A Pythagorean fuzzy set is a powerful model for depicting fuzziness and uncertainty. This model is more flexible and practical as compared to an intuitionistic fuzzy model. This research article ...presents a new model called LR-type fully Pythagorean fuzzy linear programming problem. We consider the notions of LR-type Pythagorean fuzzy number, ranking for LR-type Pythagorean fuzzy numbers and arithmetic operations for unrestricted LR-type Pythagorean fuzzy numbers. We propose a method to solve LR-type fully Pythagorean fuzzy linear programming problems with equality constraints. We describe our proposed method with numerical examples including diet problem.
•A fuzzy logic based ranking function is proposed to enhance Information Retrieval.•It is based on Composite Fuzzy Inference System with 259 fuzzy rules.•The performance is tested in terms of ...precision, recall and F-measure on CACM and CISI.•The better results are obtained as compared to Okapi-BM25 and Rubens’ approach.•A paired t-test is also conducted to perform statistical analysis.
The relevant documents from large data sets are retrieved with the help of ranking function in Information Retrieval system. In this paper, a new fuzzy logic based ranking function is proposed and implemented to enhance the performance of Information Retrieval system. The proposed ranking function is based on the computation of different terms of term-weighting schema such as term frequency, inverse document frequency and normalization. Fuzzy logic is used at two levels to compute relevance score of a document with respect to the query in present work. All the experiments are performed on CACM and CISI benchmark data sets. The experimental results reveal that the performance of our proposed ranking function is much better than the fuzzy based ranking function developed by Rubens along with other widely used ranking function Okapi-BM25 in terms of precision, recall and F-measure.
The aim of this study is presenting the solution methodology of multi-objective fuzzy transportation problem with fuzzy decision variables, where all the input parameters and decisions variables of ...the programming problems are assumed to be triangular fuzzy number and triangular fuzzy decision variables respectively. Moreover the objectives under considerations are minimization of cost of transportation and minimization of shipping time under fuzzy environment. The fuzziness of the objective functions and the fuzzy constraints of the programming problem are defuzzified using the ranking function and the equality property between two fuzzy numbers, respectively. The consequent crisp multi-objective fuzzy transportation problem is tackled by employing fuzzy mathematical programming approach. Finally fuzzy decision is made after solving the resultant mathematical programming problem using LINGO(Schrage and LINDO Systems (1997)) software. Illustrative numerical example is presented in support of the proposed methodology.
We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy ...linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions,
α
-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately.
In this paper, linear fractional programming problems have been extended to neutrosophic sets, and the operations and functionality of these laws are studied. Moreover, the new algorithm is based on ...aggregation ranking function and arithmetic operations of triangular neutrosophic sets. Furthermore, in this paper, we take up a problem where the constraints are both equality and inequality neutrosophic triangular fuzzy number. Lead from genuine issue, a few numerical models are considered to survey the legitimacy, profitability and materialness of our technique. At last, some numerical trials alongside one contextual analysis are given to show the novel techniques are better than the current strategies.
Process capability indices are numerical tools that quantify how well a process can meet customer requirements, specifications or engineering tolerances. Fuzzy logic is incorporated to deal ...imprecise, incomplete data along with uncertainty. This paper develops two fuzzy methods for measuring the process capability in simple linear profiles for the circumstances in which lower and upper specification limits are imprecise. To guide practitioners, numerical example is provided.
This article deals with a noble application of Pythagorean fuzzy set (PFS). In fuzzy set theory in particular for intuitionistic fuzzy set (IFS) we are quite familiar to pass through Attanassov’s ...concept. But to deal with non-standard fuzzy set, PFS plays an important role in many decision making problems which dominate Attanassov’s IFS. The main aim of this study is to show the effectiveness and applicability of the PFS in decision making under uncertain environment through inventory problems. Also, this works brings a solution to the situation when the sum of the membership and non-membership degree is greater than one i.e. when IFS fails. The primary goal of this study is to show how PFS has a wider space of membership degrees and it is more capable of handling uncertain information than any other fuzzy set. Here, we have considered an Economic Order Quantity (EOQ) model with customer’s income dependent demand of end-item and price-dependent supply of input component. We explicitly specify the demand as a function of customers’ income and unit selling price. We develop a crisp model for cost minimization problem first then we split the model into general fuzzy, intuitionistic fuzzy and Pythagorean fuzzy environment respectively. However, PFS lacks mathematical solution procedure. Employing the score function, we optimize the cost function using the Yager’s ranking index method. Moreover, our numerical results show the superiority of PFS with respect to the traditional model and other fuzzy environments. Finally, sensitivity analysis and graphical illustrations are made to justify the model.
Graphical abstract
Generally, linear programming (LP) problem is the most extensively utilized technique for solving and optimizing real-world problems due to its simplicity and efficiency. However, to deal with the ...inaccurate data, the neutrosophic set theory comes into play, which creates a simulation of the human decision-making process by considering all parts of the choice (i.e., agree, not sure, and disagree). Keeping the bene ts in mind, we proposed the neutrosophic LP models based on triangular neutrosophic numbers (TNN) and provided a method for solving them. Fuzzy LP problem can be converted into crips LP problem based on the de ned ranking function. The provided technique has been demonstrated with numerical examples given by Abdelfattah. Finally, we found that, when compared to previous approaches, the suggested method is simpler, more efficient, and capable of solving all types of fuzzy LP models.
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