Fuzzy Sets And Their Application-Ii - BU 2021 Question Paper

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M.Sc. IV^th Semester (CBCS) Examination, 2021

Mathematics

Optional-VII (Fuzzy Sets and Their Application-II)

[Maximum Marks : 60

Note :- All questions from each section carry equal marks. All questions are compulsory and answer limit are approximately 250 words. Start the answer of each section from new page. Maximum limit of pages of answer booklet are approximately 16 pages. Answer should be written by the student in his/her own handwriting mandatory. The first page of answersheet should be download by the student from university website is mandatory.

Define binary Fuzzy relations and Fuzzy equivalence relations. If X = {1, 2............. 10} and R (X, X) = {| x and y have the same remainder when divided by 3}, then show that R (X, × X) is an equivalence relation.

Explain the following :-

(i)

Dempster's rule of combination of basic assignments.

(ii)

Non-interactive marginal bodies of evidence.

(iii)

Difference between probability and possibility

(iv)

Belief measure

(v)

Plausibility measure

If Q =

    ⎡.1 .4 .5 .1⎤
    ⎢.9 .7 .2 .0⎥
    ⎢.8 1  .5 .0⎥
    ⎣.1 .3 .5 .0⎦

and R= [.8 .7 .5 0} then determine all solutions of P o Q = R by solution method, where P = [p_j | j ∈ J], Q = [q_jk | j ∈ J, k ∈ K], r = [r_k | k ∈ K]

Write a short note on evidence theory.

Define unconditional and unqualified Fuzzy propositions.