University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 INVENTORY MODEL WITH DEMAND AS TYPE-2 FUZZY NUMBER: A FUZZY DIFFERENTIAL EQUATION APPROACH 1 24 3576 10.22111/ijfs.2018.3576 EN Bijoy Krishna Debnath Department of Mathematics, National Institute of Technology, Agartala, 799046, India Pinki Majumder Department of Mathematics, National Institute of Technology, Agartala, 799046, India Uttam Kumar Bera Department of Mathematics, National Institute of Technology, Agartala, 799046, India Manoranjan Maiti Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India Journal Article 2016 03 12 An inventory model is formulated with type-2 fuzzy parameters under trade credit policy and solved by using Generalized Hukuhara derivative approach. Representing demand parameter of each expert's opinion is a membership function of type-1 and thus, this membership function again becomes fuzzy. The final opinion of all experts is expressed by a type-2 fuzzy variable. For this present problem, to get corresponding defuzzified values of the triangular type-2 fuzzy demand parameters, first critical value (CV)-based reduction methods are applied to reduce corresponding type-1 fuzzy variables which becomes pentagonal in form. After that $\alpha$- cut of a pentagonal fuzzy number is used to construct the upper $\alpha$- cut and lower $\alpha$- cut of the fuzzy differential equation. Different cases are considered for fuzzy differential equation: gH-(i) differentiable and gH-(ii) differentiable systems. The objective of this paper is to find out the optimal time so as to minimize the total inventory cost. The considered problem ultimately reduces to a multi-objective problem which is solved by weighted sum method and global criteria method. Finally the model is solved by generalised reduced gradient method using LINGO (13.0) software. The proposed model and technique are lastly illustrated by providing numerical examples. Results from two methods are compared and some sensitivity analyses both in tabular and graphical forms are presented and discussed. The effects of total cost with respect to the change of demand related parameter ($\beta$), holding cost parameter ($r$), unit purchasing cost parameter ($p$), interest earned $(i_e)$ and interest payable $(i_p)$ are discussed. We also find the solutions for type-1 and crisp demand as particular cases of type-2 fuzzy variable. This present study can be applicable in many aspects in many real life situations where type-1 fuzzy set is not sufficient to formulate the mathematical model. From the numerical studies, it is observed that under both gH-(i) and gH-(ii) cases, total cost of the system gradually reduces for the sub-cases - 1.1, 1.2 and 1.3 depending upon the positions of N(trade credit for customer) and M (trade credit for retailer) with respect to T (time period).

https://ijfs.usb.ac.ir/article_3576_1c33eb5cd6fc2e78a2fb684ac15ad700.pdf

University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 SHAPLEY FUNCTION BASED INTERVAL-VALUED INTUITIONISTIC FUZZY VIKOR TECHNIQUE FOR CORRELATIVE MULTI-CRITERIA DECISION MAKING PROBLEMS 25 54 3577 10.22111/ijfs.2018.3577 EN Pratibha Rani Department of Mathematics, Jaypee University of Engineering and Technology, Guna-473226, M. P., India Divya Jain Department of Mathematics, Jaypee University of Engineering and Technology, Guna-473226, M. P., India D. S. Hooda Guru Jambheshwar University of Science and Technology, Hisar-125001, Haryana, India Journal Article 2016 06 12 Interval-valued intuitionistic fuzzy set (IVIFS) has developed to cope with the uncertainty of imprecise human thinking. In the present communication, new entropy and similarity measures for IVIFSs based on exponential function are presented and compared with the existing measures. Numerical results reveal that the proposed information measures attain the higher association with the existing measures, which demonstrate their efficiency and reliability. To deal with the interactive characteristics among the elements in a set, Shapley weighted similarity measure based on proposed similarity measure for IVIFSs is discussed via Shapley function. Thereafter, the linear programming model for optimal fuzzy measure is originated for incomplete information about the weights of the criteria and thus, the optimal weight vector is obtained in terms of Shapley values. Further, the VIKOR technique is discussed for correlative multi-criteria decision making problems under interval-valued intuitionistic fuzzy environment. Finally, an example of investment problem is presented to exemplify the application of the proposed technique under incomplete and uncertain information situation.

https://ijfs.usb.ac.ir/article_3577_817d9d009ab46e0e1945d00b0cbbdef8.pdf

University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 ITERATIVE METHOD FOR SOLVING TWO-DIMENSIONAL NONLINEAR FUZZY INTEGRAL EQUATIONS USING FUZZY BIVARIATE BLOCK-PULSE FUNCTIONS WITH ERROR ESTIMATION 55 76 3578 10.22111/ijfs.2018.3578 EN Shokrollah Ziari Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran Journal Article 2016 05 12 In this paper, we propose an iterative procedure based on two dimensional fuzzy block-pulse functions for solving nonlinear fuzzy Fredholm integral equations of the second kind. The error estimation and numerical stability of the proposed method are given in terms of supplementary Lipschitz condition. Finally, illustrative examples are included in order to demonstrate the accuracy and convergence of the proposed method.

https://ijfs.usb.ac.ir/article_3578_dadf16bc5320d88699ca38f16ea27e14.pdf

University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS 77 89 3579 10.22111/ijfs.2018.3579 EN Guiwu Wei School of Business, Sichuan Normal University, Chengdu, 610101, P.R. China Journal Article 2016 04 12 In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similarity measure, weighted set-theoretic cosine similarity measure, grey similarity measure and weighted grey similarity measure. Then, we apply these similarity measures between picture fuzzy sets to building material recognition and minerals field recognition. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for building material recognition and minerals field recognition.

https://ijfs.usb.ac.ir/article_3579_78359250002654fac62dee60be8e46ac.pdf

University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 A NEW APPROACH FOR PARAMETER ESTIMATION IN FUZZY LOGISTIC REGRESSION 91 102 3580 10.22111/ijfs.2018.3580 EN GULTEKIN ATALIK Department of Statistics, Anadolu University, Eskisehir, Turkey and Department of Statistics, Amasya University, Amasya,Turkey Sevil Senturk Department of Statistics, Anadolu University, Eskisehir, Turkey Journal Article 2016 02 13 Logistic regression analysis is used to model categorical dependent variable. It is usually used in social sciences and clinical research. Human thoughts and disease diagnosis in clinical research contain vagueness. This situation leads researchers to combine fuzzy set and statistical theories. Fuzzy logistic regression analysis is one of the outcomes of this combination and it is used in situations where the classical logistic regression assumptions' are not satisfied. Also it can be used if the observations or their relations are vague. In this study, a model called “Fuzzy Logistic Regression Based on Revised Tanaka's Fuzzy Linear Regression Model” is proposed. In this regard, the methodology and formulation of the proposed model is explained in detail and the revised Tanaka's regression model is used to estimate the parameters. The Revised Tanaka's Regression model is an extension of Tanaka's Regression Model in which the objection function is developed. An application is performed on birth weight data set. Also, an application of diabetes data set used in Pourahmad et al.'s study was conducted via our proposed data set. The validity of the model is shown by the help of goodness – of –fit criteria called Mean Degree Memberships (MDM).

https://ijfs.usb.ac.ir/article_3580_f9f590713068e42b84d5b7b1b97954c4.pdf

University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 QUANTALE-VALUED GAUGE SPACES 103 122 3581 10.22111/ijfs.2018.3581 EN Gunther Jager University of Applied Sciences Stralsund, D-18435 Stralsund, Germany Wei Yao Hebei University of Science and Technology, 050054 Shijiazhuang, P.R.China Journal Article 2016 10 13 We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the quantale, is even isomorphic to our category. Finally, the category of quantale-valued metric spaces is shown to be coreflectively embedded in our category.

https://ijfs.usb.ac.ir/article_3581_e2cdd171cdf1a1b1c5932b122c4123ba.pdf

University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 ON TRUNCATED MEASURES OF INCOME INEQUALITY FROM A FUZZY PERSPECTIVE 123 137 3582 10.22111/ijfs.2018.3582 EN Reza Pourmousa Department of Statistics, Faculty of Mathematics ~and Computer Shahid Bahonar University of Kerman Kerman, Iran Journal Article 2016 03 10 In most statistical analysis, inequality or extent of variation in income is represented in terms of certain summary measures. But some authors argued that the concept of inequality is vague and thus cannot be measured as an exact concept. Therefore, fuzzy set theory provides naturally a useful tool for such circumstances. In this paper we have introduced a real-valued fuzzy method of illustrating the measures of income inequality in truncated random variables based on the case where the conditional events are vague. To guarantee certain relevant properties of these measures, we first selected three main families of measures and obtained their closed formulas, then used two simulated and real data set to illustrate the usefulness of derived results.

https://ijfs.usb.ac.ir/article_3582_8a116cc7c46a92b83fb40a6372c29f51.pdf

University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 A NEW APPROACH IN FAILURE MODES AND EFFECTS ANALYSIS BASED ON COMPROMISE SOLUTION BY CONSIDERING OBJECTIVE AND SUBJECTIVE WEIGHTS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY SETS 139 161 3583 10.22111/ijfs.2018.3583 EN Z. Hajighasemi Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran S. Meysam Mousavi Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran Journal Article 2016 05 13 Failure modes and effects analysis (FMEA) is a well-known risk analysis approach that has been conducted to distinguish, analyze and mitigate serious failure modes. It demonstrates the effectiveness and the ability of understanding and documenting in a clear manner; however, the FMEA has weak points and it has been criticized by some authors. For example, it does not consider relative importance among three risk factors (i.e., $ O, S $ and $ D $). Different sequences of $ O $, $ S $ and $ D $ may result in exactly the same value of risk priority number (RPN), but their semantic risk implications may be totally different and these three risk factors are difficult to be precisely expressed. This study introduces a new interval-valued intuitionistic fuzzy (IVIF)-decision approach based on compromise solution concept that defeats the above weak points and improves the traditional FMEA's results. This study firstly employs both subjective and objective weights in the decision process simultaneously. Secondly, there are two kinds of subjective weights performed in the study: aggregated weights obtained by experts' assessments as well as entropy measure. Thirdly, this approach is defined under an IVIF-environment to ensure that the evaluation information would be preserved, and the uncertainties could be handled during the computations. Hence, it considers uncertainty in experts' judgments as well as reduces the probability of obtaining two ranking orders with the same value. Finally, the alternatives are ranked with a new collective index according to the compromise solution concept. To show the effectiveness of the proposed approach, two practical examples are solved from the recent literature in engineering applications. The proposed decision approach has an acceptable performance. Also, its advantages have been mentioned in comparison with other decision approaches.

https://ijfs.usb.ac.ir/article_3583_a1e482e0977b7d1891e80c27fcf0934e.pdf

University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 15 1 2018 03 01 ON SOMEWHAT FUZZY AUTOMATA CONTINUOUS FUNCTIONS IN FUZZY AUTOMATA TOPOLOGICAL SPACES 163 178 3584 10.22111/ijfs.2018.3584 EN N. Krithika Department of Mathematics, Sri Sarada College for Women, Salem, Tamilnadu, India B. Amudhambigai Department of Mathematics, Sri Sarada College forWomen, Salem, Tamilnadu, India Journal Article 2016 04 13 In this paper, the concepts of somewhat fuzzy automata continuous functions and somewhat fuzzy automata open functions in fuzzy automata topological spaces are introduced and some interesting properties of these functions are studied. In this connection, the concepts of fuzzy automata resolvable spaces and fuzzy automata irresolvable spaces are also introduced and their properties are studied.

https://ijfs.usb.ac.ir/article_3584_8690026e4194f60da8e7e75afe0a7c27.pdf