Vol 34 (15) ◽

pp. 5073-5084

Author(s):

Sapan Das ◽

S.A. Edalatpanah ◽

T. Mandal

Keyword(s):

Fractional Programming ◽

Simple Structure ◽

Fuzzy Numbers ◽

Real Life ◽

Optimal Solution ◽

Linear Fractional Programming ◽

Fuzzy Variables ◽

Life Problems ◽

Fuzzy Optimal Solution ◽

Fuzzy Linear Fractional Programming

Several methods currently exist for solving fuzzy linear fractional programming problems under non negative fuzzy variables. However, due to the limitation of these methods, they cannot be applied for solving fully fuzzy linear fractional programming (FFLFP) problems where all the variables and parameters are fuzzy numbers. So, this paper is planning to fill in this gap and in order to obtain the fuzzy optimal solution we propose a new efficient method for FFLFP problems utilized in daily life circumstances. This proposed method is based on crisp linear fractional programming and has a simple structure. To show the efficiency of our proposed method some numerical and real life problems have been illustrated.

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Competence-based assignment of tasks to workers in factories with demand-driven manufacturing

Central European Journal of Operations Research ◽

10.1007/s10100-021-00739-4 ◽

2021 ◽

Vol 29 (2) ◽

pp. 553-565

Author(s):

Bożena Staruch ◽

Bogdan Staruch

Keyword(s):

Production Management ◽

Real Life ◽

Programming Models ◽

Specific Task ◽

Generalized Assignment Problem ◽

Existence Of A Solution ◽

Life Problems ◽

Generalized Assignment ◽

The Given ◽

Potential Use

AbstractThe paper is motivated by real problems concerning tasks assignment to workers in medium-sized upholstered furniture plants managed using the Demand-Driven Manufacturing. Although the methodology was developed for furniture plants it can be applied to other types of production plants. We involve competence coefficients, which describe the level of the worker’s skills or capabilities to perform a specific task. The competence coefficients are also used to block the possibility of assigning the given task to a worker that has no skills to do it. Additionally, we involve a dummy worker to the model which guarantees the existence of a solution to the problem. We present and discuss Integer Linear Programming Models for the posted problem that are closely related to the Generalized Assignment Problem. We also discuss the potential use of the presented methodology to solve real-life problems related to production management.

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Ranking Function Application for Optimal Solution of Fractional programming problem

Al-Qadisiyah Journal Of Pure Science ◽

10.29350/jops.2020.25.1.1048 ◽

2020 ◽

Vol 25 (1) ◽

Cited By ~ 2

Author(s):

Rasha Jalal

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Fractional Programming ◽

Linear Programming Problem ◽

Fuzzy Numbers ◽

Optimal Solution ◽

Ranking Function ◽

Linear Fractional Programming ◽

Fractional Programming Problem ◽

Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

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Fuzzy Analytic Hierarchy Process-Based Multi-Criteria Decision Making for Universities Ranking

Symmetry ◽

10.3390/sym12081351 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1351

Author(s):

Rashad Aliyev ◽

Hasan Temizkan ◽

Rafig Aliyev

Keyword(s):

Decision Making ◽

Analytic Hierarchy Process ◽

Performance Indicator ◽

Real Life ◽

Fuzzy Analytic Hierarchy Process ◽

Multi Criteria Decision Making ◽

Analytic Hierarchy ◽

Life Problems ◽

Types Of Information ◽

Hierarchy Process

High competition between universities has been increasing over the years, and stimulates higher education institutions to attain higher positions in the ranking list. Ranking is an important performance indicator of university status evaluation, and therefore plays an essential role in students’ university selection. The ranking of universities has been carried out using different techniques. Main goal of decision processes in real-life problems is to deal with the symmetry or asymmetry of different types of information. We consider that multi-criteria decision making (MCDM) is well applicable to symmetric information modelling. Analytic hierarchy process (AHP) is a well-known technique of MCDM discipline, and is based on pairwise comparisons of criteria/alternatives for alternatives’ evaluation. Unfortunately, the classical AHP method is unable to deal with imprecise, vague, and subjective information used for the decision making process in complex problems. So, introducing a more advanced tool for decision making under such circumstances is inevitable. In this paper, fuzzy analytic hierarchy process (FAHP) is applied for the comparison and ranking of performances of five UK universities, according to four criteria. The criteria used for the evaluation of universities’ performances are teaching, research, citations, and international outlook. It is proven that applying FAHP approach makes the system consistent, and by the calculation of coefficient of variation for all alternatives, it becomes possible to rank them in prioritized order.

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A STOCHASTIC MULTI-CRITERIA DECISION-MAKING ANALYSIS FOR A WAREHOUSE LOCATION SELECTION PROBLEM: A CASE STUDY

International Journal of Research -GRANTHAALAYAH ◽

10.29121/granthaalayah.v7.i12.2019.307 ◽

2020 ◽

Vol 7 (12) ◽

pp. 133-143

Author(s):

Şeyma Emeç ◽

Gökay Akkaya

Keyword(s):

Decision Making ◽

Real Life ◽

Multiple Criteria Decision Making ◽

Selection Problem ◽

Multi Criteria Decision Making ◽

Analytic Hierarchy ◽

Location Selection ◽

Solution Approach ◽

Life Problems ◽

Warehouse Location

The problem of a warehouse location selecting which has a significant impact on logistics costs is an important decision problem based on the best choice of alternatives under multiple conflicting criteria. Multiple-criteria decision-making (MCDM) methods are used as a solution approach for the decision problems including several criteria. In this study, a new stochastic multi-criteria decision-making approach has been developed to solve the warehouse location selection problem (WLSP) in the stochastic environment which contains uncertain situations. In the proposed approach, the SAHP (Stochastic Analytic Hierarchy Process) method was used to calculate the weight of criteria, and the alternatives were ranked and evaluated by fuzzy MOORA (Multi-Objective Optimization by Ratio Analysis). The proposed approach is applied to warehouse selection problem of a supermarket chain located in Turkey. The results of the research indicated that A2 is the best alternative. It can be said that the proposed method can be applied to the real life problems because it found a suitable solution to the problem.

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ON THE RATIO OF FUZZY NUMBERS – EXACT MEMBERSHIP FUNCTION COMPUTATION AND APPLICATIONS TO DECISION MAKING

Technological and Economic Development of Economy ◽

10.3846/20294913.2015.1093563 ◽

2015 ◽

Vol 21 (5) ◽

pp. 815-832 ◽

Cited By ~ 7

Author(s):

Bogdana STANOJEVIĆ ◽

Ioan DZIŢAC ◽

Simona DZIŢAC

Keyword(s):

Decision Making ◽

Programming Problem ◽

Membership Function ◽

Fractional Programming ◽

Fuzzy Numbers ◽

Linear Constraints ◽

Linear Fractional Programming ◽

Fractional Programming Problem ◽

Fuzzy Linear Fractional Programming ◽

Linear Fractional Programming Problem

In the present paper, we propose a new approach to solving the full fuzzy linear fractional programming problem. By this approach, we provide a tool for making good decisions in certain problems in which the goals may be modelled by linear fractional functions under linear constraints; and when only vague data are available. In order to evaluate the membership function of the fractional objective, we use the α-cut interval of a special class of fuzzy numbers, namely the fuzzy numbers obtained as sums of products of triangular fuzzy numbers with positive support. We derive the α-cut interval of the ratio of such fuzzy numbers, compute the exact membership function of the ratio, and introduce a way to evaluate the error that arises when the result is approximated by a triangular fuzzy number. We analyse the effect of this approximation on solving a full fuzzy linear fractional programming problem. We illustrate our approach by solving a special example – a decision-making problem in production planning.

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Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs

Yugoslav journal of operations research ◽

10.2298/yjor110522001s ◽

2012 ◽

Vol 22 (1) ◽

pp. 41-50 ◽

Cited By ~ 12

Author(s):

B. Stanojevic ◽

I.M. Stancu-Minasian

Keyword(s):

Linear Programming ◽

Fractional Programming ◽

Fuzzy Numbers ◽

Multiple Objective ◽

Multiple Objective Linear Programming ◽

Triangular Fuzzy Numbers ◽

Linear Fractional Programming ◽

Numerical Examples ◽

Fractional Programs ◽

Linear Fractional Programming Problem

In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. Illustrative numerical examples are given to clarify the developed theory and the proposed algorithm.

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New Ranking Functions for Interval-Valued Intuitionistic Fuzzy Sets and Their Application to Multi-Criteria Decision-Making Problem

Cybernetics and Information Technologies ◽

10.2478/cait-2021-0001 ◽

2021 ◽

Vol 21 (1) ◽

pp. 3-18

Author(s):

Melda Kokoç ◽

Süleyman Ersöz

Keyword(s):

Decision Making ◽

High Performance ◽

Intuitionistic Fuzzy Set ◽

Real Life ◽

Score Function ◽

Multi Criteria Decision Making ◽

Ranking Functions ◽

Intuitionistic Fuzzy ◽

Life Problems ◽

Interval Valued

Abstract Many authors agree that the Interval-Valued Intuitionistic Fuzzy Set (IVIFS) theory generates as realistic as possible evaluation of real-life problems. One of the real-life problems where IVIFSs are often preferred is the Multi-Criteria Decision-Making (MCDM) problem. For this problem, the ranking of values obtained by fuzzing the opinions corresponding to alternatives is an important step, as a failure in ranking may lead to the selection of the wrong alternative. Therefore, the method used for ranking must have high performance. In this article, a new score function SKE and a new accuracy function HKE are developed to overcome the disadvantages of existing ranking functions for IVIFSs. Then, two illustrative examples of MCDM problems are presented to show the application of the proposed functions and to evaluate their effectiveness. Results show that the functions proposed have high performance and they are the eligibility for the MCDM problem.

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