Download e-book for kindle: Fuzzy Preference Ordering of Interval Numbers in Decision by Atanu Sengupta

By Atanu Sengupta

ISBN-10: 3540899146

ISBN-13: 9783540899143

In traditional mathematical programming, coefficients of difficulties tend to be made up our minds by way of the specialists as crisp values by way of classical mathematical reasoning. yet in fact, in an vague and unsure setting, will probably be utmost unrealistic to imagine that the information and illustration of knowledgeable can are available in an exact method. the broader aim of the booklet is to check diverse actual choice events the place difficulties are outlined in inexact surroundings. Inexactness are as a rule generated in methods – (1) because of vague notion and data of the human professional through imprecise illustration of information as a DM; (2) because of huge-ness and complexity of relatives and knowledge constitution within the definition of the matter state of affairs. We use period numbers to specify inexact or obscure or doubtful information. for this reason, the research of a choice challenge calls for answering the subsequent preliminary questions – How should still we

  • compare and outline choice ordering among periods?
  • interpret and deal inequality relatives related to period coefficients?
  • interpret and make manner in the direction of the aim of the choice challenge?

The current examine paintings involves heavily comparable fields: methods in the direction of defining a generalized choice ordering scheme for period attributes and methods to house a few matters having program power in lots of components of selection making.

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Nardelli (2006), An interval portfolio selection problem based on regret function, European Journal of Operational Research 170 (1): 253-264. M. M. Gupta & T. , North Holland. B. Hazen (1986), Partial Information, Dominance, and Potential Optimality in Multiattribute Utility Theory, Operations Research 34 (2): 296-310. H. W. G. Patry (1995), A grey integer programming approach for waste management planning, European Journal of Operational Research 83: 594–620. M. Ida (2003), Portfolio Selection Problem with Interval Coefficients, Applied Mathematics Letters 16 (5): 709-713.

2. Graphical representation of the cases given in Fig. 1. Chapter 2 On Comparing Interval Numbers 34 cept ‘left of an interval’. Using probability-based construction, Kundu (1997) defined a fuzzy preference relationship between any two intervals A and B on the real line by the formula Left( A, B ) = max {0, PAB ( x < y ) − PAB ( x > y )} , where, PAB ( x < y ) denotes the probability that x < y, given that x ∈ A and y ∈ B are uniformly and independently distributed in the intervals A and B. Similarly, Right(A, B) can be developed by using PAB ( x > y ) − PAB ( x < y ).

Kall (1982), Stochastic programming, European Journal of Operational Research 10: 125–130. S. P. Mujumdar (2006), An inexact optimization approach for river water -quality management, Journal of Environmental Management 81: 233–248. A. M. Gupta (1985), Introduction to Fuzzy Arithmetic—Theory and Applications, Van Nostrand, Reinhold. B. Kearfott & V. Kreinovich (1996), Applications of Interval Computations, Kluwer Academic Publishers, Dordrecht, Netherlands. F. Klawonn (2003), Should fuzzy equality and similarity satisfy transitivity?

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Fuzzy Preference Ordering of Interval Numbers in Decision Problems by Atanu Sengupta

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