Journal of Fuzzy Logic and Modeling in Engineering, 2022
Background: In this article we develop a global warming indicator model under fuzzy system. It is... more Background: In this article we develop a global warming indicator model under fuzzy system. It is the light of sun that environmental pollution is responsible for the cause and immediate effect of global warming. Limited amount of oxygen in the air, continuous decrease of fresh water volume, more especially the amount of drinking water and the rise of temperature in the globe are the major symptoms (variants) of global warming. Thus, to capture the facts we need to develop a mathematical model which has not yet been developed by the earlier researchers. Introduction: An efficient literature survey has been done over the three major parameters of the environment namely oxygen, fresh water and surface temperature exclusively. In fact we have accumulated 150 years-data structure for these major components and have analyzed them under fuzzy system so as to develop an efficient global warming indicator model. Method: First of all, we gave few definitions on fuzzy set. Utilizing the data ...
This paper discusses an Economic Order Quantity (EOQ) model with two types of imperfect quality i... more This paper discusses an Economic Order Quantity (EOQ) model with two types of imperfect quality items : scrap and reworkable, where the setup cost, the holding cost and the demand areconsideredasfuzzynumbers.Thefuzzyparametersarethentransformedintocorresponding interval numbers. Minimization of the interval objective function (obtained by using interval parameters) has been transformed into a classical multi-objective EOQ problem. The order relation that represents the decision maker's preference among the interval objective functions has been defined by the right limit, left limit, center and half-width of an interval. This concept is used to minimize the interval objective function. The problem has been solved by intuitionistic fuzzy programming technique. Finally, the proposed method is illustrated with a practical numerical example. The Pareto Optimality test is used for verification of optimality of the solution.
An approach for solving a matrix game whose pay off elements are symmetric trapezoidal fuzzy numb... more An approach for solving a matrix game whose pay off elements are symmetric trapezoidal fuzzy numbers is proposed. P.Grzegorzewski’s theorem[1]has been used to transform symmetric trapezoidal fuzzy numbers to interval fuzzy number such that length of all intervals are different.Acceptability index has been defined and ordering of fuzzy numbers has been established.
Fuzzy set theory has a wide range of applications in operations research, war science, medical di... more Fuzzy set theory has a wide range of applications in operations research, war science, medical diagnosis, etc. The present monograph deals with the validity of applications of fuzzy set theory in matrix and bi-matrix games. The solution methodology of two-person matrix games with elements of pay-off matrix represented by triangular fuzzy numbers (TFNs) has been studied. Intuitionistic fuzziness in matrix/bi-matrix games can appear in many ways but three cases seem to be very natural. First one is that the goal may be intuitionistic fuzzy (I-fuzzy), second, that the elements of the pay-off matrix are I-fuzzy numbers and lastly the goals as well as the elements of the pay-off matrix are I-fuzzy. In this monograph the solution procedure of all such types of games have been investigated. A solution procedure for the matrix games where the elements of pay-off matrix are expressed by interval numbers has been explored. A number of practical implications have been incorporated to illustrat...
In this paper, we present an application of intuitionistic fuzzy programming to two person matrix... more In this paper, we present an application of intuitionistic fuzzy programming to two person matrix games for the solution with mixed strategies. We use linear membership and non membership functions for such computation. We introduce the intuitionistic fuzzy (IF) goal for the choice of a strategy in a pay-off matrix in order to incorporate ambiguity of human judgments and a player wants to optimize his/her degree of attainment of the IF goal. It is shown that this is the optimal solution of the mathematical programming problem. In addition, numerical example is also presented to illustrate the methodology.
In this paper, a soft Petri net model has been proposed based on a soft production rule. A soft i... more In this paper, a soft Petri net model has been proposed based on a soft production rule. A soft implication operator has been introduced based on logical and set theoretic operations in a soft set. The truth degree in initial marking is considered as a binary number and boolean operators are used as In, \(Out_1\) and \(Out_2\) operators in the Petri net. Algorithms have been proposed to describe an approximate reasoning process with the soft Petri net. A numerical problem related to the purchase of a beautiful flat by a rational buyer has been discussed to establish relevance of the theory proposed.
The basic aim of this paper is to an application of triangular intu-itionistic fuzzy numbers(TIFN... more The basic aim of this paper is to an application of triangular intu-itionistic fuzzy numbers(TIFNs) to a single non-cooperative bi-matrix games. Firstly, the concept of TIFNs and their cut sets are introduced as well as the in-equality relations between two TIFNs. Secondly, a bi-matrix game with payoffs of TIFNs is considered and an attempt is made to conceptualize the meaning of a Nash-equilibrium solution for such games. Practical investigations have been discussed for selling a product in a market share for two different companies.
Asia-Pacific Journal of Operational Research, 2009
A fuzzy two person interval game problem is proposed and treated in this paper which is not easil... more A fuzzy two person interval game problem is proposed and treated in this paper which is not easily tackled by the conventional methods. First, with respect to this pay-off values, a necessary and sufficient condition for the existence of a saddle point is proved. Based on interval value model, we are to find the value of interval game without saddle point. Finally, example is given to illustrate the procedure and to indicate the performance of the proposed method.
In this paper, a more general definition of triangular intuitionistic fuzzy number (TIFN) is prop... more In this paper, a more general definition of triangular intuitionistic fuzzy number (TIFN) is proposed by removing the `normality' in the definition of intuitionistic fuzzy number. The basic arithmetic operations of generalized triangular intuitionistic fuzzy numbers (GTIFNs) and the notion of (\alpha,\beta)-cut sets are defined. Also a nearest interval approximation method is described to approximate a GTIFN to a nearest interval number. Moreover the average ranking index is introduced to find out order relations between two GTIFNs. Numerical examples are also provided for illustration.
In this paper, an intuitionistic fuzzy matrix game has been considered and its solution method ha... more In this paper, an intuitionistic fuzzy matrix game has been considered and its solution method has been proposed using defuzzification method. Score functions have been defined to construct the problem and numerical example has been given in support of the solution method.
Journal of Fuzzy Logic and Modeling in Engineering, 2022
Background: In this article we develop a global warming indicator model under fuzzy system. It is... more Background: In this article we develop a global warming indicator model under fuzzy system. It is the light of sun that environmental pollution is responsible for the cause and immediate effect of global warming. Limited amount of oxygen in the air, continuous decrease of fresh water volume, more especially the amount of drinking water and the rise of temperature in the globe are the major symptoms (variants) of global warming. Thus, to capture the facts we need to develop a mathematical model which has not yet been developed by the earlier researchers. Introduction: An efficient literature survey has been done over the three major parameters of the environment namely oxygen, fresh water and surface temperature exclusively. In fact we have accumulated 150 years-data structure for these major components and have analyzed them under fuzzy system so as to develop an efficient global warming indicator model. Method: First of all, we gave few definitions on fuzzy set. Utilizing the data ...
This paper discusses an Economic Order Quantity (EOQ) model with two types of imperfect quality i... more This paper discusses an Economic Order Quantity (EOQ) model with two types of imperfect quality items : scrap and reworkable, where the setup cost, the holding cost and the demand areconsideredasfuzzynumbers.Thefuzzyparametersarethentransformedintocorresponding interval numbers. Minimization of the interval objective function (obtained by using interval parameters) has been transformed into a classical multi-objective EOQ problem. The order relation that represents the decision maker's preference among the interval objective functions has been defined by the right limit, left limit, center and half-width of an interval. This concept is used to minimize the interval objective function. The problem has been solved by intuitionistic fuzzy programming technique. Finally, the proposed method is illustrated with a practical numerical example. The Pareto Optimality test is used for verification of optimality of the solution.
An approach for solving a matrix game whose pay off elements are symmetric trapezoidal fuzzy numb... more An approach for solving a matrix game whose pay off elements are symmetric trapezoidal fuzzy numbers is proposed. P.Grzegorzewski’s theorem[1]has been used to transform symmetric trapezoidal fuzzy numbers to interval fuzzy number such that length of all intervals are different.Acceptability index has been defined and ordering of fuzzy numbers has been established.
Fuzzy set theory has a wide range of applications in operations research, war science, medical di... more Fuzzy set theory has a wide range of applications in operations research, war science, medical diagnosis, etc. The present monograph deals with the validity of applications of fuzzy set theory in matrix and bi-matrix games. The solution methodology of two-person matrix games with elements of pay-off matrix represented by triangular fuzzy numbers (TFNs) has been studied. Intuitionistic fuzziness in matrix/bi-matrix games can appear in many ways but three cases seem to be very natural. First one is that the goal may be intuitionistic fuzzy (I-fuzzy), second, that the elements of the pay-off matrix are I-fuzzy numbers and lastly the goals as well as the elements of the pay-off matrix are I-fuzzy. In this monograph the solution procedure of all such types of games have been investigated. A solution procedure for the matrix games where the elements of pay-off matrix are expressed by interval numbers has been explored. A number of practical implications have been incorporated to illustrat...
In this paper, we present an application of intuitionistic fuzzy programming to two person matrix... more In this paper, we present an application of intuitionistic fuzzy programming to two person matrix games for the solution with mixed strategies. We use linear membership and non membership functions for such computation. We introduce the intuitionistic fuzzy (IF) goal for the choice of a strategy in a pay-off matrix in order to incorporate ambiguity of human judgments and a player wants to optimize his/her degree of attainment of the IF goal. It is shown that this is the optimal solution of the mathematical programming problem. In addition, numerical example is also presented to illustrate the methodology.
In this paper, a soft Petri net model has been proposed based on a soft production rule. A soft i... more In this paper, a soft Petri net model has been proposed based on a soft production rule. A soft implication operator has been introduced based on logical and set theoretic operations in a soft set. The truth degree in initial marking is considered as a binary number and boolean operators are used as In, \(Out_1\) and \(Out_2\) operators in the Petri net. Algorithms have been proposed to describe an approximate reasoning process with the soft Petri net. A numerical problem related to the purchase of a beautiful flat by a rational buyer has been discussed to establish relevance of the theory proposed.
The basic aim of this paper is to an application of triangular intu-itionistic fuzzy numbers(TIFN... more The basic aim of this paper is to an application of triangular intu-itionistic fuzzy numbers(TIFNs) to a single non-cooperative bi-matrix games. Firstly, the concept of TIFNs and their cut sets are introduced as well as the in-equality relations between two TIFNs. Secondly, a bi-matrix game with payoffs of TIFNs is considered and an attempt is made to conceptualize the meaning of a Nash-equilibrium solution for such games. Practical investigations have been discussed for selling a product in a market share for two different companies.
Asia-Pacific Journal of Operational Research, 2009
A fuzzy two person interval game problem is proposed and treated in this paper which is not easil... more A fuzzy two person interval game problem is proposed and treated in this paper which is not easily tackled by the conventional methods. First, with respect to this pay-off values, a necessary and sufficient condition for the existence of a saddle point is proved. Based on interval value model, we are to find the value of interval game without saddle point. Finally, example is given to illustrate the procedure and to indicate the performance of the proposed method.
In this paper, a more general definition of triangular intuitionistic fuzzy number (TIFN) is prop... more In this paper, a more general definition of triangular intuitionistic fuzzy number (TIFN) is proposed by removing the `normality' in the definition of intuitionistic fuzzy number. The basic arithmetic operations of generalized triangular intuitionistic fuzzy numbers (GTIFNs) and the notion of (\alpha,\beta)-cut sets are defined. Also a nearest interval approximation method is described to approximate a GTIFN to a nearest interval number. Moreover the average ranking index is introduced to find out order relations between two GTIFNs. Numerical examples are also provided for illustration.
In this paper, an intuitionistic fuzzy matrix game has been considered and its solution method ha... more In this paper, an intuitionistic fuzzy matrix game has been considered and its solution method has been proposed using defuzzification method. Score functions have been defined to construct the problem and numerical example has been given in support of the solution method.
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