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A methodology for matrix games with payoffs of triangular intuitionistic fuzzy number

JOURNAL OF INTELLIGENT & fuzzy SYSTEMS 2014年第6期26卷 2899-2912页

作者： Nan, Jiang-Xia Zhang, Mao-Jun Li, Deng-Feng Guilin Univ Elect Technol Sch Math & Comp Sci Guilin 541004 Guangxi Peoples R China Fuzhou Univ Sch Management Fuzhou 350002 Fujian Peoples R China

The main objective of this paper is to develop a new ranking methodology for solving matrix games with intuitionistic fuzzy payoffs in terms of a value and ambiguity of triangular intuitionistic fuzzy numbers (TIFNs). In order to obtain an equilibrium solution of this matrix game, we construct two auxiliary TIFN programming models that are transformed into bi-objective linear programming models which are solved by a lexicographic methodology. The validity and applicability of the proposed methodology in this paper are illustrated with a numerical example.

关键词： triangular intuitionistic fuzzy number matrix game mathematical programming lexicographic method

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Portfolio selection model with triangular intuitionistic fuzzy number by rate of return

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JOURNAL OF INTELLIGENT & fuzzy SYSTEMS 2022年第3期43卷 3133-3139页

作者： Liao Xiaolian Chen Guohua Hunan Univ Humanities Sci & Technol Coll Math & Finance Loudi Peoples R China

A portfolio selection model with return as triangular intuitionistic fuzzy number is developed in this study to assess and select portfolios on China Stock Exchange. Although the portfolio selection has been widely investigated, and most studies have regarded return and risk as the main decisive criteria, there are many uncertainties in the financial market, such as social, political and human psychological factors, which makes it difficult for us to describe the risks in line with empirical evidence. To fill this gap, first, a literature review was conducted to clarify the current situation and shortcomings of portfolio selection. Second, the triangular intuitionistic fuzzy number was used to fuzzify the coefficients of the objective function and the constraints in the portfolio model. Third, the triangular intuitionistic fuzzy number model was transformed into a linear programming model by using the selected exact ranking function, and the model was solved by MATLAB. Finally, the historical monthly returns of 10 stocks in China's Stock Exchange from December 2017 to November 2020, lasting 36 months, were selected to demonstrate the model. The results indicate that the portfolio selection model with triangular intuitionistic fuzzy number can better meet the uncertainty of the real securities market, and more reasonable investment decision guidance can be provided for investors. Besides, the limitations of this study are pointed out, and implications and directions for future research are discussed.

关键词： Portfolio selection model rate of return triangular intuitionistic fuzzy number

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AHP based on triangular intuitionistic fuzzy number and its Application to Supplier Selection Problem

AHP based on Triangular Intuitionistic Fuzzy Number and its ...

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International Conference on Advances in Materials, Manufacturing and Applied Sciences (ICAMMAS)

作者： Nirmala, G. Uthra, G. Sri Sairam Engn Coll Dept Math Chennai 600040 Tamil Nadu India Bharathiar Univ Coimbatore Tamil Nadu India Pachaiyappas Coll Dept Math Chennai 600030 Tamil Nadu India

Analytic Hierarchy process (AHP) is an effective approach for dealing with Multi Criteria Decision Problem (MCDM). This paper investigates AHP in intuitionistic fuzzy environment. Here comparative judgments are taken in the form of triangular intuitionistic fuzzy number (TIFN). The elements of the comparison matrices are transformed into Interval valued intuitionistic fuzzy number by using Nearest Weighted intuitionistic Interval Approximation (NWIIA) which is introduced in this paper. Then, the transformed matrix is changed in to a crisp matrix by using score function. Priority values are calculated by Arithmetic mean method. This process is applied to the supplier selection problem from the paper in the literature with the same data. It is found that this method yields the same result as that of the paper more easily. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： triangular intuitionistic fuzzy number Interval valued intuitionistic fuzzy number Nearest Weighted intuitionistic Interval Approximation Score function

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Multi-criteria Decision Making with triangular intuitionistic fuzzy number based on Distance Measure & Parametric Entropy Approach 6

Multi-criteria Decision Making with Triangular Intuitionisti...

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6th International Conference on Smart Computing and Communications (ICSCC)

作者： Saini, Namita Bajaj, Rakesh Kumar Gandotra, Neeraj Dwivedi, Ram Prakash Shoolini Univ Sch Elect & Comp Sci Engn Solan 173229 HP India Jaypee Univ Informat Technol Dept Math Solan 173234 HP India

The present communication aims to study the triangular intuitionistic fuzzy Multiple Criteria Decision Making (TIF-MCDM) problem for finding the best option where the phonetic factors for the criteria are pre-characterized. In perspective of this, a new parametric entropy under alpha-cut/(alpha,beta)- cut based distance measures has been proposed and implemented for various conceivable estimations of parameters. A survey structure based on a questionnaire for the purchase of a car has also been studied and devised the ranking procedure for the evaluation criteria. Further, a ranking algorithm for TIF-MCDM issue for the accessible options by processing the various distances between the perfect option and all the accessible options has been proposed. An illustrative example to rank the alternatives in view of different opinions has also been included. (C) 2018 The Authors. Published by Elsevier B.V.

关键词： triangular intuitionistic fuzzy number Multiple Criteria Decision Making Ranking Closeness Coefficient Distance Measures

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Linear programming with triangular intuitionistic fuzzy number

Linear programming with Triangular Intuitionistic Fuzzy Numb...

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7th Biannual Conference of the European-Society-for-fuzzy-Logic-and-Technology (EUSFLAT)/17th Annual LFA Meeting

作者： Dubey, Dipti Mehra, Aparna Indian Inst Technol Dept Math New Delhi 110016 India

This paper presents an approach based on value and ambiguity indexes defined in [1] to solve linear programming problems with data as triangular intuitionistic fuzzy numbers.

ISBN: (纸本)9789078677000

This paper presents an approach based on value and ambiguity indexes defined in [1] to solve linear programming problems with data as triangular intuitionistic fuzzy numbers.

关键词： triangular intuitionistic fuzzy number fuzzy linear programming Ranking method

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A Multi-Attribute Group Decision Method Based on triangular intuitionistic fuzzy number

A Multi-Attribute Group Decision Method Based on Triangular ...

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2nd International Conference on Information Computing and Applications

作者： Yue, Xiaoyun Zou, Dewen Guo, Yajun Wang, Guosheng Hebei Normal Univ Sci & Technol Inst Math & Informat Technol Qinhuangdao 066004 Hebei Province Peoples R China Hebei Normal Univ Sci & Technol Off Sci Res Qinhuangdao 066004 Hebei Province Peoples R China

ISBN: (纸本)9783642274510

This paper proposes a new method of multi-attribute group decision by using triangular intuitionistic fuzzy number (TIFN) to represent the experts' evaluation information. At first, giving the TIFN definition and aggregation operator, such as triangular intuitionistic weighing arithmetic average (TI-WAA) operator and ordered weighted aggregation (TI-OWA)operator. Next, extending the TIFN ranking method by using the weighted average area, the model of multi-attribute group decision is constructed. Finally, a numerical example is given to illustrate application. The numberical results show that the proposed method is feasible and effective.

关键词： Multi-attribute group decision triangular intuitionistic fuzzy number Aggregation operator Rank

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Multi-criteria Decision Making with triangular intuitionistic fuzzy number based on Distance Measure & Parametric Entropy Approach

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Procedia Computer Science 2018年 125卷 34-41页

作者： Namita Saini Rakesh Kumar Bajaj Neeraj Gandotra Ram Prakash Dwivedi School of Electrical and Computer Science Engineering Shoolini University Bajhol Solan -173 229 H.P. INDIA Department of Mathematics Jaypee University of Information Technology Waknaghat Solan -173 234 H.P. INIDA

The present communication aims to study the triangular intuitionistic fuzzy Multiple Criteria Decision Making (TIF-MCDM) problem for finding the best option where the phonetic factors for the criteria are pre-characterized. In perspective of this, a new parametric entropy under α-cut/(α,/β)- cut based distance measures has been proposed and implemented for various conceivable estimations of parameters. A survey structure based on a questionnaire for the purchase of a car has also been studied and devised the ranking procedure for the evaluation criteria. Further, a ranking algorithm for TIF-MCDM issue for the accessible options by processing the various distances between the perfect option and all the accessible options has been proposed. An illustrative example to rank the alternatives in view of different opinions has also been included.

关键词： triangular intuitionistic fuzzy number Multiple Criteria Decision Making Ranking Closeness Coefficient Distance Measures

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Modified γ-operator technique for intuitionistic fuzzy multi-objective nonlinear programming problems with application in agriculture

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 273卷

作者： Kaur, Shubhpreet Mahajan, Sumati Chauhan, Abhishek Deemed Univ Punjab Engn Coll Dept Math Chandigarh 160012 India

In recent years, intuitionistic fuzzy theory has gained significant attention for its ability to handle uncertainty through both membership and non-membership degrees. This paper presents a novel modification to gamma-operator technique by introducing distinct gamma-operators for membership and non-membership functions to tackle intuitionistic fuzzy environment. The proposed technique is rigorously validated through the proof of relevant theorems that demonstrate its capability to derive efficient solutions for multi-objective nonlinear programming problems, where all parameters are represented as triangular intuitionistic fuzzy numbers. To elucidate the proposed technique, an illustrative example is presented. Furthermore, a comparative study with existing techniques is conducted, which highlights the superior performance of the proposed method. Finally, an application in the agriculture sector demonstrates the practical relevance and effectiveness of the proposed method in real-world scenarios.

关键词： Multi-objective problem gamma-operator Nonlinear programming triangular intuitionistic fuzzy number Agricultural planning

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An Approach for Evaluating Website Quality in Hotel Industry Based on triangular intuitionistic fuzzy numbers

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INFORMATICA 2017年第4期28卷 725-748页

作者： Stanujkic, Dragisa Zavadskas, Edmundas Kazimieras Karabasevic, Darjan Urosevic, Snezana Maksimovic, Mladjan Univ Belgrade Tech Fac Bor Belgrade Serbia Vilnius Gediminas Tech Univ Civil Engn Fac Res Inst Smart Bldg Technol Vilnius Lithuania Univ Business Acad Novi Sad Fac Appl Management Econ & Finance Novi Sad Serbia

Compared to fuzzy numbers, intuitionistic fuzzy numbers provide greater opportunities for solving complex decision-making problems, especially when they are related to ambiguities, uncertainties and vagueness. However, their use is more complex, especially when it comes to ordinary users. Therefore, in this paper an approach adopted for evaluating alternatives on the basis of a smaller number of some more complex evaluation criteria is proposed. The approach is based on the use of linguistic variables, triangular intuitionistic fuzzy numbers, and the Hamming distance. At the end, a case study of hotels' websites evaluation is given to demonstrate the practicality and effectiveness of the proposed approach, together with its limitations and weaknesses. Additionally, a new procedure for ranking intuitionistic fuzzy numbers is proposed and its use is verified.

关键词： intuitionistic fuzzy sets triangular intuitionistic fuzzy number aggregation operator hamming distance hotel website evaluation

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A Lexicographic Method for Matrix Games with Payoffs of triangular intuitionistic fuzzy numbers

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2010年第3期3卷 280-289页

作者： Nan, Jiang-Xia Li, Deng-Feng Zhang, Mao-Jun Fuzhou Univ Sch Management Fuzhou 350108 Fujian Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Liaoning Peoples R China Dalian Univ Technol Coll Informat Engn Dalian 116622 Liaoning Peoples R China Dalian Univ Technol Dept Econ Dalian 116024 Peoples R China

The intuitionistic fuzzy set (IF-set) has not been applied to matrix game problems yet since it was introduced by K. T. Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs). Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example.

关键词： triangular intuitionistic fuzzy number intuitionistic fuzzy set Matrix game Mathematical programming Lexicographic method

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